RADIOLOGICAL 
DEFENSE 
VoL I g g45 
Nagasaki-1102, 9 August 1945 
New Mexico-0530, 
16 July 1945 
g|kini-08&25 July 1946 
ifiikini.flQm 1 lnlv 1Q4R 
> mmm - as RADIOLOGICAL 
DEFENSE 
A 
Manual 
Prepared by the 
Joint Crossroads Committee 
Vol. I WAR AND NAVY DEPARTMENTS 
ARMED FORCES SPECIAL WEAPONS PROJECT 
P. O. BOX 2610 
Washington, D. C. 
IN REPLY REFER TO; 
22 January 19U8 
FOREWORD 
This manual, entitled ’’Radiological Defense," is a reprint of 
the same text formerly issued under the title of ’’Radiological 
Safety.” The change of name conforms to the terminology 
recently adopted by the Armed Forces. 
The original printing "Radiological Safety" was classified 
"Restricted." This volume of the manual has been reviewed and 
found to contain no restricted data under Public Law 985, 79th 
Congress, the Atomic Energy Act of The "Restricted" classi 
fication is, therefore, removed. 
In order to save the expense of preparing new plates, the 
berm "Radiological Safety" has not been removed from the interior 
pages of the'text. 
It is anticipated that Volume I will be followed by 
additional volumes which will be classified. 
L. R. GROVES 
Major General, USA ERRATA 
RADIOLOGICAL DEFENSE MANUAL, VOLUME I 
The following is a list of corrections to the Radiological Defense Manual, Volume I (Radiological 
Safety Manual, Volume I), 
Page No. Correction 
9 Equation (2) should read: — 
13 In Equation (10) and the preceding equation, substitute Q for k. 
15 Commencing with the fourth paragraph of Section 2.07, through and including Equation (28) 
on page 16, substitute VP for VP' 
16 Second column, seventh line from bottom of page should read: Nk—R, the molar gas constant, 
=8.31 joules/ 
22 Equation (12) should read: 
23 Legend for figure 3—6 should read: The magnetic field at P will be due to the effect of all of the 
small segments As. With the current direction the field at P will be into the paper. 
23 In Equations 13 and 14 change the alpha symbol to proportional sign oc 
29 First column, fourth and seventh lines: interchange symbols R and Rg 
30 First column, third line should read: “The force on a charge e will then be:” 
30 First column, second line from bottom, change e.s.u. to read e.m.u. 
30 Table II, change first line under “Work and energy” to read: V (e.m.u.)XQ (e.m.u.) = ergs. 
37 Equation (4); In the second term of the right-hand side of equation, substitute v for Greek 
letter Nu. 
75 In the nuclear reaction equation shown in first column, change the subscript of ila to 88, and the 
subscript of Rn to 86. 
75 Second column, change fourth line to read: —1,00813 m.u. (Precisely, the mass of the 
proton alone equals 1.00758 m.u. In calculation of binding energy, the nucleus is regarded as 
that of an atom in electrical equilibrium, i. e., each proton is in the presence of its corresponding 
orbital electron, and the two act as one particle insofar as mass is concerned. In formulae fol- 
lowing, for convenience, the symbol mp should be understood to represent the sum of the precise 
masses of proton plus associated electron. This principle is further extended below in dealing 
with the protons mentioned in connection with an element 2X4 which may be regarded either as 
a or as a helium atom depending upon degree of precise academic accuracy desired.) 
76 Table III: BEPP (last column) of iH2 should read 1.09. 
82 In Equation (23), place a minus sign ahead of subscript 1 to indicate negative electron, thus _ie° 
85 Next to last line, second column, delete “(see fig. 6-6).” 
86 fourth line, first column, delete subscript to make ED read E. 
May 1948 
AGO 1880A—May 771948°—48 
U. S. GOVERNMENT PRINTING OFFICE: 1948 TABLE OF CONTENTS 
Part I 
Chapter 1. Introduction 1 
Paqe 
Part II 
BASIC PHYSICS 
Chapter 2. Motion and Energy: 
2.01. Introduction 7 
2.02. Mathematical Notation 7 
2.03. Motion of Particles 8 
2.04. Inertia, Mass and Force 10 
2.05. Energy and Potential 12 
2.06. Momentum and Impulse 13 
2.07. Elementary Kinetic Theory 15 
Chapter 3. Electricity and Magnetism: 
3.01. Electrostatics 19 
3.02. Magnetism 22 
3.03. Electrical Conduction 24 
3.04. Electronics 27 
3.05. Forces or Moving Charges 29 
3.06. Electrical Units 30 
Chapter 4. Electromagnetic Radiation: 
4.01. General Properties of Waves 31 
4.02. Properties of Electromagnetic Waves 34 
4.03. The Electromagnetic Spectrum 35 
4.04. The Quantum Nature of Radiation 36 
Chapter 5. Atomic Structure; 
5.01. The Electrical Nature of Matter 41 
5.02. The Hydrogen Atom and Other Elements 41 
5.03. Atomic Nomenclature 42 
5.04. The Periodic System 44 
5.05. Atomic Spectra and Energy Levels 44 
5.06. The Bohr Atom 45 
5.07. Excitation and Ionization of Atoms 48 
5.08. X-rays 48 
5.09. X-ray Spectra and Atomic Energy Levels 50 
5.10. Interaction of X-rays with Matter 51 
5.11. The Roentgen 55 
5.12. Wave Mechanics 55 
5.13. Mass Spectroscopy 56 
5.14. Mass Spectra 58 
5.15. Stable Isotopes 60 
Chapter 6. Natural Radioactivity and Nuclear Structure: 
6.01. The Discovery of Natural Radioactivity 63 
6.02. Rays Emitted by Radioactive Elements 63 
6.03. Alpha-Particles 54 
6.04. Beta-Particles 55 
VII RADIOLOGICAL SAFETY 
PART II (Cont’d) 
Chapter 6. Natural Radioactivity and Nuclear Structure—Continued Page 
6.05. Gamma-Rays 65 
6.06. Statistics of the Decay Process 66 
6.07. Radioactive Series 68 
6.08. Equilibrium in Radioactive Transformations 70 
6.09. Equivalence of Mass and Energy 74 
6.10. Nuclear Binding Energy 75 
6.11. Nuclear Forces .. 76 
6.12. Nuclear Potential Barriers 77 
6.13. The Theory of Alpha Emission 78 
6.14. Absorption of Alpha-Particles 79 
6.15. The Theory of Beta-Decay 81 
6.16. The Absorption of Beta-Particles 83 
6.17. Nuclear Gamma Rays 85 
Chapter 7. Properties of Nuclear Radiation: 
7.01. Nuclear Bombardment 89 
7.02. Rutherford’s Alpha-Particle Bombardment 89 
7.03. Nuclear Cross Sections 90 
7.04. The Discovery of the Neutron 91 
7.05. Artificial Radioactivity 91 
7.06. The Cockcroft-Walton Experiment j 92 
7.07. Particle Accelerators 93 
7.08. Nuclear Reactions 95 
7.09. Energetics of Nuclear Reactions 95 
7.10. Positron Emission and K-Electron Capture 96 
7.11. Theory of Nuclear Reactions 97 
7.12. The Production of Neutrons 98 
7.13. Neutron Induced Reactions 99 
7.14. Energy Release from Nuclear Reactions 102 
7.15. Cosmic Radiation 102 
Chapter 8. Neutron Physics and Fission: 
8.01. The Discovery of Nuclear Fission 105 
8.02. Fission Phenomena 106 
8.03. The Energy Released in Fission 106 
8.04. The Binding Energy Equation 107 
8.05. The Theory of Fission—Energetics 108 
8.06. The Theory of Fission—Mechanics _ 110 
8.07. Types of Fission and Cross Section 111 
8.08. Fission Products and Radioactivity 111 
8.09. The Chain Reaction for Fast Neutrons 112 
8.10. The Atomic Bomb 115 
8.11. Resonance Capture in U238 116 
8.12. The Slowing Down of Neutrons 116 
8.13. Piles 117 
8.14. The Transuranium Elements 120 
VIII RADIOLOGICAL SAFETY 
Chapter 9. Principles of Instrumentation and Photographic Dosimetry; 
Page 
9.01. Introduction 121 
9.02. Ionization of Gases 121 
9.03. Ionization Currents 121 
9.04. Electroscopes and Electrometers 123 
9.05. Ionization Chamber Instruments 126 
9.06. Ionization Chamber—Amplifier Instruments 128 
9.07. Geiger-Mueller Counters 129 
9.08. The Counter Tube Gas 132 
9.09. Neutron Counters 134 
9.10. Geiger Counter Circuits 134 
9.11. Scaling Circuits 137 
9.12. Calibrations and Standards 138 
9.13. Correction of Measurements 139 
9.14. Decay Curve Measurements 141 
9.15. Photographic Dosimetry 1 142 
9.16. Film Calibration 144 
9.17. Alpha Particle Emulsions 144 
9.18. Radio-autographs 145 
Bibliography 146 
Appendix I 
Table I—Table of fission products: Characteristics 147 
Table II—Table of fission products: Chains and yields 157 
Subject Index 161 
9.19. Conclusion 145 
IX INDEX TO ILLUSTRATIONS 
Page 
Frontispiece—New Mexico (U. S. Army Signal Corps 
photograph). Hiroshima (U. S. Army Air Force 
photograph). Nagasaki (U. S. Army Air Force 
photograph). Bikini, 1 July 1946 (U. S. Navy pho- 
tograph). Bikini, 25 July 1946 (U. S. Navy 
photograph) .. II 
Figure 2-1.—The central acceleration of a body in 
uniform circular motion 10 
Figure 2-2.—Gas volume used for deriving the equa- 
tion of the kinetic theory of gases 15 
Figure 3-1.—A charge placed on a hollow conducting 
sphere distributes uniformly and exerts no force 
on a charge in the interior 20 
Figure 3-2.—Calculation of electrical potential at 
points A and B due to (charge q) by determining the 
work done in moving a unit charge . 20 
Figure 3-3.—Two insulated conductors form a con- 
denser 20 
Figure 3-4.—Spherical condensers for theoretical 
consideration 21 
Figure 3-5.—The Millikan oil drop experiment 21 
Figure 3-6.—The magnetic field at P will be due to 
the effect of all of the small segments A S 23 
Figure 3-7.—The magnetic field due to a circular coil 23 
Figure 3-8. The magnetic curve for iron 23 
Figure 3-9.—A 2-element tube, or diode, with electron 
emission from a hot filament 27 
Figure 3-10.—Circuit for obtaining the characteris- 
tics of a triode . 28 
Figure 3-11.— Mutual characteristics of a triode 28 
Figure 3-12:—The triode as a voltage amplifier 28 
Figure 3-13.—A unit magnetic pole at O will have a 
force acting on it, and by Newton’s third law there 
must be an opposite force on the wire.. 29 
Figure 4-1.— Amplitude and wave length in a wave 
motion 31 
Figure 4-2.—The relation between wave fronts and 
rays 32 
Figure 4-3.—Reflection of light at a plane surface. 32 
Figure 4-4.—The refraction of light into a medium of 
slower propagation 33 
Figure 4-5.—The interference of light passing through 
narrow slits 33 
Figure 4-6.—The electromagnetic wave in free space. 34 
Figure 4-7.—The electromagnetic spectrum 35 
Figure 4-8.—The photoelectric effect ...... 37 
Figure 4-9.—The observed energy distribution of black 
body radiation as a function of temperature 38 
figure 5-1.—Canal rays passing through a hole in the 
cathode of a cathode ray tube 41 
Page 
Figure 5-2.—Periodic table of the elements 43 
Figure 5-3a.—Emission spectrum of the hydrogen 
atom in the visible and near-ultraviolet region 45 
Figure 5-3b.—Absorption spectrum of the sodium 
atom 45 
Figure 5-4.—Energy level diagram of hydrogen. 46 
Figure 5-5.—Diagram of first orbit in the hydrogen 
atom 47 
Figures 5-6.—Sketch of X-ray tube 49 
Figure 5-7.—Typical X-ray spectrum showing char- 
acteristic and continuous radiation 49 
Figure 5-8.—Typical K series spectra 50 
Figure 5-9.—Electronic structure of the mercury atom. 51 
Figure 5-10.—Diagram of the L and M shells 51 
Figure 5-11.—X-ray absorption 51 
Figure 5-12.—Exponential absorption of X-rays 52 
Figures 5-13.—X-ray photoelectrons seen in a cloud 
chamber 52 
Figure 5-14.—Compton effect 53 
Figure 5-15.—Pair production 54 
Figure 5-16.—Cloud chamber photograph of pair 
production 54 
Figure 5-17.—Relative importance of photon absorp- 
tion processes in lead — 54 
Figure 5-18.—Diagram of a Dempster type mass 
spectrograph 56 
Figure 5-19.—Dempster type mass spectrograph 57 
Figure 5-20.—Typical mass spectra 57 
Figure 5-21.—Isotope pattern of tin 58 
Figure 5-22.—Periodic table of the elements showing 
isotope abundance 59 
Figure 5-23.—Neutron-proton plot of stable isotopes. 61 
Figure 6-1.—Rays emitted from a radium source 
placed in a magnetic field 63 
Figure 6-2.—Relative penetrating power of alpha, 
beta, and gamma radiation 64 
figure 6-3.—Radioactive decay curve 66 
Figure 6-4.—Radioactive decay curve on a logarith- 
mic plot. _ 67 
Figure 6-5.—Decay of radium to radon 69 
Figure 6-6.—The uranium series 69 
Figure 6-7.—A neutron-proton plot of the uranium 
series 71 
Figure 6-8.—Growth curve for a radioisotope 73 
Figure 6-9.—Potential energy curve for a nucleus 77 
Figure 6 -10.—Potential barrier for radium 78 
Figure 6-11.—Geiger-Nuttall relation for the three 
radioactive series 79 
Figure 6-12.—Alpha particle tracks in a Wilson cloud 
chamber 79 
X RADIOLOGICAL SAFETY 
Paeg 
Figure 6-13.—Range vs. Energy curve for alpha par- 
ticles in air 79 
Figure 6-14.—Specific ionization vs. distance for 
alpha particles from radium C 81 
Figure 6-15.—Straggling of alpha particles 81 
Figure 6-16.—Energy distribution of beta particles.. 81 
Figure 6-17.—Energy relations in beta emission 82 
Figure 6-18.—A Sargent diagram 83 
Figure 6-19.—Range vs. Energy plot for beta particles 
in air 84 
Figure 6-20.—Range vs. Energy plot for beta particles. 84 
Figure 6-21.—A typical absorption curve for primary 
beta particles 84 
Figure 6-22.—Nuclear energy level picture 85 
Figure 6-23.—Energy level scheme for thorium B, C, 
C', C", and D 87 
Figure 7-1.—Rutherford’s alpha particle bombard- 
ment experiment 89 
Figure 7-2.—Nitrogen disintegration by alpha bom- 
bardment 90 
Figure 7-3.—The concept of nuclear cross section 90 
Figure 7-4.—The linear accelerator 93 
Figure 7-5.—Principal components of a cyclotron 94 
Figure 7-6.—Mass spectrum of irradiated cadmium.. 100 
Figure 7-7.—Cross section for neutron capture by 
cadmium as a function of energy 100 
Figure 7-8.—Cross section as a function of energy for 
n-p reaction in Al27 101 
Figure 7-9.— cosmic ray intensity as a function 
of altitude 103 
Figure 8-1.—Average binding energy per nucleon 107 
Figure 8-2.—Coulomb and fission energy vs. atomic 
mass number 109 
Figure 8-3.— Energy of a nucleus as a function of dis- 
tance between two fission fragments 109 
Figure 8-4.—Potential barrier for fission 109 
Figure 8-5.— Mechanics of fission process 110 
Figure 8-6.—Uranium mass spectrum 111 
Figure 8-7.— Nuclear constituents of fission products. Ill 
Figure 8-8.— Fission products and the stability curve. 112 
Figure 8-9.— Mass distribution of fission products— 113 
Figure 8-10.—A diagram of chain reaction in U235 
(fast fission) _ 114 
Figure 8-11.—An atomic bomb 115 
Figure 8-12.—The slowing down of neutrons by carbon 
Page 
atoms 117 
Figure 8-13.— Diagram of chain reaction using a 
moderator., 117 
Figure 8-14.—Scheme of a uranium carbon pile 118 
Figure 8-15.—Daniels atomic power plant 119 
Figure 9-1.— Visible path of nuclear particles in Wilson 
cloud chamber 122 
Figure 9-2.—Variation of ion current with potential 
applied to collecting electrodes .’ 123 
Figure 9-3.—Schematic diagram of a Lauritsen 
electroscope . 124 
Figure 9-4.—Pocket dosimeter electroscope. 125 
Figure 9-5.—Condenser r meter. 127 
Figure 9-6.—Condenser r meter, cut-away view. 127 
Figure 9-7.—Ionization chamber with single stage 
amplifier circuit 129 
Figure 9-8.—Ion chamber with zero current buck- 
ing amplifier circuit.. 130 
Figure 9-9.—Ion chamber pulse size versus voltage. 131 
Figure 9-10.—G-M tube characteristic 132 
Figure 9-11.—G-M tube with a series resistance 
and a coupling condenser 134 
Figure 9-12.—Neher-Harper cpienching circuit 135 
Figure 9-13.—Neher-Pickering quenching circuit 136 
Figure 9-14.—Multivibrator quenching circuit 136 
Figure 9-15.—Pulse shapes 137 
Figure 9-16.—G-M counter scaling circuit .. 138 
Figure 9-17.—Self-absorption curve with extra- 
polated value for zero absorption 141 
Figure 9-18.—Semilogarithmic plot of the decay of a 
short- and long-lived isotope 141 
Figure 9-19.—Schematic arrangement of densitometer 
with photocell 142 
Figure 9-20.—Characteristic curve of a photographic 
emulsion 143 
Figure 9-21.—Characteristic curves for types K and 
A emulsions 143 
Figure 9-22.—Effects of developing time on gamma 
and density.. 144 
Figure 9-23.—Alpha particle tracks on a photographic 
emulsion . .. .. 145 
Figure 9-24.—Radio-autograph of a surgeon fish 
caught on the reef between Bikini and Amen 
Islands — . — 145 
XI Part I 
INTRODUCTION RADIOLOGICAL SAFETY 
Chapter 1 
INTRODUCTION 
The dropping of an atomic bond) on Hiroshima 
on the 6th of August 1945 inaugurated a new' era 
in warfare. With this one new development, new' 
horizons of offensive warfare were opened. To 
date five atomic bombs have been detonated, two 
of these in actual military operations and three for 
experimental purposes. The devastating effects 
of this new' weapon against both material and per- 
sonnel were graphically demonstrated by the two 
bombs dropped over Japan, where at Hiroshima 
alone, 10 square miles were destroyed and more 
than 100,000 casualties resulted. Although the 
Japanese military situation was already well nigh 
hopeless at the time these two bombs were deton- 
ated, they undoubtedly wrere primarily responsible 
for bringing the war to a rapid conclusion and 
eliminated the necessity for extensive amphibious 
operations. 
Despite the tremendous devastation which was 
wrought by these attacks on Japan, it appears 
likely, as a result of the tests carried out during 
the summer of 1946 at Bikini, that the atomic 
bomb has even greater potentialities for destruc- 
tion. While the atomic bomb produces damage 
by blast and fire, its most characteristic feature is 
the release of nuclear radiations in the form of 
neutrons, alpha and beta particles, and gamma 
rays. In Japan both bombs were detonated at 
relatively high altitudes so that the radiological 
effects were almost at a minimum. Most of the 
radioactive products of these atomic bomb explo- 
sions, which account for the persistent radiological 
hazards, were carried to high altitudes and dis- 
persed. Despite this, instantaneous nuclear or 
ionizing radiation wras directly responsible for an 
important number of the casualties. 
In test Baker at Bikini, however, it was shown 
that when a bomb is detonated some distance be- 
low the surface of the wrater, these radioactive 
products are not dispersed in the upper atmos- 
phere but arc to a large extent deposited on the 
surface around the point of detonation and for 
considerable distances down-wind. These mate- 
rials would not oidy produce casualties amongst 
personnel throughout an area far greater than that 
affected by the detonations in Japan but would 
also make that area dangerous for inoccupation for 
a long time thereafter. In the future these 
insidious radioactive materials may be dispersed 
without the use of an atomic bomb. Certain prob- 
lems would have to be solved, however, before 
such dispersal could be carried out effectively and 
without hazard to the user. 
While the atomic bomb was designed and used 
primarily for its direct destruction effects, no 
weapon has ever had such potentially widespread 
and serious psychological aspects, nor has any 
weapon ever been used in war which has offered 
such rich opportunity for exploiting fear of the un- 
seen and of the unknown. Indeed the psychologi- 
cal effects of the atomic bomb may constitute its 
most significant feature from the military stand- 
point. Not only will people undergoing attack 
be affected, but also both in time of war and in 
time of peace all people will be influenced by the 
fear of possible attack. It is probable that this 
will continue until such time as wars can effec- 
tively and certainly be prevented. In time of war 
the fear and panic which might be produced in 
connection with the threatened or the actual use of 
the atomic bomb against the larger cities and 
strategic centers might seriously jeopardize, if not 
actually neutralize, the military effectiveness of 
these centers. 
In considering the characteristics of atomic 
bombs which are of military or political signifi- 
cance, it is important to recognize both the poten- 
tialities and limitations which attend its many 
terrorizing effects. While no weapon used in war 
has been fraught with such opportunity for ex- 
ploiting the fear of the unknown, no weapon 
presents the same difficulties insofar as control 
of fear among our own people is concerned. The 
atomic bomb is thus a weapon possessing great 
disadvantages as well as advantages, negative as 
well as positive values. 
Long range aircraft, pilotless planes, and, per- 
haps in the not too distant future, guided missiles 
make possible the effective employment of special 
weapons of mass effect. These would include the 
atomic, biological, and chemical weapons. They 
may be employed alone, in combination, or in 
1 RADIOLOGICAL SAFETY 
conjunction with other weapons, for a diversity 
of both tactical and strategical uses. Technologi- 
cal developments in missiles require that all three 
receive more considered attention than after 
World War I, and make it incumbent on military 
planners to be intelligently aware of their potenti- 
alities and limitations. This is particularly im- 
portant in planning defensive measures and in 
the training of personnel to cope with those prob- 
lems of atomic warfare which have given rise to 
a new and highly complicated military technology 
known as radiological safety operations. 
The physiological effects are produced by the 
radioactivity in two different ways. First ex- 
ternal radiation will produce effects similar to 
those produced by X-rays. Personnel will not 
only be exposed to an external radiation hazard 
from the rays emitted at the instant of detona- 
tion, but such a hazard also exists from the radia- 
tion given off by particles of radioactive material 
which might be present in a bomb cloud or on a 
contaminated surface. This type of hazard will 
usually produce observable effects within 30 days 
of exposure. Second, the radioactivity provides 
a serious internal hazard, since inhalation or in- 
gestion of radioactive materials even in low con- 
centrations will produce serious physiological 
effects. Open wounds or cuts would also provide 
a ready means of entrance of this dangerous ma- 
terial into the body. Internal radiation hazard 
may not produce observable effects for several 
years after exposure. 
Because of the extent of the radiological hazard 
following the detonation of an atomic bomb, it be- 
comes necessary to develop methods of reducing 
its effects to an absolute minimum. Many people 
will be killed regardless of what measures are 
taken, hut there will undoubtedly be an even larger 
number of people who will be border-line cases and 
who might be saved. It has been estimated that 
20,000 lives might have been saved at Hiroshima 
if adequate safety measures had been taken. The 
larger the area affected by a single attack and the 
greater the number of people involved, the larger 
will be the number of border-line cases, and the 
greater the value of adequate defensive measures. 
Good planning and training in advance might well 
mean the difference between being overwhelmed or 
being able to continue. Panic following an attack 
might increase the size of the disaster manyfold. 
To minimize the effects of radiological hazards 
upon personnel there has been developed a phi- 
losophy and a technique of radiological safety. It 
is a new and highly specialized field requiring 
personnel trained in various technical subjects, 
and qualified at different levels of proficiency 
within these subjects. To detect and measure 
these hazards, in order that the risks to personnel 
can be properly evaluated, is the primary task of 
radiological safety personnel. Efficient training 
and the development of reasonable operating 
methods offers the only method of minimizing 
both the physiological and psychological effects. 
To plan, organize or train for radiological safety 
operations as one phase of atomic defense it is 
necessary that those responsible be familiar with 
certain technical information and scientific facts. 
There is a vast amount of information available 
on atomic energy, some relevant to the problems 
of atomic defense and some not. This informa- 
tion is scattered within a mass of reports from 
medical, scientific, and industrial laboratories 
including those of Manhattan Engineering Dis- 
trict and in the reports of Operation CROSS- 
ROADS. 
This manual has been prepared as a preliminary 
effort to provide in one place, and in an organized 
manner, source material for all groups which may 
become involved in one aspect or another of radio- 
logical defense, a field new to military science. It 
does not aim to be a textbook for specialists in any 
particular field but to provide a general back- 
ground of the many scientific, medical, and opera- 
tional aspects. For example, the medical officer 
could not expect to find all the medical informa- 
tion which he would need on radiation injury in 
the chapter on “Medical Aspects.” This chapter 
is primarily designed to acquaint non-medical 
people with the nature of the hazards so that they 
will understand the problems and be able to dis- 
cuss them intelligently with medical personnel. 
Chapters 2 to 8 include a discussion of the basic 
nuclear physics concepts necessary for an under- 
standing of the problems presented by atomic war- 
fare. While it is recognized that little, if any, 
knowledge of nuclear physics is required in order 
to carry out successfully the routine operations 
involved in radiological safety, it is felt that such 
a background is vital for all people who will be- 
come involved in the planning of radiological 
2 RADIOLOGICAL SAFETY 
safety operations or who will be faced with the 
necessity of making decisions in the event of the 
outbreak of atomic warfare. Without such a 
background it would be impossible for an indi- 
vidual to tackle new or unforseen problems. 
Since radiological defense is still an untried field, 
problems and techniques can be expected to be 
changing constantly. Since instrumentation will 
be one of the most important aspects of radio- 
logical safety for all personnel in this field, the 
theoretical and practical side of both electronic 
and photometric equipment used for detecting 
nuclear radiations are described in some detail in 
chapter 9. 
In chapter 10 the best estimates of the effects of 
an explosion of the present atomic bombs are in- 
cluded in order to provide a picture of the nature 
and magnitude of the present day problems. 
Chapters 11 and 12 are included in order to provide 
a background of oceanography and meteorology 
since these sciences are important in determining 
the movement of water-borne and air-borne con- 
tamination. Next, both the medical effects of 
different types of radiation exposure and some of 
the philosophy involved in safety operations are 
discussed. The latter is felt to be particularly 
important because of the complex nature of the 
safety problems presented by atomic warfare. 
Finally a part describing various radiological de- 
fense operations is included in order to provide a 
background for individuals who will have the 
responsibility for organizing such operations. This 
background can only serve as a starting point for 
such organization. Only at Bikini and thereafter 
have any large scale radiological safety operations 
been attempted, and these were of course carried 
out on a totally different basis from those which 
would be required during war time. Operation 
CROSSROADS was primarily a scientific test 
carried out in peacetime so that as a consequence 
no risk of any sort could be accepted. In war 
time, certain risks will be inevitable. Undoubt- 
edly problems will arise which cannot be foreseen 
in advance. Far greater flexibility will be re- 
quired to solve these problems, and therefore the 
background and training of those responsible for 
radiological safety will be even more important. 
The magnitude and seriousness of the problems 
presented by radiological warfare cannot be over- 
emphasized. 
3 
774689 0 - 48 -2 Pori II 
BASIC PHYSICS RADIOLOGICAL SAFETY 
Chapter 2 
MOTION AND ENERGY 
2.01 introduction 
It may seem unnecessary to include in a text 
on radiological safety a relatively large section 
devoted to classical and contemporary physics 
and so a few words of explanation may be in order. 
In any explosion there is a rapid release of 
latent energy. This energy, released at the point 
of detonation, can be transmitted to produce 
damage at distant points through either the high 
speed motion of particles or through waves. 
These subjects have been the intimate concern of 
physics for many years, are quite well under- 
stood, and can be of considerable help in explain- 
ing detonation phenomena. 
In an ordinary chemical explosion the energy 
is released in a single act by the rearrangement of 
molecular bonds. The reaction goes promptly 
to completion and there are no delayed phenomena. 
In an atomic explosion, on the other hand, 
the energy is released by a nuclear rearrangement 
and matter is converted into energy in accordance 
with the relation developed by Einstein: 
E—mc2 
Since c, the velocity of light, has a value of 30 
billion cm/sec, it is evident that huge amounts of 
energy can be obtained from the annihilation of 
small amounts of matter. Furthermore, all of 
the energy is not released in the primary cata- 
clysm; dangerous radiation will be emitted for 
many months after the explosion. 
If the hazards associated with the release of 
nuclear energy are to be well understood and 
adequately controlled, it is necessary to under- 
stand the mechanisms producing the energy 
release. To obtain this understanding it is neces- 
sary to become familiar with a considerable amount 
of basic and contemporary physics. 
Physics is essentially an exact science, and as 
such makes free use of all applicable mathe- 
matics. It is however a science in which mathe- 
matics is closely related and applied to physical 
concepts; in the present treatment the emphasis 
will be placed on the concepts involved, and 
mathematical expressions will be used only as 
tools to arrive at results not otherwise obtainable. 
2.02 Mathematical Notation 
Mathematical equations will be used through- 
out the text and indeed the expression 
E—mc2 
already used is such an equation. It should be 
noted that the rearrangement of an equation is 
merely a matter of convenience, and adds nothing 
new. Thus 
K F 
m — „ and c2—— 
cl m 
are merely rearrangements of the original form. 
In the equations of physics the symbols refer to 
physical quantities and since the = signs means a 
complete equality it is necessary that the two 
sides balance in kind or dimensions as well as in 
quantity. It would be absurd to suppose an 
equation correct if it stated that a distance of 20 
feet were equal to a time of 20 seconds. Other less 
obvious errors in dimensions can easily occur, and 
it is well to frequently check equations to see 
that they are dimensionally correct. It can be 
shown that all physical quantities can be reduced 
to various combinations of mass, length, and time. 
In the energy equation above it can be seen that 
energy is dimensionally equal to a mass times a 
velocity squared, and since velocity is a length 
divided by time, energy is dimensionally 
/ M2) 
The parentheses ( ) signify that the equation has 
only dimensional significance and that all purely 
numerical multipliers such as 1/2, 2tt, or any other 
pure numbers have been omitted. Whenever 
energy is equated-therefore, it must always be to a 
combination of factors which will reduce to ml2/t2. 
It will soon be noticed that physics is concerned 
with numbers that are very large or very small 
as well as with those of more ordinary size. 
Thus the velocity of light is 30,000,000,000 cm. 
per sec. and the mass of an electron is 
0.0000000000000000000000000009 grams 
Obviously it is not convenient to work with num- 
7 RADIOLOGICAL SAFETY 
hers like these, and a change to larger or smaller 
units such as the kilometer or microgram does not 
solve the problem. It is possible to express these 
numbers as powers of 10 and this provides a com- 
pact and practical notation for handling both 
large and small numbers. 
It is obvious from the definition of exponents 
that 102= 100, 103= 1,000 and so on. Thus 1,000 
can be written as 1X 103, 2,000 as 2X 103 and so on. 
In this notation the velocity of light will be 3X 1010 
cm per sec. Similarly 
the base 10 is log. These logs are known as 
common logs. A little thought will show why, 
with our decimal system of counting, logarithms 
to the base 10 are so well suited for computations. 
It is possible to develop a system of logarithms 
to any desired base, and one other base has turned 
out to he very useful. The base of this system of 
logarithms is 2.71828 . . . which is denoted by 
e. Logarithms to this base are known as Napier- 
ian or natural logarithms and are abbreviated In. 
This number turns up quite frequently in theo- 
retical calculations, and this is the reason the 
system of natural logarithms is important. 
It is sometimes necessary to convert from one 
system of logarithms to the other. To find the 
relationship between them assume any number x 
such that 
x= 10y 
Then by definition y=log x. Taking the natural 
logarithm of all the terms 
In x—y In 10 
But In e = 1.000, since e is the base of the system, 
and In 10 = 2.3 . . . so finally 
In x=2.3 log x 
and the multiplying factor 2.3 can be used to con- 
vert from common logs to natural logs. 
2.03 Motion of Particles 
In discussing the motion of a particle it might 
seem desirable to first define the word particle. 
Actually a simple rigorous definition is not possi- 
ble. For many purposes the motions of small 
objects such as atoms (the smallest stable units of 
matter), molecules (stable aggregates of atoms) 
or electrons (the fundamental unit of electricity) 
can be satisfactorily described by considering them 
as mathematical points. In other cases the size 
and shape of these particles is all important. 
Similarly, bodies like the sun and the moon may 
frequently be studied by considering them as 
particles. Consequently the decision as to whether 
or not the motion of an extended body can be 
treated like the motion of a point must be decided 
in each individual case. When it is possible to 
use the relations developed for particles, the point 
considered is the center of gravity at which point 
0,01 ~ioo io2 10 2 
and hence the mass of the electron will be written 
9X10-28 grams. The convenience of this nota- 
tion can be seen when it is necessary to perform 
multiplications or divisions. 100X 1,000= 100,000 
or in the exponential notation 102X 103=105. 
Thus multiplication requires, only the adding of 
exponents and division the subtracting. If it is 
desired to determine the energy liberated upon 
the annihilation of 2 micrograms of matter, the 
calculation is 
E—mc2 
= 2X10-6X3X1010X3X1010 
= 18 X1014 or 1.8X 1015 ergs 
The exponential notation is not confined to 
numbers which are integral powers of 10 but can 
be extended to include all numbers. Thus 
3.162X3.162 = 10 
and since 
io°-5xio°-5=io1=io 
therefore 
3.162 = 1005 
This scheme can obviously be extended so that 
corresponding to any number there will be an 
exponent to which 10 must be raised to equal the 
number. This exponent is known as the logarithm 
of the number to the base 10. In the usual nota- 
tion then 
log10 100 = 2.000 
log10 1,000 = 3.000 
logio 3.162 = 0.500 
It is not usually necessary to write the subscript 
10, and the usual abbreviation for a logarithm to 
8 RADIOLOGICAL SAFETY 
all of the matter of the body is supposed to be 
concentrated. 
As a specific example, assume a particle which 
may be moving and assume that when we start 
to study this particle it is at the zero point of a 
coordinate system. We will arbitrarily measure 
time from the instant the particle was at the zero 
point. At some later time t the particle is found 
to be a distance s from the origin. The distance s 
is known as the displacement. It is obviously a 
quantity requiring both a magnitude and a 
direction for its complete specification. For 
example the chance of being hit by a bullet 
depends strongly on the direction in which the 
bullet is moving. Shell directed quantities are 
called vectors, while quantities like time, which 
can be completely specified by a magnitude only, 
are known as scalars. 
In studying motion a distinction is made be- 
tween speed and velocity. Thus speed is a 
scalar quantity which gives the rate of displace- 
ment, or displacement per unit time, without 
regard to the direction of the displacement. 
Velocity is not only a measure of the rate of dis- 
placement, but is also a vector quantity, having 
the direction of the displacement. Velocity is a 
much more useful concept than speed. 
Returning to a consideration of the moving 
particle, assume that the velocity is r0 when 
f = 0. At the later time t the velocity is v. If the 
acceleration is constant, then the average velocity 
over this interval is 
t. It should be noted that an acceleration has 
the dimensions of a distance divided by the square 
of the time and so is expressed as cm. per sec. per 
sec. which is frequently written cm/sec2. Accel- 
eration is a vector quantity having the direction 
of the vector difference v—v0. 
Equations (1) and (2) show the relationships 
existing between the five quantities s, v0, v, t, and 
a. By algebraic manipulations two more equa- 
tions connecting these quantities can be obtained. 
It should be pointed out that these new equations 
do not add anything fundamentally new, but are 
merely rearrangements which are more convenient 
for the solution of some problems. From Eq. (2) 
V — Vq 
t = —and if this is substituted for t in Eq. (1) 
2 as — v2—v2 (3) 
Solving Eq. (2) for v 
v=at-j-e0 
Substituting this for v in Eq. (1) 
(at+2v0) 
S 2 ' 
or 
s=v0t+y2 at2 (4) 
If three of the five quantities are given any of the 
relations Eq. (1) to (4) can be used to solve for the 
other two. 
If the displacements involved are along a 
straight line, the acceleration, a, can be deter- 
mined by a simple algebraic subtraction. There is 
one very important case, however, where the dis- 
placement is not linear and where the calculation 
of a is more difficult. This is the case of motion 
at constant speed in a circle of constant radius. 
This situation is shown in figure 2-1. 
When t—0, the particle is at A and has a 
velocity v0 which has a direction perpendicular to 
the radius r. A short time t later the particle is at 
B, and the velocity v is equal in magnitude to v0 
but has a new direction. The factor v—r0 needed 
to calculate a from Eq. (2) is obtained by a vector 
subtraction in the velocity triangle as shown. 
Now the velocity triangle is similar to the distance 
triangle OAB, since both are isosceles and the sides 
adjacent to the small angles are mutually per- 
P + Pq 
9 
and so the displacement, which is cert ainly equal 
to the product of the average velocity and the 
time being considered is 
a) 
By analogy with velocity, which is the rate of 
displacement, acceleration can be defined as the 
rate at which velocity is changing. In symbolic 
form the acceleration a is 
(2) 
since a is the change in velocity over time interval 
9 RADIOLOGICAL SAFETY 
pendicular. Then corresponding sides are pro- 
portional and 
V—Vp _ v 
chord AB~ r 
If the time t is made very small, the small acute 
angles become very small and chord AB becomes 
very nearly equal to arc AB. But arc AB=vt 
hence 
vt r 
and 
„ e—Po /cx 
a = —t— — - (5) 
t r 
The acceleration has a magnitude of tfjr and the di- 
rection of (v— v0), and this is toward the center of 
the circular path as can be seen from figure 2-1. 
As the particle proceeds around the circle, the 
magnitude of the acceleration remains constant; 
but the direction constantly changes, always 
remaining perpendicular to v. This is a very 
important relation which will be used later in the 
theory of atomic structure, the description of 
high voltage accelerators, and in other equally 
important applications. 
2.04 Inertia, Mass and Force 
A few simple experiments with bodies in mo- 
tion are sufficient to show that an acceleration 
can only be brought about by some external in- 
fluence on the body. Thus a body at rest remains 
at rest unless something is done to move it, and 
a moving body will continue to move until ex- 
ternal actions bring it to rest. This tendency to 
maintain the status quo is known as inertia. 
The measure of inertia is known as mass, which 
is given the symbol m. 
In the absence of any natural standard of mass 
it was necessary to set up arbitrary definitions 
and units. This has been done and carefully 
standardized kilograms are kept in various na- 
tional laboratories. The gram, the unit of inertia 
in the metric system, has 1/1000 the inertia of a 
standard kilogram. 
The influence which changes the state of motion 
of a body is called a force: it can probably be best 
defined in terms of Newton’s first law of motion: 
“A body at rest continues at rest and a body in 
motion continues in motion in a straight line with 
constant velocity unless acted on by a jorce.” 
.Figure 2—1.—The central acceleration of a body in uniform 
circular motion. 
10 RADIOLOGICAL SAFETY 
A casual analysis of some motions may seem to 
indicate violations of this law, but more careful 
considerations will reveal elusive forces previously 
neglected. The most common force which 
changes motions is friction which appears in de- 
vious, insidious ways. 
If a force acts on a body there will be a re- 
sultant acceleration. The quantitative relation- 
ship is given by Newton’s second law of motion 
which states: 
“// a resultant force acts on a body there will he 
an acceleration which will he proportional to the 
force and inversely proportional to the mass of the 
body” 
Sjmibolically 
downward pull of gravity and indeed pushes 
downward on the table with a force equal to this 
gravitational pull. The reaction to this is the 
upward push of the table on the object. This 
must exactly equal the downward pull of gravity; 
otherwise the object would be accelerated in the 
direction of the greater force. 
In writing Newton’s second law in the form of 
Eq. (6) the tacit assumption was made that the 
mass of the body is a constant, independent of the 
state of motion of the body. This assumption 
seems a reasonable one and for nearly three 
hundred years laboratory experiments served only 
to confirm Newton’s laws. It is true that Eq. (6) 
predicts that if a force is continually applied there 
will be a constant acceleration and hence velocity 
will increase without limit. Such a conclusion 
may be philosophically disturbing, but in the 
absence of definite experimental evidence New- 
ton’s laws were accepted as universally valid 
until the early years of the present century. 
In 1905 Einstein published the first of a series 
of papers on the theory of relativity. Several of 
the conclusions drawn from this work were so 
revolutionary that they were not immediately 
accepted. Experiments soon verified many of the 
predictions, and at the present time there can be 
no doubt of the validity of the Einstein results. * 
One of the results was the equivalence of mass 
and energy, already mentioned. A second was 
that the mass of a body is not constant, but in- 
creases with velocity. It is necessary to recognize 
a rest mass, m0 and a mass m corresponding to a 
velocity v. The relationship between these masses 
is 
, F 
a—k — 
m 
Where k is a constant of proportionality. The 
units of a and m have already been fixed (cm/sec2 
and gram respectively, in the metric system), and 
it would seem reasonable to define the unit of 
force so that the constant of proportionality is 
unity and can be neglected. The metric unit of 
force, the dyne, is then defined as that force 
which gives to one gram an acceleration of one 
cm/sec2. With this definition, Newton’s second 
law becomes 
F=ma (6) 
Some idea of the magnitude of the dyne can be 
obtained from a simple experiment. If any body 
is allowed to fall freely near the earth’s surface, 
the gravitational attraction will impart to it an 
acceleration of approximately 980 cm/sec2. This 
particular acceleration is encountered so fre- 
quently it is denoted by g. If specifically the ex- 
periment is performed with a mass of 1 gram, Eq. 
(6) shows that F must equal 980 dynes, and 
hence 1 dyne is about 1/980 of the earth’s pull 
on a 1 gram mass. It cannot be said that a dyne 
is 1/980 of a gram. Such a statement is meaning- 
less, for the dyne and gram are quite different 
quantities and can have no multiplicative relation- 
ship. 
Newton’s third law of motion is almost self- 
evident, and only a little reflection is needed to 
make it seem plausible: 
“For every / or ce there is a force oj reaction equal in 
magnitude and opposite in direction.” 
An object placed on a table has acting on it the 
m0 
m= —====== (7) 
Vl-c2/ c2 
The factor v/c is the velocity of the body expressed 
as a fraction of the velocity of light and is fre- 
quently denoted by /3 (beta). 
The term v2jc2 appears in Eq. (7) as a sort of 
correction factor which is obviously negligible at all 
ordinary velocities where v is very small compared 
to c. As v approaches c, the factor v2/c2 becomes 
increasingly important and indeed Eq. (7) pre- 
dicts that if v=c the mass m must become infinite. 
Hence if a body moves under the action of a force, 
its velocity cannot increase without limit. As the 
velocity approaches the velocity of light, the mass 
11 RADIOLOGICAL SAFETY 
increases in accordance with Eq. (7), and the actual 
velocity increase will be substantially less than 
that predicted from Eq. (6). A material body can- 
not be accelerated to a velocity greater than the 
velocity of light. This prediction has been amply 
confirmed by experiment. Particles with veloci- 
ties within 0.01 percent of c have been measured; 
but no velocity greater than c has ever been 
observed. 
It might seem from the above discussion that 
Newton’s laws are of limited application: actually 
they hold with great accuracy from very low ve- 
locities to velocities of the order of 109 cm. per 
sec. They also hold for any type of acceleration, 
such as the central acceleration discussed in Sec. 2.03. 
The central force producing the acceleration is 
known as the centripetal force and the outward 
reaction to this is the centrifugal force. 
In most of the applications which will be made, 
it will be sufficient to use the rest mass, but in a 
few cases the relativity corrections must be applied. 
Table I shows how the mass/rest mass ratio varies 
with v/c. 
designing apparatus to do work, however, it is 
necessary to know the rate at which work is done. 
The rate at which work is done is known as power. 
The basic metric power unit, the erg per second, 
does not have a distinctive name but one joule 
per second is one watt, a unit of power frequently 
used in electrical calculations. 
Reference has already been made to the gravi- 
tational attraction of the earth for a mass and it 
will now be profitable to examine this force more 
closely. It appears to act without any inter- 
vening medium for it is not changed when the 
attracted body is put in the highest obtainable 
vacuum. Other examples of similar forces will 
be described later, and no attempt will be made to 
explain the mechanism of the force transmissions. 
It is important to recognize that the earth is 
surrounded by a region in which forces are exerted 
on masses. Such a region is known as a field of 
force, and in the particular case under discussion 
it is a gravitational field of force. The field 
strength, or field intensity, is the force exerted 
on a unit mass introduced at the point in question. 
It can be shown that the earth’s gravitational 
attraction is just a special case of the law of uni- 
versal gravitation which states that all masses 
have a mutual attraction which is directly pro- 
portional to each of the masses, and inversely 
proportional to the square of the distance between 
them. It may also be shown that for all points 
outside of a mass it is possible to consider all of 
the mass to be concentrated at a mathematical 
point or center of gravity. Then for two masses, 
mx and m2, whose centers are separated by a dis- 
tance r: 
Table I 
t/c 
m/mo 
o/c 
m/m0 
0.0 
1.000 
0.9 
2.30 
0.01 
1.00005 
0.95 
3.16 
0.1 
1.005 
0.99 
7.10 
0.5 
1.159 
0.999 
22.3 
0.7 
1.402 
2.05 Energy and Potential 
It is permissible to form combinations of the 
fundamental quantities previously described if 
it is useful or has a special physical significance. 
One such combination is the product of force and 
displacement, if we add the restriction that both 
must be measured in the same direction. This 
product, called work, seems a logical one, for com- 
mon experiences in raising weights against gravity 
indicate that the accomplishment should be mea- 
sured both by the force exerted and the height 
raised. In the metric system the unit of work will 
of course be the dyne-cm., and this unit is called 
the erg. For many applications the erg is an 
inconveniently small unit, and it is sometimes 
desirable to use the joule, which is equal to 107 
ergs. 
Since there is no time factor in the definition of 
work, and work done will be independent of the 
time required to make the displacement. In 
(8) 
whore G is the gravitational constant of propor- 
tionality. Since rather arbitrary units have 
already been chosen for m, r, and F, it is not prob- 
able that G will turn out to be unity. When m, 
r, and F are in grains, centimeters, and dynes, 
respectively, G has a value of 6.66X10'8. 
Although Eq. (8) shows that the gravitational 
force falls off rapidly with increasing distance, it 
is possible to consider F to be constant over a 
region where r is large and only small displace- 
ments are considered. Thus at the surface of the 
earth r—-5X108 cm and F may be considered con- 
stant up to an altitude of perhaps 106 cm. (33,000 
12 RADIOLOGICAL SAFETY 
feet). If then a body m originally at height a 
above some convenient reference point is raised 
to a height b the force required will be constant 
and equal to mg, and the work done will be 
W—mg(b—a) (9) 
The work done in moving a unit mass from one 
point to another is known as the difference in 
the gravitational potentials of the two points. 
In the example cited, the difference in potential 
is g{b — a) and the points may be said to have 
potentials of ga and gb, respectively. 
The body under discussion can do work by fall- 
ing back from 6 to a and since the ability of a 
body to do work is known as energy it has a greater 
potential energy at b than at a. From Eq. (9) 
and the definition of potential it is evident that 
the change in gravitational potential energy is m 
times the change in gravitational potential. 
To consider the general case, assume a mass M 
and suppose points a and b to be so located that 
the force can not be considered constant. To 
calculate the potential difference m2 in Eq. (8) is 
made unity. To make the calculation a small 
length A r is considered over which F is essentially 
constant. The product F A r is calculated and 
added for all values between a and b. Such a 
process is known as integration. When this proc- 
ess is carried out we obtain, 
he accelerated and the motion can he described by 
Eq. (3) 
2as=v2—vl (11) 
By Newton’s second law of motion a = E/m and 
using this in Eq. (11) 
Fs 
2 —W-rS 
m 
or 
Fs=-m{v2—vt) (12) 
The left side of Eq. (12) is obviously the work done 
on the body, and the right side is the increase in 
kinetic energy. Hence a moving mass has a 
kinetic energy 
K. E. = mvl (13) 
which will be in ergs if m is in grams and v is in 
cm per sec. It should be noted that kinetic energy 
has no direction and is not a vector quantity. 
Energy can readily be transformed from one 
form to another, a common example being a falling 
body. As the body falls, potential energy is con- 
tinuously converted into kinetic energy, which in 
turn is converted into other forms when the body 
is brought to rest. All energy exchanges are 
governed by the law of conservation of energy 
which states that “energy can be transformed but 
can not be created or destroyed.” In any me- 
chanical process, chemical or physical reaction 
there will be no loss or gain of total energy. With 
the discovery of radioactivity the law of energy 
conservation was seriously questioned, but the 
development of the Einstein mass-energy equation 
showed that the law must be retained with the 
extension that mass itself must be considered as 
one form of energy. In all chemical reactions 
the energy release is so small that the change in 
mass escapes detection. Only with the enormous 
energy releases from nuclear reactions can the mass 
changes be measured. 
2.06 Momentum and Impulse 
Although there is no doubt of the general valid- 
ity of the law of conservation of energy, it is diffi- 
cult to apply in many important cases because 
energy is easily transformed into elusive and hard- 
to-calculate forms. The collision of two auto- 
mobiles is a case in point. There is no doubt 
V*-V.=k,n (1-i) 
If the potential at infinity is arbitrarily set equal 
to zero the potential at any point r will be 
r,=-- (io) 
The minus sign indicates that as the mass is 
approached the potential becomes increasingly 
negative. This is correct because with attractive 
forces work will be done in approaching from in- 
finity, and hence the potential must he lowered. 
A similar situation will be encountered when 
electric fields and potentials are discussed. 
It is obvious that a body in motion has energy 
since it can do work, and so there must be an 
energy to be associated with velocity, just as 
potential energy is associated with position. This 
energy due to velocity is known as kinetic energy. 
If a moving body has a force acting on it, it will 
13 RADIOLOGICAL SAFETY 
371 X10-24 grams so the recoil nucleus, after the 
ejection of the alpha particle, will have a mass of 
364 X10-24 grams. The radium atom is at rest 
before the ejection, so the initial momentum is 
zero; and from Eq. (16) 
364X 10~24yj-|-6.7X 10~24X 1.5X 109 = 0 
or 
v[ — — 2.8X 107 cm. per sec. 
The ( —) sign indicates that the recoil velocity is 
opposite to that of the alpha particle. Kinetic 
energy has obviously not been conserved for ini- 
tially it was zero and after the ejection was 
K. E. (alpha particle) 
= %X6.7X10~24 (1.5X 109)2=7.5X 10~6 ergs 
K. E. (recoil nucleus) 
= 1/;>X364X 10~24 (2.8X107)2=1.4X10-7 ergs 
Another process of considerable interest is the 
perfectly elastic collision where kinetic energy as 
well as momentum is conserved. (Ch. 9, sec. 9.12.) 
Consider a particle of mass m and initial velocity 
v0 colliding with a stationary particle of mass M 
and imparting to it a velocity V. Since momentum 
is conserved 
mv-\-MV=mvo (17) 
and if kinetic energy is also conserved 
that total energy is conserved, but the amounts 
lost in heat, bending, and breaking are completely 
incalculable, and in such a process the energy 
principle is of no use in determining the final state 
of the system. Collisions are of great importance 
in atomic and nuclear physics and can be treated 
by considering momentum as well as energy. 
Momentum is defined as the product of mass and 
velocity. It is a vector quantity having the direc- 
tion of the velocity. Its importance lies in the 
fact lhat in any process whatsoever total momen- 
tum is conserved. To derive this principle con- 
sider two bodies with masses mx and m2 and veloci- 
ties vx and v2 before a collision. After collision the 
velocities will be v[ and v2. The motion of the 
first body can be described by Eq. (2) 
_ v[—vx 
1 
which by Newton’s second law of motion becomes 
F 
mx t 
or 
Ft=mxv[—mxvx (14) 
This could be used to calculate v[ if F were known, 
but in a transient process, such as a collision, F is 
usually a complicated function which can not be 
used practically. By Newton’s third law of 
motion the force on the second body will be — F 
and hence a consideration of the second body 
yields 
— Ft=m2v'2—m2v2 (15) 
The product Ft is known as impulse. The right 
hand sides of Eqs. (14) and (15) may be equated 
by changing signs. Then 
mxv[—mxvx = — m2v2-\~m2v2 
or 
mxv[+m2v2—mxvx+m202 (16) 
This shows that the total momentum before colli- 
sion is the same as the final total momentum. 
The momentum of the total system is conserved 
and nothing need be known of the forces involved. 
As a simple example of the application of this 
principle, consider the ejection of an alpha particle 
from a radium nucleus (ch. 6, sec. 6.02). The alpha 
particle has a mass of about 6.7 X10~24 grams and 
is ejected with an initial velocity of about 1.5 X109 
cm/sec. The mass of the radium nucleus is about 
mr2+- MV2 mv20 (18) 
To determine the energy transferred to the struck 
particle its final velocity V must be determined in 
terms of v0. Rearranging Eqs. (17) and (18) 
v=v°~m V (19' 
„W0 V2 (20) 
Hence 
V «• <21> 
The kinetic energy received by the struck particle 
and hence that lost by the incident particle is 
K.E. transfer y02 (22) 
14 RADIOLOGICAL SAFETY 
It can readily be shown that this will be a maxi- 
mum when M= m, and so if it is desired to absorb 
energy through elastic collisions, the particles in 
the absorber should have the same mass as the 
incident particles. 
2.07 Elementary kinetic theory 
An immediate application of the principle of 
conservation of momentum is the kinetic theory 
of gases. In this theory, a gas enclosed in a con- 
tainer is considered to consist of a large number 
of molecules, each moving and hence having 
kinetic energy and momentum. The number of 
molecules is enormous, and it is impossible 
to calculate the behavior of each one. It is 
possible, however, to resort to an averaging 
process, and here the large number has the ad- 
vantage that fluctuations from the average will 
be small. 
Specifically, assume a rectangular container 
with dimensions abc, figure 2-2, coinciding with a 
set of coordinate axes X, Y, Z. 
this will have components x, y, and z along the 
coordinate axes. From simple considerations of 
components: 
v2—xl-\-y2-\-z2 
v= -\Jx2Jry2jrz2 
Average values will be denoted by , as; v. 
Obviously v is zero and the same holds for x,y,z, 
If this were not so, there would be a movement of 
the gas in some preferred direction. If all the 
velocities are squared and then averaged, the 
mean square velocity v2 is obtained. This is not 
zero, since the squares of negative numbers are 
positive. There is still no preferred direction 
however, and: 
(23) 
The square root of a mean square velocity, -jrf, 
is known as a root mean square velocity and this 
may be used in the calculations, assuming that 
each of the n molecules has this velocity with 
components -y/j2. 
Consider the average molecule colliding with 
the face ab of the container. The velocity com- 
ponent perpendicular to the face is -yjrf. The 
molecule will make a perfectly elastic collision 
with the wall and will rebound with the same 
velocity in the opposite direction. Then by Eq. 
(14) 
Ft=2n^x2 per collision 
If the number of collisions per second is deter- 
mined, t can be put equal to unity, and the total 
force on the wall calculated. Before the molecule 
can again collide with ab, it must travel a distance 
2c which it does with an a verage velocity x2. 
Then the time between collisions is: 
2c 
■yjx2 
and the number of collisions per second with ab 
will be: 
■\Zx2 
”2c 
Figure 2-2.—Gas volume used for deriving the equation 
of the kinetic theory of gases. 
Since there are n molecules, the total collisions 
per second will be n times this and: 
Let the box contain n molecules each having a 
mass, n. One molecule will have a velocity v and 
F=---^x2 (24) 
c 
15 RADIOLOGICAL SAFETY 
Since the total force is equal to the pressure p 
times the area ah: 
ways bear a constant ratio. Thus 1 gram of 
hydrogen always combines with 8 grams of oxygen 
to form 9 grams of water. By studying a large 
number of such reactions it has been possible to 
assign to each element a number proportional to 
its combining weight. Thus oxygen is given an 
atomic weight of 16 and forms the basis of the 
system; hydrogen then has an atomic weight of 
1.008, chlorine 35.457, etc. These numbers do 
not have units, such as grams; they are merely 
relative. However, 1.008 grams of hydrogen will 
exactly combine with 35.457 grams of chlorine to 
form 36.465 grams of hydrogen chloride. This and 
other similar evidence suggests that there are the 
same number of atoms in 1.008 grams of hydrogen 
and 35.457 grams of chlorine, and that these com- 
bine one to one to form hydrogen chloride. The 
quantity of any substance having a mass in grams 
numerically equal to its atomic weight is known 
as one gram-atom, or one mole. 
The number of atoms in a gram-atom is known 
as Avogadro’s number. It has been measured in a 
number of ways, the present accepted value being 
6.1 X1023. Although gases were used in the dis- 
cussion, Avogadro’s number applies to all ele- 
ments or compounds. Thus there will be 6.1 X 
1023 atoms in: 
16 grams of oxygen 
107.88 grams of silver 
200.6 grams of mercury 
238.14 grams of uranium 
and 6.1 X1023 molecules in: 
18.016 grams of water (H20) 
32.00 grams of oxygen (02) 
36.465 grams of hydrogen chloride (HC1) 
It is now evident that Eq. (29) can be put on a 
molar basis by multiplying both sides by Avo- 
gadro’s number, N: 
Pab=~Lxi 
or 
(25) 
=n-f (26) 
The right hand side of Eq. (26) is 2/3 the total 
kinetic energy of the molecules. The left side is in 
the form of the law for perfect gases discovered 
empirically by Boyle and Gay-Lussac: 
pV=nkT (27) 
Where k is Boltzmann’s constant and T is the 
absolute temperature. Zero on the absolute 
scale is —273°C. Comparing Eq. (25) and (27): 
| a;* (28) 
Where \ is written into each side to emphasize the 
close relation between T and kinetic energy. In 
terms of y2: 
f *r=f ? (29) 
Eqs. (28) ahd (29) show that when the tempera- 
ture of a gas is raised the energy required goes into 
increasing the molecular kinetic energy. Eq. 
(29) also points out that the kinetic energy of 
a molecule is zero at absolute zero. The factor 
3 in Eq. (29) appears because the molecules con- 
sidered can absorb energy in only three ways 
(x, y, and 2 velocities), and hence are said to have 
3 degrees of freedom. In a diatomic molecule, which 
behaves much like a dumbbell, energy can, in addi- 
tion, be absorbed by two modes of rotation, and in 
this case a 5 would be required in the equation 
comparable to Eq. (29). Similarly, a triatomic 
molecule has 3 modes of rotation and a total of 
6 degrees of freedom. 
The temperature-energy equation (Eq. 29) is 
valid for a single molecule; for future applications 
it is more desirable to change to a molar basis. 
This can be done with the aid of a few observa- 
tions in simple chemistry. 
It has long been known that the weights of 
elements which combine to form compounds al- 
- NkT=~- v2 (30) 
Nk=E, the molar gas constant, = 8.31 ergs/ 
degree/mole. The right-hand side is the total 
molar kinetic energy. 
The energy required to raise the temperature 
of one gram of a substance one degree is known 
as the specific heat. For many purposes the spe- 
cific heat on a per mole basis (Cv) is used instead 
16 RADIOLOGICAL SAFETY 
of on a per gram basis. Then for a gas by Eq. 
(30): 
electrical conductivity 
thermal conductivity T 
In picking materials for protection against flash 
burns, it is obvious that thermal conductivity and 
specific beat are important factors. With a low 
thermal conductivity high surface temperatures 
can be expected and fires may break out. With 
a high conductivity and specific heat, the energy 
of the flash may be spread through a volume of 
material, and a high surface temperature avoided. 
Before leaving the kinetic theory, one remark 
should he made about the derivation of Eq. (25). 
In this derivation it was assumed that the mole- 
cules did not collide with each other and transferred 
momentum only to the walls of the container. 
Actually this is far from true and each molecule 
suffers many collisions with other molecules. If 
this were not so, the thermal conductivity of a 
gas would be equal to the average molecular 
velocity, which is of the order of several hundred 
meters per second. 
It can be shown that the treatment given above 
is not altered when inter-molecular collisions 
are considered. For some purposes, such as a 
study of the electrical conductivity of gases, these 
collisions are of great importance, and to study 
them the concept of mean free path is introduced. 
This is the average distance travelled by a mole- 
cule between collisions. This certainly depends 
in a complicated way on the size and shape of the 
molecules and a complete treatment cannot be 
given here. The mean free path would be ex- 
pected to be inversely proportional to the number 
of molecules present per unit volume and hence, 
from Eq. (26), to the pressure at constant tem- 
perature. This is the important fact for present 
purposes. At 1 atmosphere pressure, the mean 
free path is about 10~6 cm. At a pressure of 10 cm. 
of mercury, this has increased to about 10~4 cm 
=\b(T+1)-\rT=\r (31) 
This indicates that the molar specific heat of 
any monatomic gas is 12.2 joules or about 3 
calorics. For polyatomic gases these figures would 
be increased according to the number of degrees 
of freedom. It should be pointed out that Eq. 
(31) was obtained on the assumption that the 
gas was held at constant volume during the heat- 
ing. If it is allowed to expand, more energy will 
be required, but that is a complication of no 
immediate importance. 
Very substantial difficulties are encountered 
when the specific heat calculations are extended 
to solids. It has long been known from experi- 
ment that many metals obey the law of Dulong 
and Petit and have a specific heat of about 6 
calories per mole. It is known from the phenom- 
ena of electrical and thermal conduction that in a 
metal there must be about 1 free electron per 
atom. These then constitute a sort of electron 
gas which might be expected to contribute to the 
specific heat. Recent calculations show that this 
electron gas is of such a nature that it does not 
contribute to the specific heat, and hence the law 
of Dulong and Petit can be explained by neglect- 
ing the electronic contribution. 
The free electrons are of the greatest importance 
in explaining thermal and electrical conductivities. 
They are indeed responsible for both phenomena, 
and this explains the previously empirical fact 
known as the Wiedemann-Franz law that 
17 RADIOLOGICAL SAFETY 
Chapter 3 
ELECTRICITY AND MAGNETISM 
3.01 Electrostatics 
Electrical and magnetic phenomena have been 
recognized for centuries, and electricity has be- 
come one of the greatest servants of man, yet the 
fundamental nature of it remains obscure. Many 
of its properties are known, and its behavior can 
be accurately calculated. Two kinds of elec- 
tricity, positive and negative, are recognized, and 
most matter appears electrically neutral because it 
contains equal quantities of the two kinds. Only 
when there has been a separation does the elec- 
trical make-up of matter become manifest. Elec- 
tric and magnetic phenomena are intimately re- 
lated to the release of nuclear energy. This 
chapter is devoted to a discussion of those aspects 
pertinent to the main subject. 
The earliest method of charge separation was 
rubbing or close contact. If a hard rubber rod is 
rubbed with a cat’s fur and the two separated, 
each will show electrification. In particular 
sparks will jump from them, and they will attract 
light objects such as bits of paper. If two rub- 
ber rods are electrified or charged and then 
brought together, a force of mutual repulsion will 
be observed. Since the same thing must have 
happened to each rod, it is evident that like 
charges repel. Similarly the two cat’s furs will 
be found to mutually repel. When the rubber 
rod is brought near the cat’s fur, however, a force 
of attraction is observed, and this leads to the 
law that like charges repel each other and unlike 
charges attract. 
When careful measurements are made, it is 
found that an inverse square law is obeyed, and 
Coulomb’s law states that the force between two 
charges, and q2 separated by a distance r is 
present purposes, k is considered to be strictly 1.0. 
It will be noted that Coulomb’s law has the 
same form as the law of universal gravitation, 
p=a-IP (2) 
except for a constant multiplier G. The units of 
F (dynes) and r (cm.) are established, and it seems 
reasonable to define the unit of charge, or quan- 
tity of electricity, so that the need for a constant 
is eliminated. The unit charge is then that 
charge which is repelled with a force of one dyne 
by an equal charge at a distance of one cm. in a 
vacuum. The unit of charge so defined is the 
statcoulomb, or electrostatic unit of charge 
(e. s. u.), and forms the basis for a system of units 
known as the electrostatic system. 
There are many analogies between electric and 
gravitational forces. Consider, for example, a 
charge q placed on a hollow sphere of metal. 
Since the sphere is a conductor, the electricity is 
free to move about and will distribute itself uni- 
formly over the surface because of the mutual 
repulsion of the like charges. Any charge brought 
near the sphere will experience a force given by 
Eq. (1), and hence there is an electric field around 
the sphere. As in the gravitational case, the 
entire charge may be considered to be located at 
the center of the sphere; then the field strength at 
any point outside the sphere will be 
(3) 
where r is the distance from the point to the center 
of the sphere, since this E is the force exerted on 
a unit test charge brought into the field. The 
direction of the field will be the direction of the 
force on a positive charge. 
It can be shown that the field strength inside the 
sphere is zero. To make this plausible, consider 
a charged sphere, shown in figure 3-1, with a unit 
test charge at the center. Each small portion of 
the sphere will exert a force on the test charge, 
and geometrically opposite portions will exert 
equal but oppositely directed forces. These will 
r=±JP a) 
The ± sign indicates that the force may be a 
repulsion or attraction depending on the polarities 
of <7i and q2- k is the specific inductive capacitance 
or dielectric constant of the medium between the 
charges. For empty space k= 1, and it may be 
taken as unity for air in most calculations. For 
19 
774689 0 - 48 -3 RADIOLOGICAL SAFETY 
trary, but a reasonable one would be to set the 
potential at infinity (Foo) equal to zero. If this 
is done (4) becomes; 
VH (5) 
Eq. (5) shows that with like charges at 0 and A 
the potential becomes increasingly positive as a 
decreases. With unlike charges, the potential 
will also be given by Eq. (5), but must be nega- 
tive. Since the force used in deriving Eq. (5) 
was in dynes and the distances were in centimeters, 
the potential V in the electrostatic system will be 
in ergs per statcoulomb. This is called the 
statvolt or the e.s.u. of potential. The work 
done in moving any charge through a potential 
difference will be equal to the product of the 
charge and the potential difference, and will be 
in ergs if both electrical quantities are expressed 
in e. s. u. 
A very important component of electrical cir- 
cuits consists of two conductors or plates, with 
Figure 3-1.—A charge placed on a hollow conducting 
sphere distributes uniformly and exerts no force on a 
charge in the interior. 
cancel, and hence there will be no net force and 
no electric field. This can be shown to be true for 
any point inside the sphere. This fact is used in 
the electrical shielding of sensitive instruments. 
A metal shield placed around the instrument will 
provide a field-free region unaffected by charges or 
fields outside the shield. 
As in the gravitational case, electric potential 
difference between two points in a field is defined 
as the work done in taking a unit positive charge 
from one point to another. This is an important 
concept that will be used repeatedly throughout 
this text. It should be particularly noted that 
electrical potential is not analogous to water 
pressure, in spite of the popularity of the idea. 
Consider a charge -\-q located at 0, figure 3-2. 
Figure 3-3.—Two insulated conductors form a condenser. 
The plates will have equal charges of opposite sign. 
equal charges of opposite sign separated by a non- 
conductor or dielectric. The ratio of the charge 
on one plate to the potential difference between 
the plates is the capacitance, C: 
C=f (6) 
Figure 3-2.—Calculation of electrical potential at points 
A and B due to charge q by determining the work done 
in moving a unit charge. 
where V is understood to be the difference in the 
potentials. In simple cases C can be calculated 
from the geometry of the system. 
Consider an isolated metal sphere of radius a 
having a charge q. In this case the other plate is 
assumed to be at an infinitely large distance. 
From Eq. (5), the potential of the sphere is 
It is desired to calculate the potential difference 
between points A and B in the field. The total 
work in moving the charge from B to A, and hence 
the potential difference, may be calculated to be 
(4) 
F=1 
a 
and hence 
C=Hfa=° (7) 
where Vb and Va are the potentials at points B 
and A. The choice of a zero of potential is arbi- 
20 Thus the capacitance of an isolated sphere is 
equal to its radius and the e. s. u. of capacitance 
is the centimeter. In the so-called practical sys- 
tem of electrical units, based on the volt and am- 
pere, the unit of capacitance is the farad, a 
more familiar unit than the centimeter. To fix 
the size of the centimeter, it is worth remember- 
ing that, within 10 percent, one centimeter= 10~12 
farad or one micro-micro-farad. 
To consider a condenser more nearly like the 
definition, imagine a second sphere of radius h 
concentric with the first sphere and having a 
charge —q. See figure 3-4. This sphere does 
RADIOLOGICAL SAFETY 
If this is divided by 4va2, the area of the sphere, 
the result will be the capacitance per unit area. 
Also let (b-a)=s, the plate separation. Then 
C (per unit area) 
and for any area 
If the space between the plates is filled with a 
dielectric of specific inductive capacitance k the 
capacitance will be k times as large as calculated 
from Eq. (9). This is an important factor in 
constructing large condensers. Insulators such as 
paper, mica, or organic oils, have dielectric con- 
stants ranging from 2.5 to 5, and are frequently 
used in condenser construction. It should be 
noted that the capacitance of a condenser is not 
the amount of electric charge it can hold, because 
from Eq. (6) the quantity can be increased by 
increasing the potential difference. If the poten- 
tial is increased too much, however, the dielectric 
will rupture and the condenser may be ruined. 
So far electricity has been treated as if it were 
a completely divisible fluid capable of existing in 
any desired amount. Actually, this is not the 
case. Electricity is atomic in nature, and any 
charge will be an integral number of the elementary 
units. Millikan, in 1915, succeeded in measuring 
the charge by a simple method known as the oil 
drop experiment. 
Millikan used two horizontal condenser plates, 
Figure 3-4.—Spherical condensers for theoretical con 
sideration. 
not change the electric field inside itself and con- 
sequently it has a potential q/b from Eq. (5). 
Then the two spheres have a difference of potential: 
•6-i) 
Then, by 6): 
C1FF) 
=~ (8) 
h—a 
Figure 3-5.—The Millikan oil drop experiment. The oil 
drop will carry a charge picked up in the spraying. 
If now both a and b become very large in such a 
way that (b-a) remains small, the curvature of 
the plates decreases and the construction ap- 
proaches the usual parallel plate condenser: 
separated by a distance S and connected to a po- 
tential difference V. A fine mist of oil was 
sprayed into the air above the top plate, and an 
occasional droplet would fall through a hole in 
the top plate and into the field of the microscope 
b—a 
21 RADIOLOGICAL SAFETY 
rod is magnetized, one end will be a north pole and 
the other end will be a south pole. No amount 
of division or other treatment of the rod will 
result in a single isolated pole, and the conclusion 
is reached that the two poles are inseparable. It 
is sufficient for present purposes to consider the 
iron to be composed of tiny elementary magnets. 
In the non-magnetized state these have a random 
orientation which results in a neutralization. 
When magnetized, the elementary magnets line 
up, leaving an unneutralized pole near each end. 
By working with long thin rods it is possible to 
approach single pole conditions, since the inter- 
fering poles are placed at a considerable distance. 
As in electrostatics, it is found that like poles 
repel and unlike poles attract, and that the force 
obeys an inverse square law: 
M. In the process of spraying, most of the drop- 
lets became electrified and so were influenced by 
the electric field between the plates. If a unit 
charge is taken from one plate to another, the work 
done will be V ergs, and since the distance is S the 
force or electric field strength will be \/S. If an 
oil drop of mass m has acquired a charge q the 
downward pull of gravity will be mg, and the 
electric force will be Vq/S. If V is adjusted so that 
the drop remains stationary: 
—j2=mg (10) 
All quantities except g can be measured. Milli- 
kan determined the charge on hundreds of oil 
drops. Many different values were found but in 
every case the charge was an integral multiple of 
4.8 X10-10 e. s. u. It appears, therefore, that this 
is the size of the elementary unit of electricity and 
no smaller quantity is known to exist. 
A large number of experiments indicate that the 
unit of negative charge is carried by a small 
particle known as the electron. Positive charges 
are associated with matter and are demonstrated 
only when the normally neutralizing electrons are 
removed. An electron has a mass of only 9 X 10~28 
grams, about 1/1840 the mass of the lightest atom, 
and moves about freely in electric fields. An 
electric current consists of a mass movement of 
electrons, the positive charges remaining fixed in 
their equilibrium positions. The strength of an 
electric current, I is equal to the amount of charge 
that passes a given point per second. That is 
F=±Wh (12) 
where ju is the magnetic permeability of the inter- 
vening medium. For most purposes, n=l except 
in magnetizable materials such as iron and certain 
alloys. As in the case of electric charge, the unit 
of pole strength m can be defined to eliminate 
constants (except n). The unit magnetic pole is 
then the pole which is repelled with a force oj one 
dyne by an equal pole one cm: distant in a vacuum. 
This definition forms the basis for the electro- 
magnetic system of units e.m.u. 
If it is found that a magnet has a force exerted 
on it, there is a magnetic field at that point. The 
strength of the field is equal to the force in dynes 
exerted on a unit pole. The direction of the field 
is the direction of the force on a north pole. 
A most important fact is that a wire carrying an 
electric current is surrounded by a magnetic field. 
The direction of the field will be perpendicular 
to the direction of current flow, and can be repre- 
sented by a series of concentric circles around the 
wire. If the fingers of the right hand are curled 
as if to grasp the wire, and the thumb is extended 
along the wire in the direction of the current flow, 
the curled fingers will show the direction of the 
magnetic field. 
The calculation of the field produced is made 
through the law of Biot and Savart. If a current 
I flows, the magnetic field strength at any point P 
will be the sum of the effects of small segments 
of the wire. The effect of each segment will be 
i=f (id 
I and Q will be measured in the same system of 
units. 
3.02 Magnetism 
The qualitative aspects of magnetic pheno- 
mena have been known for centuries, and magnets 
and magnetism are everyday experiences. Only 
a brief discussion is needed to establish the aspects 
of magnetism essential to the present discussion. 
The concept of a magnetic pole is somewhat 
more complicated than the corresponding electric 
charge, because the existence of a single magnetic 
pole has never been demonstrated. If an iron 
22 RADIOLOGICAL SAFETY 
proportional to the current, the length of the 
segment As, the sine of the angle 9 between the 
segment and the line to the point P, and inversely 
proportional to the square of the distance r to P. 
been defined, it seems reasonable to replace the 
proportionality by an equality and use Eq. (14) 
to define the e.m.u. of current (abampere) 
H=—~ (15) 
In passing, it may be noted that 1 abampere=10 
amperes, the latter being the unit of current in the 
practical system. The magnetic field strength, 
H, which is in dynes per unit pole, is expressed in 
oersteds. 
It is obvious from the derivation of Eq. (14) that 
if n turns of wire are used, H will be n times as 
large, and thus many turns of wire are used to 
obtain strong magnetic fields. To produce still 
stronger fields, an iron core may be put inside the 
coil. The magnetic field produced by the coil 
will magnetize the iron, and this will increase the 
total magnetism or magnetic flux, </>, produced by 
the current. The flux per unit area, Bu is some- 
what analagous to the field strength Hu and a plot 
of B against H will show the gain in magnetism 
obtained by the use of iron. Figure 3-8 shows 
such a B-H plot, or magnetization curve. 
Figure 3-6.—The magnetic field at P will be due to the 
effect of ail of the small segments, S. With the current 
direction the field at P will be into the paper. 
That is 
AHa (13) 
A particularly simple case occurs when a wire 
carrying a current I is bent into a circle of radius r. 
See figure 3-7 
Figure 3-8.—The magnetic curve for iron. The curve is 
not strictly correct as the exact shape depends on the 
previous magnetic history of the iron. 
Figure 3-7.—The magnetic field due to a circular coil. 
The field inside the coil will be directed into the paper. 
Then for each segment sine 0=1, 
and the summation of As is equal to one circum- 
ference of the circle or, 2 irr. Then 
Although the magnetism can be increased by the 
use of iron, it no longer depends linearly on I as it 
does in air, Eq, (15). This was to be expected 
from the assumption that the iron is made up of 
tiny elemental magnets. For example, the satura- 
tion effect shown in figure 3-8 is explained by the 
fact that the elemental magnets have been com- 
TT 2 rrl 2 7rl nA. 
II a —2~ or a —- (14) 
r* r 
Since the unit of current in this system has not 
23 RADIOLOGICAL SAFETY 
pletely rotated, and any further increase in H 
can not produce further rotation. Another dis- 
advantage of iron is the heating effect produced 
when the direction of the field is rapidly changed 
There are several reasons for this heat production. 
One source comes from the fact that the elementary 
magnets appear to move in a viscous medium and 
the resulting frictional losses produce considerable 
heating. If an alternating current is sent through 
a coil it is necessary to construct the core of thin 
sheets of special alloys so that the heat loss is kept 
within reasonable bounds. 
3.03 Electrical Conduction 
The magnetic effects of an electric current have 
been discussed above without any particular 
reference to the mechanism of conduction of the 
current. This mechanism will now be considered 
for solids, liquids, and gases, each medium having 
features quite different from the other two. 
The use of metal wires for conducting electric 
currents is well known, and the use of other 
materials as non-conductors or insulators is equally 
important. The present conception of a metal is 
as an aggregate of atoms rigidly bound into a more 
or less regular crystal structure. These atoms 
are immobile and do not take any active part in 
the conduction. In addition to the bound atoms, 
the metal contains a large number of free electrons, 
about one for each atom. These electrons form 
a sort of electron gas (Sec. 2,07) and have a 
thermal motion much like kinetic motion of gas 
molecules. 
When a potential difference is applied to the 
ends of a wire, an orderly motion is superimposed 
on the random motion of the electrons and an 
electric current flows. The velocity of the con- 
duction electrons is low, but the rate of propaga- 
tion of the electric force along the wire has a 
velocity almost equal to the velocity of light. 
Therefore the conduction takes place almost 
instantaneously. 
As the free electrons move under the acceleration 
of the applied potential, they will suffer frequent 
collisions with the rigidly bound atoms. At each 
collision, the electron will lose energy, will then 
again be accelerated, and will again collide and 
lose energy. The situation is analagous to the 
mean free path in kinetic theory. 
Since energy is lost at each collision, heat will 
be developed in the wire, and a potential difference 
will be required to maintain the current. Ohm 
showed experimentally in 1826 that the potential 
difference is proportional to the current. This is 
written: 
V=IR (16) 
where R is the resistance of the conductor. This 
equation, which is known as Ohm's law, is appli- 
cable in any system of electrical units, but only 
the practical system is ever actually used. With 
V in volts and I in amperes, R will be expressed 
in ohms. This equation can be applied to any 
circuit or portion of a circuit remembering that 
the resistance R will be that between the points 
at which the difference of potential is measured. 
Measurements show that the resistance of a 
conductor is proportional to its length and 
inversely proportional to its cross-sectional area. 
Thus: 
R=P~i (17) 
where I is the length and A is the cross-sectional 
area, p is a constant characteristic of the material, 
known as the specific resistivity. Table I shows 
the enormous variations in p found in common 
substances. It should be noted that for most 
materials p increases with temperature. 
Table 
I.—Specific resistivity 
Material: 
Ohm-cm 
Copper 
1.7X10-0 
Aluminum 
2.8X10-9 
Iron 
1X10-9 
Carbon _ 
3X10-3 
Amber 
5X1016 
Quartz 
5X1018 
Since there is a potential difference V across the 
ends of a resistor, the electrical work done W will 
be 
W=VQ (18) 
where Q is the total quantity of electricity 
transported. This will be exactly equal to the 
heat developed in the resistance. It is more cus- 
tomary to express this as the rate at which heat is 
developed by replacing Q by the current I. In 
which case 
P=VI (19) 
where P will be in watts or joules per second, if V 
is in volts and / is in amperes. If V and I are 
24 RADIOLOGICAL SAFETY 
both expressed in either e.s.u. or e.m.u., the 
power P will be in ergs per second. Eq. (19), 
which is known as Joule’slaw, may be transformed 
by an application of Ohm’s law into two other 
useful forms: 
P=PR (20) 
and 
V2 
P==~R (21) 
Any of the three forms of Joule’s law may be used. 
In addition to the consistent units which are 
usually used in Eq. (18) to obtain the work in ergs 
or joules, there is one inconsistent combination 
commonly used in nuclear physics. The intro- 
duction of such a hybrid unit can only be justified 
by its practicality. If a charge equal to one elec- 
tronic charge is accelerated by a potential of one 
volt, the work done is known as one electron volt. 
Since V in volts times Q in coulombs yields W in 
joules, and since the electronic charge is 1.6X10-19 
coulombs—one electron volt 
(ev) = 1.6 X 10~19 joules 
= 1.6 X10-12 ergs (22) 
A second frequently used unit is the million elec- 
tron volt (Mev) which is obviously 
1 Mev=1.6X10~6 ergs (23) 
In all circuits used for measuring radiation, 
many resistors are used with resistance values 
ranging from 1 to 1011 ohms. Resistances below 
about 108 ohms present no particular probem. 
For precision work or where stability is essential 
wire wound resistors are available in values up 
to 106 ohms. Thin metal deposits or graphite 
films may be used where extreme stability is not 
required. Above 108 ohms, however, the con- 
struction and mounting becomes important. Leak- 
age across the resistor terminals can then have a 
resistance comparable to that of the resistor itself, 
and since this may be variable depending on 
humidity and other conditions, great care must be 
taken to reduce surface leakage. High resistance 
units are now available, mounted in a vacuum in 
glass containers whose surfaces are especially 
treated to reduce surface leakage. These units 
must be handled carefully, as fingerprints may 
spoil the surface coating. 
In some instruments it is necessary to use the 
very best insulating materials to insure proper 
operation. Outstanding insulators are quartz, 
sulphur, amber, and polystyrene. Whenever 
these materials are used they must be handled 
with great care to avoid surface leakage. Instru- 
ments requiring these insulating materials are 
described in chapter 9. 
The effects of moisture on high resistors have 
been mentioned above, where it was implied that 
aqueous solutions are relatively good conductors. 
This is indeed the case, but the mechanism of 
liquid conduction is quite different from that of 
metallic conduction. 
Imagine some compound such as silver nitrate, 
AgN03, dissolved in water. Now water has a 
dielectric constant of about 80, and hence by 
Eq. (1) the electrical forces holding a molecule 
together will be reduced by a factor of 80. The 
forces are no longer adequate, and most of the 
molecules will split into two charged portions or 
ions, Ag+ and NOa, the + and — signs showing 
the electric charge carried by each ion. Thus Ag+ 
indicates that one of the needed to obtain 
neutrality is missing, and NO3 indicates that the 
ion has one extra electronic charge. 
If two electrodes are immersed in the solution 
and a potential difference applied, the ions will be 
attracted, each to the oppositely charged elec- 
trode. The Ag+ ions will move to the negative 
electrode, or cathode, where each ion will acquire 
an electron and become a neutral silver atom, 
which will be deposited on the cathode. This is 
the basis of the process of electroplating. The 
electrons required for neutralization must be sup- 
plied by the external source of potential, and hence 
a current flows in the circuit. The solution 
exhibits a resistance but this is a complicated 
function of the concentration of the solution and 
the temperature and is of no immediate interest. 
It is the relation between the flow of electric charge 
and the mass of metal deposited that ie of im- 
portance. 
About 1835 Michael Faraday announced the 
fundamental laws governing liquid or electrolytic 
conduction. The mass of metal deposited depends 
only upon the quantity of electricity which flows, 
and not upon current, voltage, solution concen- 
tration, or any other variable. The amount of 
any chemical element deposited by a given quan- 
25 RADIOLOGICAL SAFETY 
ity of electricity is proportional to the atomic 
weight of the element. In particular 96,500 
coulombs of electricity will deposit 107.88 grams 
or one gram atomic weight of silver. The atomic 
weight of copper is 63.57 and it is found that only 
63.57-4-2 grams are deposited by 96,500 coulombs. 
This strongly suggests that silver is present in the 
solution as Ag+, needing only one electron for 
neutralization, while copper is ionized as Cu++, 
and thus yielding only one-half of the deposit per 
coulomb. The number of charges on each ion is 
equal to the valence of the element. 
The quantity, 96,500 coulombs, is known as the 
Faraday. It can be determined quite accurately 
and by combining it with the results of the Milli- 
kan oil drop experiment tt is possible to calculate 
Avogadro’s number. The electronic charge is 1.6 
X10~19 coulombs and so one Faraday will neu- 
tralize 
pressures the mean free path (sec. 2.07) will be 
short, and the energy acquired by the accelerated 
charges will be dissipated in a large number of 
collisions. At low pressures, the mean free path 
becomes large, and a charge can attain a consider- 
able kinetic energy before experiencing a collision. 
If it has sufficient energy, a charge will split up or 
ionize a gas molecule upon collision. The ions into 
which a neutral molecule is split are charged, and 
each will be attracted toward the proper electrode 
and produce further ionization by collision. Ions 
reaching the electrodes are neutralized and are 
then available for further ionization. Thus a 
discharge started by a stray charge will continue 
as long as a potential is applied to the electrodes. 
The discharge in gases is of great importance in 
radiation measuring instruments and in the 
production and study of molecular beams and 
will be discussed in detail in chapters 7 and 9. 
It is to be noted that the mechanism of ioniza- 
tion in a gas is quite different from that in the case 
of electrolytic conduction, where ionization by 
collision plays no part. No attempt is made to 
determine the resistance of the gas as this is a 
complex function of the kind of gas, the pressure, 
and the current. In fact, because of the cumula- 
tive ionization, the current may tend to increase 
to a very high value unless limited by external 
means. If the current through the discharge 
increases, there will be an increase in the number 
of ions, and because of the better conduction the 
voltage may drop and the discharge show a 
negative resistance. 
If the discharge does take place as described, 
there should be a stream of negatively charged 
particles moving toward the positively charged 
anode, and a stream of positive ions moving 
toward the cathode. The negative particles, 
coming from the vicinity of the cathode, were 
originally called cathode rays. They are now 
known to be electrons moving with high velocity. 
They have the same properties regardless of the 
gas in the tube, and these properties are the same 
as found for electrons from quite different sources. 
The positive ions have a much greater mass and 
it is now certain that they are the positively 
charged residues of atoms from which one or more 
electrons has been removed by collision. The posi- 
tive ions are best studied by separating them from 
the electron stream. This was done by 
1023 charges 
Since the Faraday will neutralize 107.88 grams or 
one gram atom of silver, it is evident that one 
gram atom of silver contains 6.1 X 1023 atoms which 
is Avogadro’s number. The same value will be 
obtained for any other element if the proper val- 
ence is taken into account. These experiments in- 
dicate clearly that matter as well as electricity is 
atomic in nature and can be divided down to 
elementary unit structures. In the case of matter 
the unit structure is different for each element, 
but the electron has the same properties wherever 
it is found. 
A further insight into the structure of matter is 
obtained by considering the conduction of elec- 
tricity through gases. At pressures of one atmos- 
phere or higher, all gases are excellent insulators 
and only extremely high voltages can produce an 
appreciable current flow. At low pressures the 
situation is quite different, as is readily seen by 
the neon and mercury signs in our cities. A series 
of complex phenomena take place at pressures of 
about 1 mm of mercury. A complete description 
of these phenomena is not possible nor necessary: 
only the essential features of the mechanism will 
be described. 
If a potential is applied to electrodes in a gas, 
any stray charges in the gas space will bo 
accelerated toward the proper electrode. At high 
26 boring holes in the cathode to allow the ions to 
pass through into a discharge-free region. The 
ions were originally known as canal rays because 
of this arrangement. (See chap. 5, fig. 5-1.) 
3.04 Electronics 
In the previous section the phenomena ac- 
companying the passage of electricity through 
gases were briefly described. If the gas pressure 
in a discharge tube is reduced by continued evacu- 
ation, the discharge will stop when there is no 
longer a sufficient number of gas molecules to pro- 
vide the ions necessary for conduction. With a 
very high vacuum and with cold electrodes the 
tube becomes a very good insulator, and no ap- 
preciable current will flow even when many kilo- 
volts are applied to the electrodes. 
If one electrode is hot, as would be a filament of 
fine wire carrying a current, the situation is quite 
different, and currents will pass through the 
vacuum to a cold electrode with potentials of only 
a few volts. Such a device forms the basis of the 
modern vacuum tube, a very powerful tool that 
is used in many instruments in nuclear physics 
and radiological safety measurements. The funda- 
mental construction of a two element tube or diode 
is shown in figure 3-9. 
RADIOLOGICAL SAFETY 
When the temperature of the metal filament is 
raised the average kinetic energy of its free elec- 
trons will be increased, and some of them near the 
surface of the wire will acquire sufficient velocity 
to escape from the metal into the surrounding 
empty space. With no potential on the cold 
electrode or plate, there is no electric field in the 
space around the filament, and the escaped 
electrons will remain close to the filament and form 
a space charge. As the filament loses electrons, it 
becomes positively charged, and this will attract 
some of the electrons back into the metal so that 
a state of equilibrium exists with a constant 
space charge. The amount of space charge ob- 
viously depends on the filament temperature, but 
in all of the following discussion this will be as- 
sumed constant at the value recommended by the 
manufacturer of the tube. In many tubes the 
electrons are not emitted directly from the filament 
but from an indirectly heated cathode. This is a 
thin metal cylinder surrounding a ceramic tube. 
The filament inside the cylinder merely serves to 
heat the cathode and does not enter into the 
electrical function of the tube. The cathode surface 
is usually coated with various oxides to obtain a 
copious electron emission at low temperatures. 
If the plate is made negative with respect to the 
filament, the space charge will be repelled, and no 
current will flow in the tube. When the plate is 
positively charged, some of the space charge elec- 
trons will be attracted to the plate, and a current 
will flow through the tube. Thus the current flow 
in a tube is unidirectional. If an alternating po- 
tential is applied to the plate the tube will conduct 
only on the positive halves of the cycle and acts as 
a rectifier. The use of diodes in radiological safety 
apparatus is almost entirely confined to the recti- 
fication of alternating current from power lines to 
provide direct current for various purposes. 
The introduction of a third electrode or grid in 
the space charge region forms a triode and is the 
basic construction for all modern amplifying tubes. 
The grid consists typically of a spiral of fine wire 
closely surrounding the cathode. The electrons 
can pass freely from the cathode to the plate, but 
they will be strongly influenced by the potential 
of the grid. 
The operation of a triode can best be described 
by a discussion of the characteristic curves obtained 
from the circuit of figure 3-10. If the plate volt- 
Figure 3-9.—A 2-element tube, or diode, with electron 
emission from a hot filament. 
27 RADIOLOGICAL SAFETY 
The importance of the grid lies in two main 
features: 
(а) Over the linear portion of the charcteristic 
the grid can control the plate current but draws 
practically no current. In this region the grid 
current will not exceed 10“8 amperes and may be 
as low as 10~15 amperes. Thus the power input 
to the grid is very small, yet the grid can control 
substantial amounts of plate current power. 
(б) A change in grid voltage will have as great 
an effect on the plate current as a much larger 
change in plate voltage. For example, a change of 
grid voltage of 1 volt might change the plate cur- 
rent by 3 milliamperes, whereas the plate voltage 
would have to be changed by 100 volts to produce 
the same change in plate current. Since 1 volt on 
the grid has the same effect as 100 volts on the 
plate, the tube has an amplification factor of 100. 
It is this ability of a triode to amplify small signals 
that makes it such a powerful tool. 
When vacuum tube circuits are examined, more 
complicated typos of tubes will be found, but in 
general the fundamental action will be the ampli- 
fying effect of the triode. Five element tubes or 
pentodes are used in place of triodes when high 
amplification factors (up to 1,500) are desired, 
but the two additional grids are maintained at 
constant potentials and do not enter into the 
amplifying of the signal impressed on the grid. 
More complex tubes are constructed for radio 
use but are not of immediate interest. 
If it is desired to obtain a voltage output from 
a tube instead of a plate current change, resistance 
must be inserted in the plate circuit. (See fig. 
3-12.) A constant voltage EB is applied to the 
plate through resistor R and Ec is adjusted to 
bring the tube to the desired operating point on 
Figure 3-10.—Circuit for obtaining the characteristics of a 
triode. 
age EP is held constant and the grid voltage Eg is 
varied the values of the true plate current Ip 
can be plotted against Eg as is figure 3-11. When 
the grid is strongly negative all electrons are re- 
pelled to the cathode, no current flows and the 
tube is said to be cut off (point A). As the grid 
becomes less negative some current flows and the 
characteristic shows a linear portion BC. When 
the grid becomes positive, every emitted electron 
is attracted from the space charge and the tube is 
saturated (point D). 
Figure 3-11.—Mutual characteristics of a triode 
The linear portion of the characteristic lies 
entirely on the negative side of the grid voltage 
axis. This is an important region because here 
the variations in plate current will accurately 
follow the variations in grid voltage. Over the 
curved portions of the characteristic the variations 
in plate current do not vary linearly with grid 
voltage. 
Figure 3-12.—The triode as a voltage amplifier. 
28 RADIOLOGICAL SAFETY 
its characteristic curve. This will usually be at 
the center of the linear portion BC oi figure 3-11. 
Suppose now a small positive signal voltage ap- 
pears across R. The grid voltage will then 
become less negative and the plate current will 
increase. But if the plate current increases, the 
voltage drop across Rg will increase by Ohm’s 
law and hence the plate will become less positive. 
Thus the positive input signal has become an 
amplified negative signal. This phase reversal is 
important when tubes are used in Geiger counter 
circuits where pulses of one polarity are received 
from the counter tubes. 
Before leaving vacuum tubes it should be noted 
that the action is nearly instantaneous. The 
time of passage of an electron from cathode to 
plate is of the order of 10“10 seconds, and hence 
a grid signal appears with almost no delay in the 
plate circuit. Only in special applications is the 
time lag of practical importance. 
3.05 Forces on Moving Charges 
Electric and magnetic fields exert forces on 
moving charges and these forces can best be 
studied in the gas discharge, for here the charges 
are free from the restraint of a conducting wire. 
The case of the electric field is a simple one. The 
force on the charge is Ee and is in the direction 
of the field. It is independent of the velocity of 
the charge. The field strength E is usually easily 
determined from the dimensions of the apparatus. 
If the field is produced between parallel plates, 
E=V/s as in the Millikan oil drop experiment. 
It is easy to see qualitatively that when a mag- 
netic field acts on a moving charge, the force 
produced will be at right angles to both the mag- 
netic field and the velocity of the charge. To 
obtain the quantitative relations consider again 
the circular coil of wire shown in figure 3-7. 
From Eq. (14) the magnetic field strength at the 
center of the coil is 
(25) 
This force may be thought of as the action of the 
magnetic field of the unit pole at the center on the 
current I. The field strength of the unit pole is 
by Eq. (12): 
H=-2 (26) 
and since each portion of the coil finds itself in 
this field, 1/r in Eq. (25) may be replaced by Hr 
from Eq. (26) and 
F=2wrIH 
Since 2-irr—l (the length of the wire in the field) 
this reduces to: 
F=HIl (27) 
As can be seen from figure 3-13, the force F is 
perpendicular to both the direction of I and H. 
Figure 3-13.—A unit magnetic pole at 0 will have a force 
acting on it and by Newton’s Third Law there must be 
an opposite force on the wire. 
The force F will be in dynes if H and I are ex- 
pressed in e. m. u. and I is in cm. This is a most 
important equation and forms the basis of all 
electric motor designs, for F is precisely the force 
which is utilized to obtain useful work from motors. 
For present purposes, however, it is desirable 
to transform Eq. (27) slightly to obtain the force 
on a single moving charge rather than on an 
electric current in a wire. By definition, the 
current I consists of I units of electric charge 
flowing past any given point in the wire per second. 
If each of the charges is moving with a velocity v, 
all of the charge in v cm of wire will flow past in 
one second. There are, then Ijv charges per cm. 
of wire, or Il/v charges in I cm. of wire. But Eq. 
ff=— (24) 
r 
From the definition of H this will be the force 
exerted on a unit magnetic pole at the center. 
Now by Newton’s third law, if there is a 
unit magnetic pole at the center there will be a 
force of reaction on the wire, and this will be 
equal to 
29 RADIOLOGICAL SAFETY 
(27) gives the force on I cm. of wire, so the force 
per unit charge is: 
By this type of measurement the masses of all 
types of charged particles can be determined to a 
high accuracy. 
3.06 Electrical units 
It will be noticed that three consistent systems 
of units have been introduced, and a unit of work, 
the electron volt, belonging to no particular sys- 
tem, has been added. All of this may seem like 
an unnecessary complication. Actually it is not, 
and all attempts to simplify the electrical systems 
have been unsuccessful. The fundamental diffi- 
culty lies in the fact that electric charge and mag- 
netic poles are quite different things which require 
separate definitions and yet must be brought 
together because of the interaction between 
them. In Table IT the relations between the 
various systems are collected for convenient 
reference. Some of the electrical quantities not 
needed in the present text have been omitted. 
v HIl 
F ~n 
V 
=Hv 
The force on a charge will then be: 
F=Hev (28) 
where e must be in e.m.u. v in Eq. (28) has the 
same direction as I in Eq. (27), and consequently 
F is perpendicular to v. This is precisely the 
condition necessary for circular motion (sec. 2.03), 
and consequently a charge moving in a magnetic 
field will move in an arc of a circle, or in a com- 
plete circle if the field is strong enough. Setting 
the magnetic force equal to the required centrip- 
etal force: 
TT mv2 
Hev—— 
r 
or 
-=w- (29) 
m Hr ' 
Table II 
Quantity 
Practical 
E. S. U. 
E. M. U. 
Charge (Q) 
1 coulomb. _ 
=3X10* statcoulombs.. 
= 10-1 abcoulombs. 
Current (I) 
1 ampere... 
=3X10* statamperes.. 
= 10_1 abamperes. 
Potential (V) 
1 volt 
Resistance (R) 
1 ohm 
= 1/9X10U statohm 
= 10* abohms. 
Capacitance (C)._ 
1 farad 
=9X10» cm... 
Magnetic field (H) 
1 oersted... 
= 1/3X10* statoersted.. 
= 10 aboersteds. 
The ratio ejm is a very important property of 
charged particles. There are various methods for 
measuring all of the quantities on the right-hand 
side. When this is done for electrons, the ratio 
ejm turns out to be 1.77 X107 e. m. u. per gram. 
Since the oil drop experiment showed that the 
electronic charge is 1.6 X10-20 e. s. u.: 
Work and energy 
V (e. s. u.)XQ (e. s. u.)=ergs, 
V (e. m. u.)XQ (c. m. u.)=ergs. 
V (prac.) X Q (prac.) = joules. 
V (prac.)XQ (electrons) = electron volts = 1.6 X 10~12 ergs. 
1 6X10'20 
mass of e!ectron=m== =9X10~28 grams 
30 RADIOLOGICAL SAFETY 
Chapter 4 
ELECTROMAGNETIC WAVES 
4.01 General Properties of Waves 
It is easy to visualize the transmission of energy 
by fast moving particles which can give up their 
kinetic energy upon collision with stationary 
targets. Less obvious, but equally important is 
the transfer of eifergy by wave motions. All of 
the sun’s energy reaching the earth is transmitted 
by electromagnetic waves, all audible sounds are- 
transmitted by sound waves, and some of the 
greatest nuclear radiation hazards arise from short 
wave length electromagnetic waves. It is there- 
fore necessary to inquire into the nature of waves 
in general, and electromagnetic waves in par- 
ticular. 
The general concept of wave transmission is a 
simple one. Some type of transmitter vibrates 
and sets up strains in the surrounding medium. 
The medium, in attempting to return to its original 
unstrained state, propagates the strains which 
travel out from the source and act on some suitable 
receiver. Thus, when human vocal chords vibrate, 
a succession of pressure impulses are applied to the 
surrounding air. Pressures above and below 
normal exist and are transmitted by each small 
volume of air to the volume immediately beyond. 
The pressure variations travel out from the source, 
and when they strike an eardrum, it is set into 
vibration and a sound is heard. 
It should be noted that the medium transmitting 
the waves does not move from source to receiver. 
A disturbance of the medium does travel but the 
medium itself does not move appreciably, A 
stone thrown into a quiet pool will produce a series 
of waves which spread out in concentric circles 
from the source of the disturbance. A cork 
floating on the surface bobs up and down as the 
waves pass, but it does not move outward from the 
source as it would if there was an actual outward 
flow of water. 
The most obvious property of a wave is its 
frequency or number of vibrations per second, 
denoted by the Greek letter v. Frequency is really 
to be associated with the source of the disturbance 
since the wave is merely the transmission of the 
disturbance. The frequency of the wave is, of 
course, the same as the frequency of the source. 
It is sometimes more convenient to use the time 
of one vibration, T, also known as period, instead 
of the frequency. The two are related by the 
equation 
"=f (1) 
Since a wave is propagated, there will be a 
velocity, v, associated with the wave motion. 
The velocity is a property of the medium and not 
of the source, for once the disturbance has been 
transmitted to the medium it is independent of 
the behaviour of source. This text is concerned 
almost exclusively with electromagnetic waves 
which have a velocity in a vacuum of 3X1010 
cm. per second, denoted by c. This is one of the 
fundamental constants of nature which appears 
frequently in many unexpected places. 
If a source is vibrating steadily with a frequency 
v and the velocity of wave propagation is c, at 
the end of one second there will be v waves spread 
over a distance c in space. One wave will occupy 
a distance X, where 
*—* <2) 
The distance X, or wave length, is the shortest 
distance between consecutive similar points on 
the wave train. Thus it is the distance between 
consecutive crests or peaks, or consecutive troughs, 
figure 4-1. 
Figure 4-1.—Amplitude and wave length in a wave 
motion. 
31 RADIOLOGICAL SAFETY 
Figure 4-1 illustrates another characteristic of 
wave motion; namely amplitude, A. XY repre- 
sents the undisturbed position of the medium, 
and as shown the amplitude is the distance from 
this undisturbed position to a point of maximum 
displacement. In an electromagnetic wave there 
is no actual displacement of a medium, and the 
concept of amplitude is a little more abstract, 
but can be thought of as the maximum strain in 
the medium. As might be expected, the ampli- 
tude is closely related to the energy carried by 
the wave. 
If a source starts a wave motion in the sur- 
rounding medium, the waves will in general 
spread out uniformly in all directions. Consider 
again the case of a stone thrown into a quiet pool. 
If at some later time, an instantaneous photo- 
graph is taken of the water, a series of concentric 
rings of maximum upward displacement (crest) 
will be observed, and in between these there will 
be a series of concentric rings of maximum down- 
ward displacement (trough). Each circle drawn 
through points having the same displacement (or 
phase) is known as a wavefront. The wavefronts 
move out from the source as the wave proceeds. 
At every point the direction of propagation is 
perpendicular to the wavefront. Lines drawn 
in the direction of propagation are called rays. 
Figure 4-2 shows the situation for the water 
waves described above. U, U', U" are wave- 
fronts of maximum upward phase; D, D', D" 
are wavefronts of maximum downward phase; 
and R, R', R" are rays. 
There is sometimes a confusion in terminology 
between waves and rays. Thus it has become 
customary to speak of radio waves and X-rays. 
Actually each is a wave motion, having both wave 
fronts and rays. It should also be noted that in 
the older literature, the terms, “alpha ray” and 
“beta ray” are commonly used. These are now 
known to be high speed particles and so should 
be called, respectively, alpha particles and beta 
particles, rather than rays. 
All wave motion exhibits certain phenomena 
when it strikes a new medium. One of these is 
reflection. (See fig. 4-3.) If a bundle of rays, 
A, A', and B, Bf, with a wave front AB, strike 
a reflecting surface, the ray A' will be reflected, 
while B' still has to travel to B", before being 
reflected. The result will be a bundle of rays 
Figure 4-2.—The relation between wave fronts and rays 
Figure 4-3.—Reflection of light at a plane surface. The 
angle of incidence i is equal to the angle of reflection r. 
reflected so that the angle of reflection, r, is 
equal to the angle of incidence, i. All waves 
exhibit reflection, but all phenomena showing 
reflection are not necessarily waves. For example 
a tennis ball, neglecting other external forces, 
will bounce off a wall with an angle of reflection 
equal to the angle of incidence. 
32 RADIOLOGICAL SAFETY 
Wave motions are refracted when they enter a 
new medium having a different velocity of propa- 
gation. Figure 4-4 shows a bundle of rays 
entering a medium of slower propagation. While 
B' travels to B" in the old medium, A' travels 
the shorter distance to A" in the new medium. 
Thus the rays in the new medium will proceed 
with a new direction A', A", A'". Refraction is 
also exhibited by motions other than waves. 
Figure 4-5.—The interference of light passing through 
narrow slits. 
the wave front will enter each of the slits. Because 
of diffraction these small portions of the wave 
front will spread out in hemispherical waves after 
passing through the slits. If a point C on the 
screen is so chosen that the distance SXC is exactly 
one wavelength greater than S2C, there will be 
constructive interference and light will be seen at 
C. If, again, SXD is one half wavelength greater 
than S2D, there will be destructive interference 
and no light will be seen at D. Thus a series of 
light and dark bands will appear on the screen. 
It is evident that this experiment serves not 
only to demonstrate the wave nature of light, but 
can be used to measure the wavelength. The 
wavelength of visible light is only about 5X10-5 
cm. and consequently diffraction is small and can 
be seen only in specially designed equipment. 
The wavelength of sound, however, is about 30 
centimeters, the angles of diffraction are large, 
and sound readily travels around corners. There 
is only a small diminution in sound intensity when 
a speaker turns his back; if he has a flashlight in 
his hand, the reduction in light intensity will be 
to zero. 
The wave properties described are very general 
and hold for any type of wave motion. Waves 
may be classified in many ways, the most common 
being on the basis of the direction of the displace- 
ment. In a sound wave, the small to-and-fro mo- 
tions of the air molecules are along the direction of 
Figure 4-4.—The refraction of light into a medium of 
slower propagation. The refracted rays make a smaller 
angle with a perpendicular to the surface. 
Diffraction and interference, however, are pheno- 
mena which are unique to wave motions. If two 
waves of equal wave length, but opposite phase, 
are superimposed, crest will fall on trough; the 
combined additive effect will be a complete can- 
cellation, and the two waves are said to interfere 
destructively. If the two superimposed waves 
are in phase, crest will fall on crest, an increased 
intensity will result, and the two waves show con- 
structive interference. It is extremely difficult 
to conceive of particles showing constructive or 
destructive interference. Interference is most 
easily demonstrated through the diffraction or 
bending of waves in passing through small open- 
ings. Consider a wave front, AB, of visible light, 
striking a diaphragm with two small openings or 
slits Sl and S2 (fig. 4-5). Only a small portion of 
33 RADIOLOGICAL SAFETY 
propagation. This is called a longitudinal wave. 
If the end of a rope is given a displacement side- 
ways, a wave will travel down the rope, but the 
direction of propagation is at right angles to the 
displacement and the wave is transverse. The most 
common example of a transverse wave is visible 
light, which is one member of the family of electro- 
magnetic waves. The remainder of this chapter 
will deal exclusively with electromagnetic waves. 
4.02 Properties of Electromagnetic Waves 
In chapter 3 it was shown that moving electric 
charges produce a magnetic field, and conversely 
that a changing magnetic field produces an electric 
field. It appears, therefore, that the two types of 
fields are closely linked, and that if one exists the 
other will also be present. In a radio antenna, 
electric charges are accelerated back and forth, 
along the wire. This produces a changing electric 
field in the vicinity of the antenna, which in turn 
produces a magnetic field, and so an electromag- 
netic wave is propagated outward from the an- 
tenna. The identification of similar waves with 
visible light was first made by Maxwell. The pre- 
dictions made by Maxwell in this connection have 
been verified by many experiments. 
An electromagnetic wave consists of an oscil- 
lating electric field and an oscillating magnetic 
field, both at right angles to the direction of 
propagation. Each component vibrates with the 
same frequency, and in free space the two com- 
ponents are in phase (fig. 4-6). 
The frequency of the wave depends upon the 
source emitting the energy, and an enormous 
range of frequencies is now known. This fact 
will be discussed more fully below. It is found, 
however, that the velocity of propagation in free 
space is independent of the frequency. For all 
but the most exact calculations 3X1010 cm. per 
second is a sufficiently accurate value. It is 
perhaps not surprising that a constant velocity is 
observed. The velocity of a wave motion depends 
on the properties of the medium and the nature of 
the wave being produced. All electromagnetic 
radiation is alike in that it consists of an oscillat- 
ing electric field and an oscillating magnetic field. 
The same type of strain therefore appears in the 
medium at every frequency, and a constant 
velocity might be expected. 
Figure 4-6.—The electromagnetic wave in free space. 
The electric and magnetic vibrations are at right angles 
to each other and to the direction of propagation. 
The term free space has been used several times 
without definition: it is understood to mean space 
devoid of all demonstrable matter; i. e., a perfect 
vacuum. A sound wave, consisting of variations 
in air pressure, cannot be transmitted by a 
vacuum; but an electromagnetic wave is propa- 
gated without loss in the highest attainable 
vacuum. It is difficult to conceive of a wave 
being propagated without a propagating medium. 
What then is the medium which transmits electro- 
magnetic radiation? 
This problem was a serious difficulty in physics 
for many years. The medium was known as the 
luminiferous aether, or simply ether. Some of its 
properties could be predicted but it was never 
isolated or identified. Interest in the ether 
gradually waned and at present the experimental 
fact is accepted: electromagnetic waves can travel 
through free space and at a velocity independent 
of frequency. 
When electromagnetic waves travel in a rec- 
ognized medium they do not necessarily proceed 
with the velocity c; actually the velocity varies 
with frequency. The variation of velocity with 
frequency is known as dispersion, and this is 
responsible for the dispersing or separating of a 
beam of white light into its component frequencies 
by a glass prism. Blue light travels slower than 
red light in glass, and as a result blue light suffers 
more refraction or bending in passing through the 
prism. It is important to remember that there 
is no known way of preventing the propagation 
of electromagnetic waves by removing the prop- 
agating medium, as can be done for sound waves. 
34 RADIOLOGICAL SAFETY 
4.03 The Electromagnetic Spectrum 
The known electromagnetic radiations may be 
arranged on the basis of frequency or wavelength 
into the electromagnetic spectrum. (Table I 
and fig. 4-7.) The spectrum is divided into 
several regions but it must be realized that the 
divisions are arbitrary and not at all rigid. In 
the main, the divisions are based on the methods 
used to produce the radiation, and it is quite 
possible to produce a given frequency by two 
or more methods. It is, for example, possible 
to produce by gaseous discharge ultraviolet 
radiation having a wavelength of 10-6 cm. This 
Table I.—The electromagnetic spectrum 
Type of radiation 
Frequency range (per second) 
Wave length range (cm.) 
Electric waves_ 
0-10* 
oo-3X106 
Radio waves. _ 
104-10” 
3X106-0. 3 
Infrared __ 
10U-4X 1014 
0. 3-7. 6X10-5 
Visible 
4X1014-7. 5X1014 
7. 6X10-5-4X10-5 
Ultra violet 
7. 5X 1014-3X 1018 
4X10-5-10-6 
X-rays 
3X 1016-3X 1020 
IQ-6-10-10 
Gamma rays.. 
3X 1019-3X 1022 
10-9-10-12 
Cosmic rays 
3X 1021- 
IQ-9- 
Figure 4-7.—The electromagnetic spectrum. Note the small portion occupied by the visible region 
even on a logarithmic plot. 
35 RADIOLOGICAL SAFETY 
same wavelength can be produced by X-ray meth- 
ods. The properties of the radiations are identical 
and are independent of the method of production; 
only the frequency is important in determining 
the properties. 
The electromagnetic spectrum is interesting and 
warrants a thorough study. A casual inspection 
reveals the enormous range of frequencies involved. 
Electric power lines radiate electromagnetic waves 
at the generator frequency, which is usually 60 
cycles per second, but it would not be difficult 
to generate frequencies much lower than this. 
Thus, for all practical purposes, the lower fre- 
quency limit is zero. All frequencies are known, 
through the normal and ultra high frequency 
radio waves and the infra-red. It is somewhat 
startling to see how small a fraction is taken up by 
visible light. All sense of color and indeed all 
vision, is conveyed in a frequency range somewhat 
less than one octave. It is also interesting to note 
that the limits of the visible range as determined 
by the human eye are more sharply defined than 
any of the others. 
The range of the electromagnetic spectrum is so 
great that several units are used in measuring 
wavelength. Wavelengths in the radio frequency 
region are commonly measured in meters. Visible 
light wavelengths are usually expressed in centi- 
meters or in Angstroms, A (1 Angstrom= 10~8 
cm.) or in microns, /x (1m==10-4 cm.). The 
Angstrom is also used almost exclusively in 
measuring wavelengths in the X-ray and gamma 
ray region. 
By the time visible light is reached, the fre- 
quency has already become nearly 1016 cycles per 
second but this is still low compared to the fre- 
quency of 1020 cycles per second associated with 
gamma or cosmic rays. It might seem that with 
improved techniques still higher frequencies might 
be observed. This may be true but it is probable 
that the upper limit is being approached, and it 
is certain that the upper limit does not extend to 
infinity. 
Although the fundamental nature of all parts 
of the electromagnetic spectrum is identical, 
the methods of producing the various wavelenths 
vary tremendously. All wavelengths from infin- 
ity down to the infra-red can be produced by 
purely electrical means. It is possible to make 
oscillating circuits of a natural frequency so high 
that there is actually an overlap with the infra- 
red. 
In most of the infra-red region, however, the 
frequencies are too high to be produced by oscil- 
lating electric circuits, and most infra-red radia- 
tion is obtained as radiation from hot bodies. 
Because of this, infra-red radiations are commonly 
known as heat waves or rays. This terminology 
is unsatisfactory since all radiation is eventually 
absorbed as heat. Infra-red waves are emitted 
from the rotations and the vibrations of the 
atoms making up the hot body. 
As the temperature of the hot body is raised, 
visible light is emitted. Some of this radiation is 
produced by the same mechanism that emits infra- 
red. Some visible light is also produced by elec- 
tron movements which will be described in detail 
in chapter 5. 
When an electric arc is struck between metal 
electrodes, or when an electric current passes 
through a gas, visible, and ultraviolet frequencies 
are produced. The ultraviolet frequencies are 
due entirely to the electronic excitation resulting 
from the current. By increasing the energy of 
excitation, high ultraviolet frequencies can be pro- 
duced, and some will overlap the upper limit of 
the X-ray region. 
X-rays are produced by bombarding a heavy 
metal target with high speed electrons. The X-rays 
are produced by the rapid deceleration of the 
bombarding electron, or by the excitation of high 
energy electrons in the target. As the energy of 
the bombarding electrons is increased, the radia- 
tion frequencies increase and overlap into the 
gamma ray region. Gamma rays, which have an 
even shorter wavelength, are emitted from the 
nuclei of atoms. Much more will be said about 
gamma rays in chapter 6. Electromagnetic 
waves form only one component of cosmic radia- 
tion, and a discussion of this will be postponed to 
Ch. 7, sec. 7-15. 
4.04 The Quantum Nature of Radiation 
All of the components of the electromagnetic 
spectrum exhibit wave properties and can be re- 
fracted, diffracted, and show interference. These 
are necessary conditions for wave motions and 
it might seem that the whole story had been told. 
There are, however, other phenomena which can 
scarcely be explained on a wave basis. Examples 
36 RADIOLOGICAL SAFETY 
of such phenomena are the radiation from hot 
bodies (black body radiation), the production of 
X-rays, and the photoelectric effect (Ch. 5, sec. 
5.10). The photoelectric effect will serve as an 
example of the inadequacy of the wave concept 
of radiant energy. 
In the photoelectric effect a beam of light 
(infra-red, visible, ultra violet, etc.) falls on a 
metal surface, figure 4-8. The light may eject 
earlier work by Planck, that radiation is not a 
smooth, continuous flow of energy as pictured by 
the wave theory, but is rather a series of discon- 
tinuous packages of energy. The energy in each 
package, which is known as a photon or quantum, 
increases with the frequency of the light, being 
given by 
E=hv (3) 
where 27 erg-sec is Planck’s constant 
and E the energy of the quantum in ergs. 
A photon is apparently indivisible, and either 
exists or disappears completely upon giving up 
its energy in some process such as the photoelectric 
effect. The energy relations in the photoelectric 
effect will be given by the Einstein Equation, 
hp=<f>-\~— mv2 (4) 
The left-hand side of this equation is the energy 
available in the incoming photon. <£ is the energy 
required to remove an electron from the surface 
of the metal, known as the work function. If the 
photon has an energy greater than <t>, the electron 
will be ejected with a kinetic energy given by the 
last term in Eq. (4). 
This immediately explains the photoelectric 
behaviour of light of different frequency. Red 
light has a low frequency and the associated 
quantum energy, by Eq. (3), may be less than <j>, 
and hence no amount will liberate an electron. 
Blue light has a higher frequency, and the associ- 
ated quantum energy may be larger than <f> and 
hence sufficient to produce a photoelectric current. 
A series of experiments by Millikan completely 
verified the predictions of Eq. (4) and there can 
be no doubt that here radiation is behaving likeli 
discontinuous series of energy packages. 
Furthermore, a reverse application of Eq. (4) 
quantitatively explains the production of X-rays, 
Here the incident electron has a kinetic energy 
\mv2 and can produce no radiation of frequency 
greater than that given by 
(5) 
In this case the work function 0 is so small com- 
pared to 2 that it is neglected. This relation 
has also been completely verified by experiment. 
A little reflection on Eqs. (4) and (5) will show 
that a sort of double-talk is involved. Radiation 
Figure 4^8.—The photoelectric effect. Electrons re- 
moved from the cathode surface by the incident light 
are attracted to the anode and constitute a current in 
the circuit. 
electrons from the metal, and if this is in an 
evacuated bulb together with a positively charged 
collecting electrode, the electrons will be pulled 
over and a current will flow. 
According to wave theory, the vibrations of the 
incoming electromagnetic waves set the electrons 
into \ibration with increasing amplitude until 
they had acquired sufficient energy to break loose 
from the metal. It would seem then that a weak 
light would require more time to liberate an 
electron than a strong light, and there might be a 
light wave so weak that the electrons could never 
attain the energy necessary for escape. Such a 
prediction is at complete variance with the facts. 
It is observed that the color or frequency of the 
light plays a very important role in producing 
photoelectrons. Thus the most intense beam of 
red light (low frequency) will not yield a single 
photoelectron from most metals, while the feeblest 
blue light (high frequency) will instantly produce 
a few. This suggested to Einstein, following some 
37 RADIOLOGICAL SAFETY 
is pictured as discontinuous and composed of 
photons of discrete energy, while at the same time 
the concept of frequency and wavelength is re- 
tained. This may be disconcerting and many 
people have spent much time and effort in trying 
to decide whether radiation is a quantum or a wave 
phenomenon. Actually it is necessary to assume 
a dual nature. Radiation may consist of some as 
yet unknown phenomenon which has some wave 
and some quantum characteristics. In its pro- 
pagation through space and its transmission 
through non-absorbing media it behaves like a 
wave motion. In interactions with matter where 
energy exchanges are involved, the quantum nature 
predominates. The quantum behaviour becomes 
more pronounced at high frequencies and since 
radiological safety is primarily concerned with 
X-rays and gamma rays it is important to under- 
stand the quantum nature of radiation. 
The first application of quantum ideas was made 
by Planck in 1901, to the problem of the radiation 
emitted by hot bodies. Physicists had developed 
the idealized concept of a black body, which is 
capable of emitting and absorbing radiations of 
all frequencies. This ideal is approached by an 
enclosed furnace with a small opening through 
which the interior radiations may be observed. 
Many measurements had been made of the 
amounts of energy radiated at various frequencies. 
Figure 4-9 shows the experimental results. At 
each temperature there is a frequency at which 
maximum energy is radiated. The frequency of 
this maximum increases with temperature accord- 
ing to Wien’s displacement law which is usually 
written in terms of wavelength rather than fre- 
quency: 
\mT— Constant (6) 
XM=wavelength of maximum energy XM 
emission. 
T= absolute temperature. 
Constant=0.29 cm. degrees. 
This is a very useful relation since by its use the 
temperature of inaccesible hot bodies may be 
determined. For example the maximum energy 
of the sun is emitted at a wave length of about 
4.5X10-5 cm. (green light) which corresponds to 
a temperature of about 6,000° C. 
In the same way measurements of the energy 
radiated from the detonation of an atomic bomb 
Figure 4-9.—The observed energy distribution of black 
body radiation as a function of temperature. 
can be used to determine the temperature. If the 
maximum temperature reached in an atomic 
bomb explosion is 1,000,000° C., then XM will lie 
in the X-ray region. Therefore X-ray wave 
lengths will be emitted simply as temperature 
radiation, as distinct from the gamma and X-rays 
from nuclear disintegrations. 
Many attempts had been made to explain the 
shape of the observed emission curves assuming 
38 RADIOLOGICAL SAFETY 
radiation to be a continuous wave motion, but all 
of these efforts yielded curves that were too high 
at the high frequencies. When Planck intro- 
duced the idea of radiation quanta, the difficulties 
disappeared, and the predicted curves agreed in 
all details with those experimentally observed. 
This is another example of the dual nature of 
radiation, and it should be noted that the original 
theories failed at the high frequencies where the 
quantum characteristics become more pronounced. 
Before leaving the discussion of black body 
radiation it should be pointed out that the curves 
of Figure 4-9 represent the total energy radiated 
at each wave-length. The size of each emitted 
quantum increases steadily as the wave-length 
decreases in accordance with (Eq. 3), but the 
energy emitted is of course equal to the product of 
the number of quanta and the energy of a single 
quantum. At high frequencies the number of 
emitted photons is so low that the emission curves 
decrease as shown. 
It is customary to measure radiant energy in 
ergs, but with the development of nuclear physics 
other units have been introduced. Thus, it is 
common to speak of a “50 kilovolt X-ray” or a 
“1 Mev gamma ray.” This is really a specifi- 
cation of the energy of a single photon and not 
of the total energy of all photons in a beam. 
Because of the enormous frequency range of the 
electromagnetic spectrum it is necessary to use 
a variety of instruments and methods of energy 
measurement. The methods used for the determ- 
ination of X-rays and gamma rays will be dis- 
cussed in Chapter 9. It might be pointed out 
in passing that the human eye is a remarkable 
instrument over its limited frequency range. It is 
most sensitive to green light having a wave- 
length of about 5.5X10~6 cm. and at this wave- 
length a sensation is obtained from about 10 
photons or 3.6X10-11 ergs. The eye is able} 
moreover, to function satisfactorily at intensities 
1010 times greater. This is an operating range not 
approached by any single man-made radiation 
measuring instrument. Even this tremendous 
range is unable to cope with the brilliance of 
the earliest phase of an atomic bomb detonation 
in air. At 10 miles this may have a brilliance 30 
times as great as the sun and absorbing goggles 
must be worn to prevent eye injury. 
39 RADIOLOGICAL SAFETY 
Chapter 5 
ATOMIC STRUCTURE 
5.01 The Electrical Nature of Matter 
It has already been demonstrated that electrons 
can be liberated from matter in a number of ways, 
e.g., by thermionic emission, by the photoelectric 
effect, and by other means. Regardless of the 
techniques employed to produce them, these 
electrons have the same properties. Exacting 
experiments have shown that these minute parti- 
cles are identical. These negatively charged 
particles are therefore regarded as elementary con- 
stituents of matter. They are furthermore known 
to be fundamental particles, for no smaller unit of 
negative electricity has ever been observed. 
The investigation of the conductivity of gases 
at low pressures has shown that in addition to 
electrons there are also positively charged particles 
which are much heavier than electrons. Their 
existence can be verified by using the equipment 
shown in figure 5-1. In the gas discharge tube, 
or electric field to the tube shows that the positive 
rays may be deflected from their otherwise straight 
trajectory. 
Since the gas between the electrodes m figure 
5-1 was non-conducting prior to the application 
of the high voltage to the terminals of the tube, 
it is clear that the gas was electrically neutral. 
When the high voltage source is connected to the 
terminals, the gas is made conductive and is said 
to be ionized. It is reasonable to assume that 
neutral particles of the gas are subject to separa- 
tion into positively and negatively charged com- 
ponents which are then accelerated in opposite 
directions by the electric field, thus forming the 
canal rays and cathode rays. 
In the case of hydrogen gas, which has the 
lowest molecular weight of any element, it has 
been found that the hydrogen molecule (//2) 
breaks up into two positively charged particles, 
(//+), which are called protons. The magnetic 
and electric deflection of the protons gives a 
measurement of their mass. Actually the ratio 
of charge to mass is measured, but this is equiva- 
lent to a mass measurement since the charge can 
be measured by other means. The proton has a 
mass 1.661 X10-24 gm. and a charge of 160 
X10-19 coulombs. Its charge is opposite in sign 
to that of the electron but is identical in magni- 
tude. The electron, with a mass of 8.98X10-28 
gm., weighs only 1/1840th as much as the proton. 
Although many exhaustive experiments have 
been carried out with hydrogen, no more than 
one electron is ever found associated with a single 
proton. This evidence proves that the hydrogen 
atom contains only one electron. As a result of this 
discussion, it is clear that the breaking up of the 
simplest atom into its components results in two 
electrically charged particles (//+ ion, or proton, 
and e~, or electron). This is the basis for the fol- 
lowing discussion of the atomic structure of 
hydrogen. 
5.02 The Hydrogen Atom and Other Elements 
It is now known that this simplest of all atoms 
consists of a central heavy core (the proton) and a 
single outer electron. Lord Rutherford first 
Figure 5-1.— Canal rays passing through a hole in the 
cathode of a cathode ray tube. 
the electrons move toward the anode while the 
positively charged particles move toward the 
negatively charged cathode. If, as indicated, 
there is a small hole or “canal” in the cathode, 
these positive rays will fly through the aperture 
and impinge upon the end of the glass tube where 
they will cause fluorescence. By darkening the 
room, the path of the positive rays, sometimes 
called canal rays, is faintly visible in the space 
behind the cathode as a glow characteristic of the 
gas in the tube. Application of either a magnetic 
41 RADIOLOGICAL SAFETY 
showed that the atom consists of a compact core 
or nucleus which is small in diameter as compared 
with the whole atom. Actually the hydrogen 
atom has a diameter of about 10~8 cms. (1 Ang- 
strom unit), while the nucleus (proton) is only 
about 3 X10"13 cms. in diameter. Thus the proton 
and electron are separated by relatively vast 
distances. The clue to the mystery of this empty 
atom occupied only by a minute nucleus and a 
still smaller electron is found in the nature of the 
electric field which exists inside the atom. A dis- 
cussion of this subject is given in section 5.06. 
Until relatively recently it was thought that 
helium was the next heaviest atom after hydrogen. 
However, Dr. Urey and his collaborators dis- 
covered a rare form of hydrogen which was twice 
as heavy as ordinary hydrogen. Since it was dis- 
covered in the form of water, the discoverers 
called this heavy water. Ordinary water has the 
chemical formula H20, whereas heavy water is 
often written as D20, indicating that the heavy 
water molecule is made up of one oxygen atom and 
two heavy hydrogen atoms, the symbol D stand- 
ing for deuterium which is the technical name given 
to heavy hydrogen. The deuterium atom is 
chemically identical with the hydrogen atom. 
Since the H-atom is composed of one proton 
and one electron, it might be logical to assume 
that the' D-atom, which is twice as heavy, would 
be made up of two protons and two electrons. 
However, it is known experimentally that the 
deuterium atom contains only 1 electron and 1 
proton. Furthermore, the exact weight of the 
deuterium atom is not the same as that which 
would result if two protons were in its nucleus. 
This dilemma perplexed the physicist for a long 
time until the discovery of a neutral particle of 
almost the same mass as the proton. When this 
new particle—the neutron—was discovered it was 
the key to the riddle of the structure of deuterium, 
as well as to that of all other elements. 
Prior to the discovery of the neutron, physicists 
conceived of the deuterium nucleus as being made 
up of 2 protons and 1 electron; the electron inside 
the nucleus was postulated in order to leave a 
single positive charge on the nucleus, for the 
negative electron would neutralize the charge of 
one of the protons. However, conclusive evidence 
showed that it is not possible for electrons to exist 
within the nucleus. In spite of this fact, some 
recent hooks persist in using the term “nuclear 
electrons.” 
With the discovery of the neutron, the deuterium 
atom was assumed to consist of a nucleus of 1 
neutron and 1 proton. This assumption has 
been justified by the corrections of the results 
predicted for many nuclear experiments. These 
two elementary particles can be used to build up 
the nuclei of all heavier elements, such as helium, 
lithium, beryllium, iron, lead, and uranium. 
5.03 Atomic Nomenclature 
Before proceeding to a discussion of the heavier 
elements, it will greatly simplify the discussion to 
introduce a consistent set of definitions and sym- 
bols. The following symbols will be used in this 
manual: 
Z=atomic number. The number of protons 
in the nucleus of an atom. This atom carries 
Z elementary positive charges in the nucleus 
and Z electrons outside the nucleus. 
A = mass number. The sum of all neutrons 
and protons in the nucleus of an atom. 
N— neutron number. The number of neutrons 
contained in the nucleus of an atom. 
n=the symbol for the neutron. 
p = the symbol for the proton. 
<? = the symbol for the electron. 
Nucleon=& word coined to refer to either 
nuclear constituent, the neutron or the 
proton. 
Isotopes — two nuclei having the same number 
of protons but different numbers of neu- 
trons. 
In writing the formula for any isotope, the 
following form will be followed: 
(Symbol of element)A or of element)'4 
Thus for normal hydrogen; the form would be jH1, 
for heavy hydrogen the form would be !H2 or jD2, 
for normal helium the form would be 2He 4, for 
uranium 235 the form would be 92U235. Strictly 
speaking it is not necessary to include the sub- 
script since its value is fixed when the name of 
the element is given. It will be used frequently 
since it is convenient for balancing nuclear trans- 
formation equations. 
42 RADIOLOGICAL SAFETY 
PERIODIC ARRANGEMENT OF THE ELEMENTS 
Seri**« 
IVrio«l 
ZERO 
GROUP 
GROUP I 
RiO 
GROUP II 
RO 
GROUP III 
RiOj 
GROUP IV 
RH« ROj 
GROUP V 
mil RjO. 
GROUP VI 
RHj ROj 
GROUP VII 
RH RjOr 
GROUP VIII 
0 
1 
HYDROGEN 
11 1.0078 
No. 1 
2 
I 
HELIUM 
Hr. =4.002 
No. 2 
LITHIUM 
Li -6.940 
No. 3 
BERYLLIUM 
He. -9.02 
No. 4 
BORON 
B -10.82 
No. 5 
CARBON 
C -12.00 
No. 6 
NITROGEN 
N - 14.008 
No. 7 
OXYGEN 
0-16.000 
No. 8 
FLUORINE 
F-19.00 
No. 9 
:t 
2 
NEON 
Nc. -20.183 
No. 10 
SODIUM 
Na -22.997 
No. 11 
MAGNESIUM 
Mg. -24.32 
No. 12 
ALUMINUM 
At -26.97 
No. 13 
SILICON 
Si -28.06 
No. 14 
PHOSPHORUS 
P -81.02 
No. 15 
SULFUR 
S -32.06 
No. 16 
CHLORINE 
Cl -35.457 
No. 17 
4 
ARGON 
A. -39,944 
No. 18 
POTASSIUM 
K 39.10 
No. 19 
CALCIUM 
Ca. -40.08 
No. 20 
SCANDIUM 
Sc. - 45.20 
No. 21 
TITANIUM 
Ti -47.90 
No. 22 
VANADIUM 
V -50.95 
No. 23 
CHROMIUM 
Cr -52.01 
No. 24 
MANGANESE 
Mn -54.93 
No. 25 
IRON 
Fe - 55.84 
No. 26 
COBALT 
Co --58.94 
No. 27 
NICKEL 
Ni =58.69 
No. 28 
■> 
UOPl’ER 
Uu. 63.57 
No. 29 
ZINC 
Zn. -65.38 
No. 80 
GALLIUM 
Ga -69.72 
No. 81 
GERMANIUM 
Ge. -7260 
No. 82 
ARSENIC 
Aa -74.93 
No. 83 
SELENIUM 
Sr -79.2 
No. 84 
BROMINE 
Br -79.916 
No. 35 
6 
KRYPTON 
Kr. -82.9 
No. 36 
RUBIDIUM 
Rb.- 85.44 
No. 37 
STRONTIUM 
Sr. -87.63 
No. 38 
YTTRIUM 
Y -88.92 
No. 89 
ZIRCONIUM 
Zr. -91.22 
No. 40 
COLUMBIUM 
Cb -93.3 
No. 41 
MOLYBDENUM 
Mo. -98.0 
No. 42 
MASURIUM 
Ma -7 
No. 43 
RUTHENIUM 
Ru - 101.7 
No. 44 
RHODIUM 
Rh - 102.91 
No. 4 5 
palladium 
P d «106 T 
No. 46 
7 
SILVER 
Ag. - 107.880 
No. 47 
CADMIUM 
C'd -112.41 
No. 48 
INDIUM 
In -114.8 
No. 49 
TIN 
Sn. -118.70 
No. 50 
ANTIMONY 
Sb- 121.76 
No. 61 
TELLURIUM 
Te -127.5 
No. 52 
IODINE 
I -126.932 
No. 53 
H 
XENON 
Xe. - 130.2 
No. 54 
CAESIUM 
Ca - 132.81 
No. 55 
BARIUM 
Ba. -137.36 
No. 56 
LANTHANUM 
La -188.90 
No. 57 
CERIUM 
Ce -140.13 
No. 58 
9 
10 
HAFNIUM 
HI -178.6 
No. 72 
TANTALUM 
Ta. - 181.4 
No. 73 
TUNGSTEN 
W -184.0 
No. 74 
RHENIUM 
He. -186.31 
No. 75 
OSMIUM 
Oa. 190.8 
No. 76 
IRIDIUM 
Ir. -193.1 
No. 77 
PI-AT1NUM 
Pt. - 195.23 
No. 78 
1 1 
GOLI > 
Au -197.2 
No. 79 
MERCURY 
Hg-200.61 
No. 80 
THALLIUM 
T1 -204.39 
No. 81 
LEAD 
Pb -207.22 
No. 82 
BISMUTH 
Hi. -209.00 
No. 83 
POIX1NIUM 
Po. -209.99 
No. 84 
ALABAMINE 
Am. - 7 
No. 85 
« 
7 
RADON 
Rn -222 
No. 86 
VIRGINIUM 
Va 7 
No. 87 
RADIUM 
Ra -225.97 
No. 88 
ACTINIUM 
Ac -227.02 
No. 89 
THORIUM 
Th -232.12 
No. 90 
PROTOAC- 
TINIUM 
Pa, -231.03 
No. 91 
URANIUM 
U -238.14 
No. 92 
No. 93 
ELEMENTS NOT CLASSIFIED IN THE TABLE ABOVE 
praseodymium neodymium illinium samarium europium gadolinium terbium 
Pr.-140.92 Nd. -144.27 11.-146.(7) Sm. -150.43 Eu.-152.0 Gd.-157.8 Tb.-195.2 
No. 59 No. 60 No. 61 No. 62 No. 63 No. 64 No. 65 
DYSPROSIUM HOLM1UM ERBIUM THULIUM YTTERBIUM LUTECIUM 
Dy.-162.46 Ho.-168.5 Er.-167.64 Tm.-169.4 Yb.-173.5 Lu.-175.0 
No. 66 No. 67 No. 66 No. 69 No. 70 No. 71 
NEW ELEMENTS 
NOTE: The following ai ament a have been 
diacovered in ooniunctlon with the work 
of the Manhattan Project. 
NEPTUNIUM. Np. At. No. 93, At Wt. 23» 
PLUTONIUM, Pu. At. No. 94, At. Wt 289 
AMERICIUM. Am, At. No. 96 
CURIUM. Cm. At. No. 96 
Figure 5-2.—Periodic table of the elements. 
43 RADIOLOGICAL SAFETY 
5.04 The Periodic System 
radiation is emitted, this radiation can be dispersed 
by either a diffraction grating or a prism into a 
series of lines as shown in figure 5-3. The sum of 
all the series lines emitted by hydrogen is known 
as the atomic or line spectrum of hydrogen. It 
was found experimentally that the Balmer series 
of lines (fig. 5-3 (a)) has wavelengths (X) which 
can be empirically expressed by the relation 
Among the many elements, there are certain 
ones which bear remarkable relationships to one 
another in their physical and chemical character- 
istics. For example, this relationship is particu- 
larly striking in the case of the alkaline earth 
metals, Be, Mg, Ca, Sr, Ba, and Ra, all of which 
have similar chemistry. All have the same chem- 
ical valence, are metallic, have low density, exhibit 
similar atomic spectra, and have similar physical 
characteristics. 
Mendeleeff arranged the elements in a series 
of groups as shown in figure 5-2. Such an ar- 
rangement is known as a Periodic Table of Ele- 
ments. Elements which are m the vertical groups 
are all chemically related to one another. In the 
table, the number following the chemical symbol 
for the element gives the atomic weight of the 
element and the lowest number in each box indi- 
cates the atomic number of the element. 
Examination of any group in the Periodic Table 
reveals that the differences between the atomic 
numbers of the members of a group follow a pat- 
tern—8, 8, 18, 18, 32. The electrons in an atom 
determine its chemical characteristics, so this regu- 
larity suggests that there is a building-up pattern 
followed by the electrons in the elements. The 
building-up principle requires that the electrons 
group themselves in definite shells about the 
nucleus. Each shell is characterized by having 
an upper limit to the number of electrons which 
it can hold. 
All matter can be thought of as composed of 
the three elementary constituents: neutrons, pro- 
tons, and electrons. Differences in the number of 
protons in the nucleus result in different chemical 
elements, for there must be an equal number of 
electrons outside the nucleus to make the atom 
electrically neutral. It is now necessary to look 
at the problems of atomic structure more quan- 
titatively and in particular to investigate the 
arrangement of electrons. 
5.05 Atomic Spectra and Energy Levels 
Every element emits a characteristic optical 
spectrum which can, in fact, be used as an analyt- 
ical means of identifying the element. If, for 
example, some hydrogen gas is placed in a dis- 
charge tube and electrically excited so that visible 
1/X=i?^—where M=3, 4, 5 ....«> (1) 
The quantity 1/X is usually written as r and is 
called the wave number. It is simply the number 
of wave lengths in a centimeter. R is a constant 
equal to 109,677 cm-1 and is known as the 
Rydberg constant. 
In addition to the Balmer series of hydrogen 
lines which is located in the visible region of the 
spectrum, there is found another series in the 
ultra violet region; this is called the Lyman 
series. It can also be represented by an empirical 
expression as follows: 
r=R (j2— where M=2, 3, 4, . . . . (2) 
Empirically, the wave lengths and wave num- 
bers corresponding to lines in the Balmer and 
Lyman series are known quite accurately and are 
listed in table I. 
Table I.—Balmer and Lyman series 
[Wave lengths and wave numbers] 
Balmer 
series 
Lyman series 
X 
T 
X 
T 
6562.2 A (Ha) 
15,233 cm-i 
1215 A 
82,258 cur 
4861.3 
20,264 
1026 
97,482 
4340.5 
23,032 
972 
102,823 
4101.7 
24,373 
950 
105,290 
SERIES LIMIT 
3646.0 A 
27,419 cm-1 
911 A 
109,677 cm- 
By substituting M— 3 in Eq. (1), the wave 
number of Ha is found to be 15,233 in agreement 
with the value listed in column 2 of table I. 
Instead of using the empirical equations, a new 
type of scheme can be employed to illustrate a 
fundamental principle of atomic spectra. The 
wave numbers of the series limits given in table I 
have been plotted in figure 5-4, putting the 
Lyman series limit value of 109,677 cm-1 as the 
44 RADIOLOGICAL SAFETY 
the emission or absorption of a spectrum line of a 
characteristic wave number determined by the 
difference between the energy levels. 
Not all atoms emit a spectrum as simple as that 
of hydrogen, nor indeed is the hydrogen spec- 
trum as simple as has been described. Figure 
5-3 (b) shows a sodium absorption spectrum, 
each line of which is really a doublet instead of a 
single line. In general, the heavier elements emit 
correspondingly more complex spectra. Iron, for 
example, emits over 10,000 separate lines, all of 
which have been carefully measured and cata- 
logued. 
5.06 The Bohr Atom 
The concept of the hydrogen atom as a proton 
and electron has already been introduced but no 
explanation was advanced to account for the 
stability of this system, nor for the emission of 
sharp and discrete spectrum lines from it. Be- 
tween the proton and the electron there is an 
attractive force given by the equation 
Figure 5-3a.—Emission spectrum of the hydrogen atom 
in the visible and near-ultraviolet region. 
Figure 5-3b.—Absorption spectrum of the sodium atom. 
From Atomic Spectra and Atomic Structure by Oerhardt Herzberg, second 
revised edition, Dover Publications, Inc. 
f=Mi 
r2 
(3) 
lowest line and the Balmer series limit as the 
next line. Similarly the series limits for successive 
series in the hydrogen spectrum (not previously 
mentioned) are located on succeeding lines in order 
of decreasing magnitude upward from the lowest 
level. It is seen that taking the difference between 
wave numbers corresponding to the level M'= 1 
and M' =2 yields 109,677—27,419 = 82,258 the 
wave number of the first line in the Lyman 
series. It should be noted that the value of M' 
corresponds to the constants in the first term of 
Eqs. (1) and (2). This process has been dia- 
gramatically indicated in the drawing by vertical 
lines which are called transitions. In words, 
this principle can be stated as follows: There 
always exist for the spectrum of any atom, a 
series of wave numbers (term values), differences 
between which yield the wave number of the 
observed spectrum lines. This is known as the 
Ritz Combination Law, and tables used in connec- 
tion with it (such as table I) are called term 
tables. This principle signifies that every atom 
has definite energy levels. Transitions within the 
atom from one energy level to another result in 
where in this case ql=g2=e. If the electron 
were at rest, it would be pulled into the proton 
by the Coulomb field. It must therefore be in a 
continuous state of motion. From classical elec- 
trodynamics an electron whirling about a proton 
would be accelerated. Since an accelerated elec- 
tric charge should radiate energy, the electron 
would quickly spiral into the nucleus after pro- 
ducing a continuum of photons. Thus in the 
classical picture there was no explanation of the 
stability of the hydrogen atom or of the emission 
of discrete line spectra. 
The Danish scientist, Niels Bohr first proposed 
a solution to this difficult problem by applying 
Planck’s quantum hypothesis to an atomic 
system. As pointed out in section 4.04, Planck 
assumed that electromagnetic energy is emitted 
in quanta of energy E given by the relation 
E=hv (4) 
where h, Planck’s constant, =6.65X10-27 erg-sec. 
and v is the frequency of the emitted electromag- 
netic radiation. Bohr saw the relation between 
45 radiological safety 
Figure 5-4.—Energy level diagram of hydrogen. 
46 RADIOLOGICAL SAFETY 
the Kitz Combination Principle and Planck’s 
equation and proposed the relation 
hv=E2—Ei (5) 
where: 
v is the frequency of the emitted electro- 
magnetic radiation. 
Eo is the initial energy of the atom (prior 
to emission). 
Ei is the final energy of the atom (after 
emission). 
Recalling that \v=c, where c is the velocity of 
light, this equation can be written: 
r=l/X=E2/hc—Ei/hc (6) 
From Eq. (6), it is clear that the values of a 
term in an atomic term table is equal to the 
energy of a state of an atom multiplied by the 
constant factor 1/hc. Analytically the energy 
of an atomic state Ex is given by the relation 
Ei=hc/\ (7) 
This is equivalent to stating that there exists, for 
every atom, discrete stationary states, each having 
a characteristic energy value. In addition, radia- 
tion is emitted from an atom whenever it jumps 
from one stationary state to another; this transi- 
tion results in a radiation of wave number given 
by Eq. (6). It should be emphasized that while 
the atom is in a stationary state it does not 
radiate. This is contrary to classical theory. 
According to the Bohr picture, the simple hydro- 
gen atom should appear as in Figure 5-5. The 
electron revolves about the nucleus, which is as- 
sumed to be stationary, in discrete orbits corre- 
sponding to stationary states of the atom. Bohr 
further assumes that these stationary states are 
such that the momentum of the electron, mv, is 
restricted (quantized) to certain integral multiple 
values of h/2-n-T. 
The first condition is fulfilled if the force required 
to accelerate the electron in its orbit (mv2jr) is 
balanced by the electrostatic (Coulomb) force be- 
tween the two particles. This yields 
Figure 5-5.—Diagram of first orbit in the hydrogen atom. 
The second condition may be stated as: 
nh 
mvr—Tz- 
Ztt 
where: 
n= 1, 2, 3, 4, ... oo (9) 
Using these relations the total energy of an electron 
in one of its orbits can be calculated. This calcu- 
lation is sketched as follows: The total energy of 
the electron equals its kinetic plus its potential 
energy 
E—-mv2—~ (10) 
2 r ' 
Substituting from Eqs. (8) and (9) 
jr /i -I \ 
E~ nW <H) 
The fact that the energy is negative follows 
from the fact that the energy of the electron far 
removed from the atom (i. e. at infinity) is taken 
as zero. Since the force between the particles is 
attractive, work is done by the system in bringing 
the electron toward the atom, and the energy in- 
volved is negative. The energy will have a differ- 
ent value for each value of n which corresponds to 
a different electron orbit in the atom. 
(8) 
r r1 
47 RADIOLOGICAL SAFETY 
By Eq. (5), the frequency emitted by the transi- 
tion of the electron from orbit 3 to orbit 2 is 
the beam is dropped below 13.5 e.v., ionization 
ceases, but inelastic collisions between the incident 
electrons and hydrogen atoms occur and give rise 
to excitations of different series, and indeed, 
different lines in these series. Potentials necessary 
to cause emission of a characteristic line in, say, 
the Lyman series are called excitation potentials 
for those lines. 
Atomic spectra can be excited in many ways 
other than in a gaseous discharge tube. Common- 
ly used techniques are the carbon arc, the electric 
spark, and the hot flame. 
In the heavier elements, it can be shown that 
the emission of ultra-violet, visible, and infra-red 
radiation is the result of transitions which occur 
on the part of the outermost electrons. Such 
radiations are completely independent of the 
inner electrons. 
As the energy which is inelastically imparted to 
an atom increases, it is obvious from the relation 
he 
E=hv=— that the wave length of the most ener- 
A 
getic radiation which can be emitted decreases. 
Thus if E is very small, the wave lengths which can 
be excited may be in the far infra-red. Then as 
E increases, the wave length decreases, passing 
through the visible region and down into the ultra- 
violet. Through the use of special techniques, 
atomic spectral lines as short as 100 Angstroms 
can be observed. Radiations much shorter than 
100 A are usually known as X-rays and are char- 
acteristically produced in special vacuum tubes 
with which everyone is familiar. Because the 
study of these rays yields much information about 
the inner arrangement of the electrons of the atom 
as well as a wealth of other data, they will be 
discussed in detail. 
5.08 X-Rays 
The German physicist, Roentgen, discovered 
X-rays in the year 1895 while working with a high 
voltage gaseous discharge tube. The penetrating 
rays which he named “X-rays” are often referred 
to as Roentgen rays. Figure 5-6 shows a modern- 
type tube which is used to produce these rays. It 
is merely a high vacuum tube containing a heated 
filament, and a target, and as such is simplv a diode 
across which is applied a high voltage. Electrons 
which are emitted from the heated cathode are 
accelerated toward the target, which they strike 
„=g] —1/3=) (12) 
It is seen that the above equation is exactly the 
same as Eq. (1) where M=3, if the Rydberg 
constant is taken as 
(13) 
The value of R, obtained by substituting the 
constants in Eq. (11) is in excellent agreement with 
the experimental value and is a remarkable result 
of Bohr’s theory. 
5.07 Excitation and Ionization oF Atoms 
In the normal state, the electron in the hydrogen 
atom is in orbit 1 (i. e. n= 1) or in the ground 
state. In order to raise this electron to higher 
orbits farther away from the nucleus, energy must 
be supplied to the system. This energy is 
normally supplied by means of collisions with 
other atoms or electrons. It is easy to calculate 
how much energy must be supplied to the H-atom 
to completely remove the electron from the atom. 
Such a process is known as ionization, and the 
resulting atom is ionized. It is equivalent to 
setting n— °° for the final state of the atom. 
Thus: 
j-, 2ir2meif 1 1\ 2 tr2md , 
E=-v (14) 
E= 22X10 12 ergs or 13.5 electron volts 
using m=9X10 28 gm, e=4.8X10 10 e.s.u. and 
: =6.6X 10-27 erg-sec. 
The energy required to remove the electron from 
the H-atorn can be measured and checks very 
closely with this calculated value. The potential 
necessary to ionize any atom is known as the 
ionization potential. 
The experiment to determine the value of the 
ionization potential in hydrogen consists of shoot- 
ing a beam of electrons of known energy (voltage) 
into a tube of hydrogen gas at low pressure. If the 
energy of the bombarding electrons is high 
enough, it will cause the characteristic spectrum 
lines to be emitted from the gas, and these can be 
observed with a spectroscope. As the energy of 
48 RADIOLOGICAL SAFETY 
Figure 5-6.—Sketch of X-ray tube 
with a high velocity. This velocity, v, can be 
calculated by equating the kinetic energy of the 
electrons to the work done on the electrons by the 
electric field, in accelerating them across a poten- 
tial difference of V volts. This work is given by 
the product e times V and thus: 
2=eV (15) 
When the electron strikes the target, which is 
usually made of a heavy metal, such as copper or 
tungsten, part of its energy is lost in the form of 
heat and part goes into producing X-rays. If all 
of an electron’s energy goes into X-radiation, the 
wave length of this radiation is given by substitu- 
ting the expression eV for E in the equation 
E=hc/\; thus: 
x=iv (16> 
From this expression, it is clear that as the poten- 
tial V across the tube is increased, the wave length 
of the emitted radiation decreases. Since it is 
experimentally known that the shorter the wave 
length of the X-rays, the greater is their pene- 
trating power, it is obvious that as the potential 
V is increased, more penetrating (harder) radia- 
tion is produced. For example, let us calculate the 
shortest wave length emitted from an X-ray tube 
operating with V—100,000 volts. Substituting in 
Eq. (16) yields: 
Figure 5-7.—Typical X-ray spectrum showing character- 
istic and continuous radiation. Spectrum taken with 
molybdenum target, 35 kv. across tube. 
Two distinctly different types of X-rays appear in 
this spectrum: 
a. Continuous or “white” X-rays which 
have a sharp lower wave length limit, rise to a 
maximum, and then taper off toward the 
longer wave lengths. 
b. Characteristic or line X-rays which 
appear in the spectrum as sharp peaks super- 
imposed on the continuous spectrum. These 
peaks or lines are uniquely characteristic of 
the element which is used as the target in the 
X-ray tube. 
The most significant property of X-radiation is 
its high penetrating power. Almost everyone has 
at some time or other had an X-ray photograph 
made of his chest or some other part of his body 
and is thus familiar with the fact that X-rays can 
penetrate through many inches of human tissue. 
In X-raying the bones in the body a physician is 
able to record the shadow of the bones on a photo- 
graphic plate because the bones, being composed of 
elements of higher atomic weight and being more 
dense than human tissue, absorb the radiation 
much more than does human flesh. X-rays pro- 
duced by modern betatrons can penetrate many 
inches of solid lead, even though lead, in common 
with elements of high atomic number, is a much 
more efficient absorber for X-rays than is a lighter 
element. 
X-rays can also cause fluorescence when they 
he (6.6X 10~27) (3 X1010) 
Amln‘ 50,000 (4.8 X 10~10) (1.6 X TO2) 
eX 300 
kmin.=0.26X 10~8 cm. or 0.26 A (17) 
It is possible to devise an X-ray spectrometer, 
analogous to the spectrometer used in the optical 
region of the spectrum to split up the X-radiation 
coming from the target into its component wave 
lengths. Such a spectrum is shown in figure 5-7. 
49 RADIOLOGICAL SAFETY 
strike certain materials which are particularly 
sensitive to this radiation. But far more import- 
ant for the purpose of this discussion is the fact 
that X-rays act very efficiently to ionize gases 
through which they pass. 
5.09 X-ray Spectra and Atomic Energy Levels 
The continuous X-rays are produced by a 
mechanism which will not be discussed here, for it 
does not yield too great a contribution to our 
understanding of atomic structure. Instead, the 
mechanism of the production of the characteristic 
or line X-rays will be discussed, for it reveals very 
clearly much information that bears on atomic 
structure. The fact that each element yields a 
distinctly different line spectrum which is uniquely 
characteristic of the element, yet bears a 
similarity to the line X-ray spectra of other ele- 
ments close to it in atomic number, suggests that 
these spectrum lines may be caused by electron 
transitions in the electron shells deep within the 
atom. Figure 5-8 shows a typical set of such 
Substantiating the assumption that the K-line 
X-rays arise from electron transitions deep within 
the atom, is the fact that the innermost electrons 
would be expected to be bound most strongly to 
the nucleus. If the K-line spectra of a series of 
contiguous elements are studied, it can be deduced 
(as was done by Moseley) that the wave number 
for any X-ray line can be analytically expressed as 
(18) 
Except for the factor (Z—S) this equation is iden- 
tical with the equation for the wave number of 
any line in the optical spectrum of hydrogen. 
In the expression, Z is the atomic number of the 
element, and S is a constant factor introduced to 
take acount of screening or reduction of the 
nuclear field due to electrons adjacent to and inside 
of the one undergoing a transition. If nx is taken 
equal to 1 and n2 = 2 it is found that the expression 
r=3/4R{Z-S)2 
gives the wave number of the most intense (Ka) 
line for any element of atomic number Z. It can 
be shown that the staggering of the Ka lines 
(fig. 5-8) toward longer wave lengths with 
decreasing atomic number is completely explained 
by this expression. The latter is known as Mose- 
ley’s law. In words, this law can be roughly 
stated as follows: X-ray line spectra for consecu- 
tive elements are similar to each other but are 
displaced relative to each other by a definite 
interval which increases regularly with decreasing 
atomic number. This law is more often written 
in the form. 
v*=K{Z-S) (19) 
where v is frequency and K is a universal constant 
for all elements. 
All of these results yield information about the 
structure of the atom but not of the nucleus of the 
atom. The physicist Kossel postulated that elec- 
trons arrange themselves in shells about the 
nucleus. These shells have definite limits to the 
number of electrons which can be placed in them 
and are illustrated for the mercury atom in 
figure 5-9. The mercury atom has Z=80, and 
therefore has to have 80 electrons arranged in 
shells about the positively charged nucleus in order 
Figure 5-8.—Typical K series spectra. 
spectra for the set of elements which lie on either 
side of iron in their atomic number. In this case, 
the shortest wave length X-ray line series have 
been illustrated. These are called the K-series 
lines. Longer wave length series are called L, 
M, N, etc. 
50 RADIOLOGICAL SAFETY 
Figure 5-9.—Electronic structure of the mercury atom. 
to be electrically neutral. These shells are built 
up as follows: 
K shell has only 2 electrons and is closest to 
the nucleus, therefore these are the most 
tightly bound electrons in the mercury 
atom. 
L shell has 8 electrons, called L electrons, 
which are not as tightly bound to the atom 
but yet require the input of more energy 
to the atom for their removal than do the 
electrons in the M, N, 0, P, and Q shells. 
Similarly the M, N, and 0 shells are filled 
or saturated by 18, 32, and 18 electrons, 
respectively. The K shell corresponds to 
the shell with nx — \ in Eq. (18). Just as 
optical spectral lines are produced in the 
mercury atom by, say, an electron falling 
into ring P from Q, or from still more remote 
orbits into the empty orbit Q, so also is an 
X-ray spectral line produced by an electron 
falling from shell L into the K shell. There 
must be a vacancy in the K shell since the 
L electron cannot possibly crowd into the 
K shell if 2 electrons are already there. In 
the production of X-ray line spectra, a K 
electron is ejected from its orbit by the 
collision of a high speed electron which is 
accelerated toward it with energy sufficient 
to remove it from its shell. Thereupon an 
L electron falls down to fill the vacancy in 
the K ring and the energy difference due to 
this transition from the L to K shell appears 
as a K X-ray line. 
The L shell does not consist of just one energy 
level, but has in fact several levels, as do the M, 
N, and other shells. As seen in Figure 5-10, this 
accounts for the existence of three Ka lines. 
5.10 interaction of X-rays with Matter 
It has already been stated that X-rays of long 
wave length are absorbed more strongly by an 
Figure 5-10.—Diagram of L and M shells 
element than similar rays of shorter wave length. 
As yet nothing has been said about the processes 
by which X-radiation is absorbed in matter. 
Experimentally it is known that a beam of X-rays 
is exponentially absorbed or reduced in intensity 
in traversing matter. For simplicity it is as- 
sumed that a beam of monochromatic X-rays, 
that is, X-rays of the same wave length, are inci- 
dent upon a slab of absorbing material of a given 
Figure 5-11.—X-ray absorption. 
element. Let the initial intensity of the beam at 
the surface of the slab, where x=0, be 70; then, 
as will be shown later, the intensity I at any dis- 
tance x from the surface is given bv 
I=I0e-»x (20) 
where ix is called the linear absorption coefficient. 
Figure 5-12 illustrates how this relation appears 
when plotted on a linear scale. The symbol n 
implies that there is a fractional decrease of in- 
tensity per unit thickness of absorber. This is 
significant, for it means that a certain fraction, 
51 
774689 0 - 48 -5 RADIOLOGICAL SAFETY 
Chamber when it is irradiated with X-rays. 
Each ion serves to form a nucleus for the conden- 
sation of a water drop upon it, for otherwise it 
could not be seen. (See Ch. 9, sec. 9.02 for 
details of the operation of a cloud chamber.) The 
ions created by the ejected photo-electrons form 
many separate zigzags in the chamber. A cloud 
chamber photograph of an X-ray beam is shown 
in figure 5-13. It will be observed that there are 
Figure 5-12.—Exponential absorption of X-rays. 
albeit very small, will always penetrate through 
any finite thickness of absorber. 
There are two general ways in which an X-ray 
can be caused to disappear from the X-ray beam. 
First, it can interact with an atom and have its 
energy transferred to another particle. Second, 
it can be scattered from the beam by elastic col- 
lisions with atoms. Specifically, three processes 
for X-ray absorption will be considered. 
(a) The photoelectric effect.—When an X-ray 
quantum or photon collides with an atom, it may 
impinge upon an orbital electron and transfer all 
of its energy to this particle by ejecting it from 
the atom. If the incident photon carried more 
energy than that necessary to remove the orbital 
electron from the atom, it imparts to the electron 
its additional energy in the form of kinetic energy. 
This process is known as the photo-electric effect 
and obeys the Einstein photoelectric equation: 
Figure 5-13.—X-ray photoelectrons seen in a cloud 
chamber. 
Courtesy of The Royal Society 
few very long tracks of these photoelectrons. 
This indicates that interactions which produce 
photoelcctrons of high energy must be quite 
infrequent. From Eq. (21) it follows, then, that 
for X-rays of very short wave length the photo- 
electric effect will be less important. 
It should be obvious that the ejection of a photo- 
electron leaves a gap in the electron shell, and 
this gap will be filled by an electron transition 
from a higher shell. Let it be assumed that a 
photoelectron is ejected from the K shell; then 
an L electron will jump to the K shell, emitting 
a Ka X-ray. This process leaves a gap in the L 
shell, and an M electron may make a transition 
to it and emit an L X-ray. Thus if a block of 
material, preferably a dense element, is placed in 
an X-ray beam, it will itself become a source of 
X-rays for the reasons just presented. This 
radiation is usually called characteristic or fluor- 
escence radiation. The former name is given to 
it, since it is obvious that the radiation will be 
uniquely characteristic of the element in the 
radiated block. This secondary radiation is 
usually very homogeneous, that is, it consists of 
only a few sharply defined wave lengths. 
(b) The Compton Effect.— For X-rays of shorter 
wave lengths, another process occurs. It is ex- 
tremely important to the physicist, for it shows 
that X-ray photons behave as small particles and 
hv=(t>-\-\mv2 (21) 
Here, hv represents the total energy of the inci- 
dent photon; </> represents the energy required to 
remove the electron from its atom; and \ mv2 rep- 
resents the kinetic energy of the ejected electron. 
Electrons which have thus been ejected from 
atoms are called photoelectrons. These electrons 
are responsible for the ionization produced by 
X-rays. They may have considerable energy 
and cause ionization to occur in neighboring 
atoms. This effect is readily appreciated by 
observing the tracks which form in a Wilson Cloud 
52 RADIOLOGICAL SAFETY 
undergo billiard-ball typo collisions, even though 
a photon was formerly thought to have essentially 
wave characteristics. This process was first 
discovered by Arthur H. Compton and so is 
called the Compton Effect. 
the foregoing discussion that in a Compton col- 
lision, the photon is actually heavier than the 
electron at rest. 
Application of the laws of conservation of 
energy and momentum to the Compton collision 
process allows an accurate calculation of the 
direction of the recoil electron and also it permits 
a calculation of the change in wave length of the 
scattered photon. Since the recoil electron (often 
called the Compton electron) takes energy from the 
incident photon, the wave length of the scattered 
photon must be longer than that of the incident 
one. 
The calculations made on the assumptions 
stated in this section are accurately confirmed by 
experiment. If a beam of X-rays, all having the 
same wave length, is allowed to fall upon a block 
of an element, such as carbon, the X-rays are 
scattered by the outermost loosely bound carbon 
electrons. Close examination of the scattered 
radiation shows that some of the scattered rays 
are of longer wave length than those in the primary 
beam irradiating the carbon. Many photons 
scattered by the carbon electrons will not be 
changed in wave length. These rays are said to 
undergo pure scattering, in contrast to those 
which suffer Compton scattering and a change in 
wave length. 
Pure scattering, considered on the basis of 
classical views, is explained by an electromagnetic 
interaction of the X-ray photons with electrons in 
the scattering element. The X-rays, acting as 
waves, excite the electrons to oscillation and these 
reemit the radiation with no change in frequency. 
Such radiation is scattered uniformly in all 
directions. 
(c) Pair production.—In general, at still shorter 
wave lengths where neither of the two effects just 
discussed is appreciable, a new and rather start- 
ling phenomenon takes place. 
Figure 5-15 is a rough sketch of the simple pair 
production process. A high energy photon in the 
vicinity of the nucleus may give rise to the crea- 
tion of a pair of electrons. One of these electrons 
is of the ordinary type carrying a negative charge, 
but the other is a particle equal in mass to that of 
an electron but bearing a positive charge of -j-e. 
It is called a positron and is denoted by the 
symbol e+. The symbol e~ or simply e refers to 
the ordinary negative electron. A term, the 
Figure 5-14.—Compton effect. 
Suppose a photon of energy hv collides with 
an electron e. As a result the incident photon is 
scattered at an angle <t> away from its original 
direction, and the struck electron recoils in a 
direction at an angle d to the trajectory of the 
primary photon. The incident photon can be 
treated as if it were a particle of mass given by 
the equation. 
hv 
(22) 
In table II are shown wave lengths and associated 
masses of several photons. 
Table II.- 
—Masses of 
photons of different wave lengths 
X 
hv 
m 
W»/7Be 
Wave length 
Energy 
Mass 
Ratio of mass 
of photon to 
mass of elec- 
tron 
r 
10,000 A 
ergs 
2X10-*2 
gms 
2X10-33 
2.4X10-6 
1.2 ev 
100 A 
2X10-10 
2X10-31 
2.4X10-4 
120 ev 
10 A* 
2X10-9 
2X10-30 
2.4X10-3 
1,200 ev 
1 A .. 
2X10-8 
2X10-29 
2.4X10-2 
12 Kev 
0. 1 A 
2X10-7 
2X10-28 
0.24 
0.12 Mev 
0.01 A 
2X10-6 
2X10-27 
2.4 
1.2 Mev 
From this table it is seen that an infra-red photon 
corresponding to an energy of about 1 electron 
volt has a mass about a millionth that of an 
electron (the mass me is the mass of the electron). 
For a photon to have a mass equal to that of an 
electron at rest, it must be about 0.02 A in wave 
length or about 0.5 Mev in energy. Since the 
Compton process is important for photons of 
relatively high energy, say, 2 Mev, it is clear from 
53 RADIOLOGICAL SAFETY 
in the cloud chamber is a 1 cm. load plate upon 
which a 5 Mev photon is incident. Note that the 
upper half of the plate is devoid of tracks since the 
5 Mev photon is non-ionizing. As the photon 
strikes the lead plate, it disappears and creates a 
pair of electrons which diverge from their common 
point of origin. 
It is interesting to note here that the positron 
finally undergoes a reaction which is the inverse 
of the pair production process. Just as the 
photon materialized into two particles, the positron 
is annihilated and gives rise to two photons of 
equal energy. These photons are called annihila- 
tion radiation. 
Figure 5-15.—Pair production. 
negatron, may sometimes be found to refer to a 
negative electron, but it is not in common usage. 
In the process of pair production, all of the 
photon energy is used up and goes into forming 
the electron pair and into imparting kinetic energy 
to this pair. Before a pair can be produced, the 
incident photon must have a minimum energy of 
1 Mev. Usually a much higher energy is neces- 
sary, especially in the light elements. For ex- 
ample, in lead, photons of 3 Mev lose about 50 
percent of the their energy in pair production, 
whereas in aluminum only a few percent of the 
energy is similarly expended. 
Figure 5-17.—Relative importance of photon absorption 
process in lead. 
Figure 5-17 shows the relative significance of 
the three absorption processes for the element 
lead. It should be remembered that such a set 
of curves is valid for only one element, since each 
of the processes depend upon the atomic number of 
the absorbing element. An important point to 
note in figure 5-17 is that the total effect as shown 
by the dotted curve has a minimum absorption 
at 3 Mev. In other words, lead is most trans- 
parent to radiation of 3 Mev energy and is more 
opaque at both higher and lower energies. The 
minimum absorption for iron occurs at an energy 
of about 7 Mev. 
Figure 5-16.—Cloud chamber photograph of pair pro- 
duction. 
The process of pair production is often referred 
to as the materialization of radiation. It is graph- 
ically illustrated in cloud chamber photographs 
such as the one shown in figure 5-16. Centered 
54 RADIOLOGICAL SAFETY 
5.11 The Roentgen. 
Up to now, whenever X-radiation has been 
mentioned, its intensity has been given in terms 
of arbitrary units. It is convenient to define a 
standard unit for the measurement of the in- 
tensity of this radiation. The practical unit of 
X-ray quantity which has been adopted is called 
the roentgen and is denoted by the symbol r. 
It is that amount of X-rays which will produce 1 
electrostatic unit of ions in 1 cubic centimeter of 
air under standard conditions of temperature and 
pressure. For a rigorous definition, it must also 
be required that, in making the measurement, 
certain complicating effects such as those due to 
secondary electrons and to the influence of the 
wall of the measuring instrument chamber be 
considered. 
The unit of X-ray intensity is given in terms 
of 1 roentgen per unit time. There is frequently 
confusion as to the difference between quantity 
and intensity of X-radiation. Intensity is the 
quantity of X-radiation measured at any point per 
unit time. For example, an X-ray tube may 
give an intensity of 0.30 roentgens per second 
(r/sec) at a distance of 1 meter from the tube. 
But if one were to stand at this point for 10 min- 
utes the total quantity or dose of X-rays received 
at that local point would be 180 roentgens, 
quite different from the intensity, or dose rate 
which would be 0.3 roentgens/sec. A dose of 180 
r, if delivered over the entire human body, would 
result in serious consequences to the individual. 
For this reason, considerable research has been 
done to determine just how much (remember 
that this means quantity or roentgens), X-radia- 
tion can be accepted by a human per dry for an 
indefinitely long period so that the individual may 
suffer no harmful effects. In Chapter 13 this 
problem will be discussed in greater detail. 
Instruments used for measuring X-radiation 
will be discussed in chapter 9, and therefore no 
mention is made hero of the practical means by 
which the Roentgen unit is measured. 
5.12 Wave Mechanics 
The evidence from both optical and X-ray 
spectra has been used in the foregoing sections to 
throw light upon the structure of the electronic 
shells which surround the nucleus. As a result of 
the quantum theory and of the Bohr model of the 
atom, the problem of atomic structure, at least so 
far as the orbital electrons are concerned, seems to 
be fairly well solved. It should be borne in mind 
that only a small fraction of the problem has been 
treated here and it must be accepted on faith that 
problems not treated are equally well susceptible 
to solution by the application of quantum-mechan- 
ical methods. 
When the Bohr theory was applied to atoms 
more complex than simple hydrogen-like systems, 
grave difficulties arose which could not be resolved 
by then existing mathematical and analytical 
techniques. In fact, the next most complex atom, 
helium, presented an impasse to the theoretical 
physicists. The introduction of new theories, 
known as wave mechanics and matrix mechanics 
by Schroedinger and Heisenberg removed many 
of the objections present in the old quantum 
theory and yielded correct results when applied to 
the helium atom. The introduction of the quan- 
tum conditions in Bohr’s theory was very arbi- 
trary and subject to criticism. In the new wave 
mechanics, the quantum conditions are introduced 
naturally and today the validity of wave mechani- 
cal treatment of atomic systems is well substanti- 
ated. 
The subject of wave mechanics is too involved 
for treatment in this text and would require an 
extensive mathematical background to follow 
even an elementary discussion of it. According 
to the principles of wave mechanics, every particle 
of mass m has associated with it a phase wave of 
wave length given by the De Broglie relation 
X-A (23) 
mv 
where h is again Planck’s constant and v is the 
velocity of the particle. This equation expresses 
the dual nature of matter. That is, it endows 
every particle with certain wave characteristics 
and thus resolves the difficulty which perplexed 
physicists for so long when they tried to determine 
whether light was wave-like or corpuscular. It 
is now known that light in common with other 
electromagnetic photons behaves both as a wave 
and as a particle, depending upon the conditions 
of the experiment. A proton moving with Ko 
55 RADIOLOGICAL SAFETY 
the velocity of light has, according to Eq. (23) an 
associated wave length of 
effectively collimates the ion beam. Upon enter- 
ing slit S3, the ions are bent by the 90° electric 
field of several thousand volts, whereupon they 
emerge from this field and pass through a defining 
slit Si. At this point, all those ions of velocity vx 
come to a common focus; the faster ions of velocity 
v2 come to a second common focus. There is, 
therefore, a velocity spectrum of ions over the 
breadth of this slit. As the ions enter the mag- 
netic field they are bent through 180°, and all 
ions having the same ejm ratio (charge to mass), 
are focused at a common point on the photographic 
plate, where they produce an image. This latter 
type of focusing is known as direction focusing 
and is independent of the velocity of the ions. 
Figure 5-20 is a reproduction of a typical mass 
spectrum taken with the instrument shown in the 
preceding figure. The spectrum shown was ob- 
tained from the impurities which were present in a 
sample of uranium which was being analyzed. 
Some of these elements were present to the extent 
of only 1 part in 1 million and yet they are readily 
identified in the plate. Since the instrument 
focuses all ions of the same efm ratio, singly 
ionized atoms of mass 7 (lithium) fall at the same 
point on the plate as doubly ionized atoms of mass 
14 (nitrogen). In fact the strong line between 
lithium and beryllium is due to doubly charged 
oxygen. 
In 1913 Thomson used a mass spectrograph in 
establishing that the element neon had two 
separate components, one of mass 20 and one of 
mass 22. Prior to his discovery of neon 22, the 
fact that the atomic (chemical) weights of many 
elements differed widely from whole numbers had 
no reasonable explanation. Indeed, chlorine with 
an atomic weight of 35.46 diverged widely from 
the whole numbers 35 and 36. Thomson solved 
this vexing problem by assuming that each element 
may have atoms which have different mass but 
are chemically identical. Such atoms are called 
isotopes. From Thomson’s assumption it follows 
that the chemical atomic weight is an average 
weight of the various isotopes of that element. 
Chlorine, for example, has been shown to have two 
isotopes, one, Cl35, which is about three times more 
abundant than Cl37, the other isotope. The 
weighted average of these isotopes yields an 
average atomic weight in good agreement with the 
measured weight. 
6.6X10-27 = 1 4X10-12 cm 
* (1.6X10-24) (3X109) A-4A1U cm- 
That such protons actually exhibit wave proper- 
ties corresponding to this short wave length is 
verified in diffraction experiments wherein a beam 
of protons is diffracted by a thin gold foil. 
5.13 Mass Spectroscopy 
Earlier in this chapter (see sec. 5.01) mention 
was made of the fact that positive ions could be 
deflected with appropriate electric and magnetic 
fields and thus they could be weighed. Instru- 
ments designed specifically for analyzing and 
weighing positive ions arc known as mass spectro- 
graphs. A diagram of a Dempster type double- 
focusing mass spectrograph appears in figure 
5-18. In figure 5-19 is shown the corresponding 
Figure 5-18.— Diagram of a Dempster type mass 
spectrograph. 
spectrograph box. This box fits between the 
poles of a large electromagnet and connects to a 
vacuum system which maintains the box assembly 
at a pressure of less than 10-5 mm. Hg pressure. 
Positive ions are produced by sparking together 
two electrodes in a vacuum. The ions thus 
generated are accelerated by a high voltage source 
of about 15,000 volts into a slit system which 
56 RADIOLOGICAL SAFETY 
Figure 5-19.—Dempster type mass spectrograph. Auxiliary equipment (magnet, etc.) not shown. 
(a) Light Element Impurities in Metal Sample 
(b) Impurities in Metal Sample 
Figure 5-20.—Typical mass spectra 
57 RADIOLOGICAL SAFETY 
From the discussion given earlier, it is clear that 
the Ne22 isotope which Thomson discovered differs 
from Ne20 in that its nucleus contains 2 more 
neutrons. As long as the number of protons in the 
nucleus remains the same, the presence of more 
neutrons in the nucleus does not change the 
chemical characteristics of the element. 
5.14 Mass Spectra 
In the case of optical and X-ray spectra, it was 
found that these spectra were invaluable in un- 
raveling the mystery of the electron shell structure. 
It might therefore be expected that mass spectra 
will be of similar value in giving clues about the 
inner structure of the nucleus. 
Every element has one or more isotopes. In 
some cases, it may have only one isotope—in such 
a case this particular isotope has a 100 percent 
abundance. Other elements, such as tin, may 
have as many as 10 isotopes with abundances 
varying from a small fraction of 1 percent to many 
percent. Figure 5-21 shows what is called an 
isotope pattern or sometimes isotope profile. It is 
simply an intensity plot of the isotope abundances 
listed in table III. 
Figure 5-21.—Isotope pattern of tin. 
With precision mass spectrographs at their dis- 
posal, physicists were able to determine accurately 
the atomic masses of the elements. The chemists 
had already selected oxygen as the standard ele- 
ment upon which their system of atomic weights 
was based; this choice was rather unfortunate, 
since oxygen has three isotopes. In comparing 
atomic weights, physicists use the most abundant 
isotope of oxygen as a standard in the physical 
atomic weight scale and take it equal to 16.00000. 
The masses of isotopes of other elements can be 
accurately measured with respect to 016; some 
values so obtained are tabulated in table IV. 
Table III.—Relative abundance of naturally occurring tin 
isotopes 
Isotope No.: 
Percentage 
abundance 
112 
1.1 
114 
. 8 
115 
. 4 
116 
15.5 
117. 
9. 1 
118 
119 
9. 8 
120 
122 
5. 5 
124 
6 8 
100 
Table IV.—Exact masses of various elements 
Atomic 
Element 
Symbol 
z 
weight=M 
(mass units) 
Hydrogen 
H1 
1 
1. 008123 
Deuterium 
H2 or D 
1 
2. 014745 
Helium 
He4 
2 
4. 003905 
Lithium __ . 
Li7 
3 
7. 01657 
Carbon . , - . _ 
C“ 
6 
12. 00398 
Nitrogen 
N« 
7 
14. 0073 
Oxygen _ 
qi« 
8 
16. 0000 
Q18 
8 
18. 0057 
Fluorine . 
JT19 
9 
19. 0045 
Neon_ _ . 
Ne20 
10 
19. 9988 
Calcium, - . - __ 
Ca40 
20 
39. 9738 
Nickel 
Ni«° 
28 
59. 94977 
Tin 
Sn120 
50 
119. 93 
Mercury _ 
Hg200 
80 
200. 028 
Thorium _. 
Th282 
90 
232. 12 
Uranium 
XJ2S5 
92 
235. 125 
U2*8 
92 
238. 132 
Certain regularities in the number of naturally 
occurring isotopes per element are manifest in the 
periodic chart shown in figure 5-22. For example, 
the odd groups contain elements having usually 
only a single or at most two isotopes, whereas the 
even groups rarely contain elements with single 
isotopes (per element) and more often each element 
has more than two isotopes. The significance of 
this isotope distribution among the elements will 
be discussed in chapter 6. 
58 RADIOLOGICAL SAFETY 
1 
11 
1 1 1 
IV 
V 
VI 
VI 1 
0 
OR VIII 
1 
1 H 
2 
He 
2 
02 
> 
~I0 5 
3 
Li 
4 
Be 
5 
B 
6 
C 
7 
N 
8 
0 
9 
F 
10 
Ne 
2 
, . 
75 
10 
,J 
' ' 
IS 20 
!• 
04 
20 
IOO 0 
22 - 
27 
9 72 
II 
No 
12 
Mg 
13 
A 1 
14 
SI 
15 
P 
16 
s 
17 
Cl 
18 
A 
3 
24 
774 
22 
99 l 
lOOO 
20 - 
too 0 
29 - 
0 2 
21 
- 100 0 
24 
4 2 
27 
24 0 
20 
00. 
19 
K 
20 
Co 
21 
Sc 
22 
Ti 
23 
V 
24 
Cr 
2? 
Mn 
26 
Fc 
27 
Co 
2 J 
Ni 
42 
04 
40 - 
7*5 
C r « 
AO 
• s 
52 
00 
20 7 
41 _ 
• •I 
49 - 
Jl 
lOO 0 
52 
9 42 
• OO 0 
57 - 
59 
I oo 0 
« i 
> 2 
4 
44 
50 - 
9 24 
50 
20 
IT 
00 
29 
Cu 
30 
lr\ 
il 
Ga 
32 
Ge 
33 
As 
34 
Se 
9 
33 
Br 
36 
Kr 
•5 
\%m 
M 
2 7 3 
09 
O i 2 
72 
27 2 
#0 - 
2 0> 
JSI 
70 
9 
70 - 
* 5 
00 
02 - 
40 0 
• 2 
o* — 
5 7 11 
17 47 
37 
R"b 
38 
Sr 
ii# 
Y 
40 
Zr 
41 
Ob 
42 
Mo 
Ma 
44 
Ru 
45 
Rh 
46 
Pd 
*2 — 
14 9 
90 - 
5 00 
a? 
J72 
00 - 
9 00 
* 
- 
I : 5 
*9 — 
*9 — 
>2 Oi 
104 - 
7 02 
f o 
12 70 
IOO 0 
100 
2 ’ 2 
s 
•I 
' 5 
*0 
100 - 
24 1 
9 29 
102 
>04 — 
?• 27 
<00 
MO — 
20 0 
I 2 9 
47 
Ag 
48 
Cd 
4y 
In 
50 
S n 
51 
Sb 
52 
Te 
53 
I 
34 
Xe 
K)7 
K>* 
Si.* 
44 1 
11 
13 
in 
*n 
1 12 
4 5 
|i 
r 
121 
90 0 
120 
(22 
<22 
124 - 
2 9 
• 0 
4 9 
i|_ 
20 |3 
ill- 
II 
■!! 
I 20 
t 20 
i 20 
l * 0 
22 0 
22 i 
35 
C» 
56 
6o 
72 
Hf 
73 
Ta 
74 
W 
75 
Re 
76 
Os 
77 
Ir 
78 
Pt 
til 
124 • 
ifU 
047 
Ilf 
nil 
57 - 71 
1 7 
- 
10 
5 20 
100 
102 
22 0 
>04 
ioe 
it.7- 
• 0 9 — 
190 
IK 
<92 
• 94 
0 
Rare Eorths 
• 7 
171 
— 
27 12 
12 05 
«4 
0? 0 
20 4 
192 
0* 9 
t*5 
• 90 
39 3 
20 0 
A 
10 
• 92 
4 1 0 
>00 
7-3 
79 
Au 
80 
Hg 
81 
T 1 
82 
Pb 
83 
Bl 
84 
Po 
85 
Ab 
86 
Rn 
ill- 
.o!s 
20- 
I 5 
29 i 
20 
— 
22 0 
&“ 
205 
70 * 
20 
204 
—— 
— 
22 0 
92 2 
7 
87 
Vi 
88 
Ro 
89 
Ac 
90 
Th 
91 
Pa 
92 
U 
93 
Np 
94 
Pu 
224 
oo* 
57 
- 71 
57 
La 
58 
|» 
C« 
It 
59 
Pr 
It 
:x- 
Nd 
w 
61 
II 
62 
iii - 
Sm 
•3 ? 
63 
Eu 
s; 
Chicefo, Illinois 
Roro 
Eorths 
IS- 
m 
ui- 
■11 
• 56 - 
Hi — 
11 5 
fit 
>93 
CHART Of NATURAL ISOTOPES 
G d 
65 
Tb 
86 
Dy 
67 
Ho 
68 
Elr 
69 
Tm 
70 
Yb 
71 
Lu 
If - 
iff- 
i 
-rooqq 
ml 
ii|— 
!M~ 
ii\ 
nt 
ill 
Isotopic Abundances From 
iaE: 
IS 
in- 
'll- 
> 70 
2 5 
Seebor j. Re* Mod Phys ,Jan I94> 
Figure 5-22.—Periodic table of the elements showing isotope abundance. 
59 RADIOLOGICAL SAFETY 
Inspection of this table shows that all the masses 
of the isotopes are approximately whole numbers. 
The difference between the mass number M of any 
isotope and the nearest whole number is called the 
mass defect and is written as A. 
A = M-A (23) 
A term which is often found in the literature is the 
packing fraction and it is simply the mass defect 
per nuclear particle. It is thus the same as the 
mass defect divided by A: 
Packing fraction / = (24) 
In this text these terms will not be generally used; 
they are included here for the sake of complete- 
ness. 
5.15 Stable Isotopes 
The relative abundance of the isotopes of tin 
has been given in table III. It is remarkable that 
this same abundance is obtained for any sample 
of tin, no matter where it was mined. Further- 
more, the isotope ratio does not change with 
time, and there is no reason to believe that it ever 
will undergo a natural change. For this reason, 
tin is said to consist of stable isotopes. There are 
only a relatively few naturally occurring elements 
which do not always exhibit the same isotope ratio 
regardless of their origin. One of these is lead. 
It is found that samples of lead taken from the 
Belgian Congo show a different isotope ratio 
than lead mined in some other parts of the world. 
There is no reason to believe, however, that any 
sample of lead, independent of its origin, changes 
its isotopic ratio with time. Thus lead is said to 
be made up of stable isotopes. The reason why 
different samples of lead show different isotopic 
abundances will be explained in Ch. 6, sec. 6.07. 
The term stability as applied to an isotope is 
really a relative term. It implies that during any 
time interval of observation the isotope does not 
change its atomic number or mass. Thus an 
isotope may be said to be stable if it remains 
unchanged for a period of time which is long 
compared with whatever time period the observer 
is concerned. As will be seen in chapter 6, some 
isotopes are unstable, i. e., they change their mass 
or charge in extremely short time intervals while 
others change over a period of many years. This 
concept of stability and instability will become 
clearer after the phenomenon of radioactivity has 
been discussed. 
Figure 5-23 is an N-P diagram for stable 
isotopes. It simply represents a graphical plot of 
the number of neutrons for any isotope and the 
corresponding number of protons in the nucleus of 
the same isotope. The smooth curve which is 
drawn through the points representing all the 
stable isotopes of the 92 elements is called the line 
of stability. Initially the slope of this curve is 
almost 45°. With increasing proton numbers, the 
slope becomes increasingly steeper; i. e., the N/P 
ratio becomes greater than 1. 
In figure 5-23, it will be noted that there is often 
more than one isotope having the same value of N 
plus P but having a different proton number. In 
fact there are some cases where isotopes of three 
different elements have exactly the same isotopic 
weights. Such isotopes are known as isobars. 
No cases are known where there are more than 3 
isobars for any value of N plus P. An example of 
a triple stable isobar shown in figure 5-23 is: 
40Zr96, 4oMo96, and 44Ru96 
where 
60 RADIOLOGICAL SAFETY 
Nuclei in line perpendicular to Z axis ore isotopes 
Nuclei in line perpendicular to A axis are isobars 
Triple Isobars are indicated by t 
Double Isobars ore indicated by t 
Figure 5-23.—Neutron-proton plot of stable isotopes RADIOLOGICAL SAFETY 
Chapter 6 
NATURAL RADIOACTIVITY AND NUCLEAR STRUCTURE 
6.01 The Discovery of Natural Radioactivity 
In the year 1896 a French physicist, Henri 
Becquerel, found that certain uranium salts emit- 
ted penetrating radiations similar to those which 
Roentgen had found only a year earlier. In find- 
ing that certain ores naturally give off rays similar 
to X-rays, Becquerel became the discoverer of the 
phenomenon of radioactivity. The tremendous 
importance of this discovery was not,immediately 
apparent. However, a few years later, the Curies 
(Pierre and Marie) gave added stimulus to the 
investigation of the new field hy announcing that 
they had succeeded in isolating from a uranium 
mineral (pitchblende) two substances which were 
many times more radioactive than uranium. These 
new substances were shown to be two new ele- 
ments, polonium and radium. It is important to 
emphasize that these radioactive elements spon- 
taneously emit radiation without the addition of 
energy. Later it will be shown that there is still 
another kind of radioactivity which is produced 
by adding energy to a nucleus in order to disrupt 
it. Such nuclei are said to be made artificially 
radioactive. 
In addition to the radioactive elements which 
have been mentioned, the disintegration products 
from radium are also naturally radioactive. In- 
vestigation of the disintegration or decay products 
led to the identification of other radioelements 
ranging in atomic number from uranium (92) to 
bismuth (83). Such radioelements are now known 
to be intimately related to each other in what are 
called radioactive series. These series will be dis- 
cussed in section 6.03. 
6.02 Rays Emitted by Radioactive Elements 
The problem of identifying the rays which are 
emitted by the radioactive elements was not an 
easy one, and the world’s most skillful physicists 
worked for a period of several years before they 
were able to identify the mysterious radiations. 
Rutherford showed that some of the rays could 
be deflected by a magnetic field and thus sepa- 
rated from one another. It was actually shown 
that these rays were of three distinctly different 
types. In figure 6-1 a radium source is shown 
Figure 6-1.—Rays emitted from a radium source placed 
in a magnetic field. The field is perpendicular to the 
plane of the paper and directed inward. 
inside of a lead sphere into which is bored a small 
diameter hole. Since the sphere is thick enough 
to absorb the penetrating rays, the only way in 
which they can emerge is through the opening. 
Thus a parallel beam of radium rays escapes from 
the sphere. If one were able to see the trajec- 
tories of these invisible rays in the presence of a 
magnetic field, they would look as sketched in 
figure 6-1, Those most easily deflected by the 
magnetic field are called /3 (beta) particles. Those 
deflected only slightly by the field are called 
63 RADIOLOGICAL SAFETY 
a {alpha) particles, while those which are unaffected 
in their trajectories are known as 7 {gamma) rays. 
From the fact that the a-particles are de- 
flected to the left in a magnetic field directed 
perpendicularly into the plane of the paper, it is 
known that they must be positively charged 
particles. By similar reasoning, the /3-particles 
must carry a negative charge, and the 7-rays 
must be uncharged or electrically neutral. 
Having thus investigated in a preliminary way 
the electrical nature of the radiations, it is natural 
to determine the penetrating power of each of 
only slightly reduced in intensity by the absorber. 
Finally C shows that an absorber of 5 centimeters 
of lead greatly reduces the 7-ray intensity but 
does not completely absorb all the 7-rays. 
Later on in this chapter, the problem of the 
emission of a- and /3-particles and 7-rays from 
nuclei as well as the mechanisms of their absorp- 
tions in matter will be treated in detail. For the 
present, having indicated something about the 
electrical nature and penetrating power of the 
rays, a summary of other properties of the 
radiations is given. 
Figure 6-2.—Relative penetrating power of alpha, beta, and gamma radiation 
the three types. To illustrate this, imagine 
an experiment of the type shown in figure 6-2. 
Here an extended radium source emits a- and /3- 
particles and 7-rays. In A an absorber, consisting 
of a few sheets of ordinary paper, is placed over 
the source. The a-particles are stopped by the 
paper, but the /3-particles and 7-rays pass through 
it without being diminished appreciably in in- 
tensity. In B the effect of an absorber, consisting 
of a few millimeters of aluminum sheet, is shown. 
Here both a- and /3-particles are filtered out or 
absorbed by the aluminum, but the 7-rays are 
6.03 Alpha Particles 
Experiments involving such instruments as the 
Wilson cloud chamber and magnetic spectro- 
graphs have shown that an a-particle carries a 
positive electric charge equal to exactly twice the 
electron charge. Furthermore, it has a mass the 
same as that of a helium nucleus and has, in fact, 
been shown to be exactly that. Thus a-particles 
are simply helium atoms, which carry a double 
positive charge and which are ejected from 
nuclei of radioactive isotopes with very high 
64 RADIOLOGICAL SAFETY 
velocity. The velocity with which these particles 
leave the nuceleus determines the distance which 
they will travel in any substance'—this distance is 
called the range R of the a-particle. R is usually 
given in terms of the number of centimeters of air 
under standard conditions which the a-particle 
will traverse before being stopped. Range is 
related to the initial velocity v0 of the a-particle 
by the simple relation: 
v03=aR (1) 
where a is a constant. As an example, an a-particle 
from RaC' (a radioelement to be discussed later) 
has an initial velocity of 1.9 X 109 cm/sec., or less 
than Koth the velocity of light, and has a range of 
almost 7 centimeters in air. Upon being stopped 
an a-particle picks up two electrons and becomes 
a normal helium atom. As evidence that the 
latter reaction occurs, it can be demonstrated that 
a strong a-emitter sealed in a glass capsule even- 
tually produces enough helium gas to be identified 
by its characteristic atomic spectrum. 
Simple absorption experiments show that for 
any given radioisotope which is an a-emitter there 
may be a series of ranges for the a-particles. 
These ranges can be classified in groups and yield 
valuable information about nuclear structure, in 
much the same way that optical spectra revealed 
the existence of atomic energy levels. 
6.04 Beta Particles 
A magnetic spectrographic analysis shows that 
/3-particles have a single negative electrical charge 
equal to that of an electron, and that they also 
have a mass equal to that of an electron. Thus 
/3-particles arc simply high speed electrons which 
result from a nuclear disintegration. One should 
not jump to the conclusion that there arc electrons 
as such within the nucleus, for such is not the case. 
Beta particles emitted from nuclei may travel 
with velocities only slightly less than the velocity 
of light, i. e., about 0.95 c, where c is the velocity 
of light. In contrast with a-particles, which are 
found to have very definite ranges and, therefore, 
discrete energies, /3-particles in general exhibit a 
continuous distribution of velocities. Thus, to 
these /3-particlcs, only mean or average velocities 
can be assigned, and such /3-particles are known 
as primary /3-particles. 
Another class of /3-particles are emitted from 
certain atoms. These have discrete energies, 
analogous to a-parlicles, and are known as second- 
ary /3-particles. Unlike primary /3-particles, these 
secondary rays do not originate in the nucleus, but 
are produced in the electronic outer shells of 
atoms by a photoelectric process discussed in the 
section 6.05. 
Among the fastest or hardest /3-particles which 
are known among the natural radioisotopes are 
primaries emitted by RaC (radium C, a decay 
product of radium). These particles have an 
upper energy limit of about 3.1 Mev, and travel 
with velocities only 1 percent less than that of 
light. In this connection, it can be observed 
experimentally in a strong electric and magnetic 
field that /3-particles of this velocity have a mass 
greater than that which they have when traveling 
at low velocities. This startling fact, namely that 
the electron increases in mass with increasing 
velocity, is readily explained by Einstein’s theory 
of relativity. A consequence of this theory is 
that the mass m of an}’- body moving with veloc- 
ity v is related to the rest mass m0 of that body, 
i. e., y=0, by the relation 
m0 
m=VKT) 
whoro c is the velocity of light (see sec. 2.04). If 
this equation is applied to an electron of rest mass 
m0 moving with velocity v=0.9c, then its mass at 
that velocity is m — 2.3 m0. 
6.05 Gamma Rays 
Gamma rays arc photons similar in character to 
X-rays, but differing in that they are of shorter 
wave length. Radioactive nuclei emit 7-rays of 
discrete energies, and hence 7-ray spectra consist of 
a scries of sharply defined wave lengths. . How- 
ever, in emerging from the nucleus, some of the 
7-rays do not escape through the electronic cloud 
around the nucleus; instead they may transfer 
to one of the electrons sufficient energy to eject it 
from the atom. Photons thus absorbed within 
the electronic shells arc said to be internally con- 
verted while the electrons ejected by the process 
are called internal conversion or secondary elec- 
trons. The process of internal conversion usually 
takes place in the and in some atoms almost 
65 RADIOLOGICAL SAFETY 
all of the 7-rays emitted by the nucleus are inter- 
nally converted. Since the nuclear 7-rays and the 
K electrons have discrete energies, the internal 
conversion electrons will be ejected with discrete 
energies. This process thus accounts for the line 
spectra of /3-particles that is superimposed 
upon the continuous /3-particle spectra of some 
radioisotopes. 
Since 7-rays are of exactly the same physical 
nature as X-rays, they are also absorbed by the 
same processes, namely: 
a—Photoelectric effect 
h—Compton effect 
c—Pair production 
Wave lengths of 7-rays are often given in 
X-units, where 1 X-unit =10~n cms. The natural 
radioisotopes emit 7-rays of wave lengths ranging 
from 2 to 300 X. U. (X-units). 
6.06 Statistics of the Decay Process 
Very early in the history of radioactivity, it 
was discovered that the activity of the elements 
decreased with time. For a given quantity of a 
radioelement, the activity might decrease very 
rapidly in a matter of seconds, or it might change 
more slowly over a period of years. The rate of 
change of activity was found to be characteristic 
of the specific radioisotope under study. Figure 
6-3 represents a graphical plot of a radioisotope 
which decreases in activity by a factor of 50 
percent every four hours. If there is, say, 100 
percent activity initially, after 4 hours there will 
be 50 percent left. After another 4 hours there 
will be 50 percent of this remaining activity, or 
only 25 percent of the initial amount. The time 
T which is required for a radioisotope to lose 50 
percent of its activity is called its half-life. Two 
abscissa units are indicated in figure 6-3: one in 
hours, the other in multiples of the half-life, T. 
Figure 6-3, when plotted in terms of the half-life, 
is a universal curve which applies equally as 
well to the decay of an isotope with half-life 
T=10-8 seconds as to one with T=107 years. 
The form of the curve in figure 6-3 suggests 
that the decay is a logarithmic process. That is, 
if the activity is plotted on a logarithmic scale 
against the time on a linear scale, the resulting 
curve should be a straight line. Figure 6-4 illus- 
trates that this is the case when a semi-logarithmic 
plot is made of relative activity versus time. 
From an analytical viewpoint, the problem can 
be approached in the following manner: we know 
experimentally that radioactive decay takes place 
in such a way that the number of decays occurring 
per unit time is proportional to the total number 
of radioactive atoms present. Analytically, the 
number (AN) of atoms disintegrating in a given 
time interval (AT) is proportional to the number 
(N) of the radioactive atoms present. 
AN— — \NAt (3) 
where X is the constant of proportionality and is 
called the decay constant. The negative sign in the 
equation is introduced because the process leads 
to a decrease in the number of atoms with time. 
By means of calculus, this equation is integrated 
and yields: 
N=N0e~'Kt (4) 
where N0 is the total number of atoms present at 
t=0. This equation expresses the number of 
particles N existing at time t when AT0 radio- 
active atoms were present initially. The range 
of validity of this equation is truly enormous, 
since it applies to processes which decay extremely 
rapidly (T:=10~6 seconds) as well as for those 
which decay slowly (T=10n yrs.). 
9 i 1193? 
Figure 6-3.—Radioactive decay curve. 
66 RADIOLOGICAL SAFETY 
Figure 6-4.—Radioactive decay curve on a logarithmic plot 
67 
774689 0 - 48 -6 RADIOLOGICAL SAFETY 
There is one condition that must be fulfilled in 
order for this equation to be rigorously applicable. 
That is, the total number of radioactive processes 
being considered must be sufficiently large so that 
statistical methods are valid. For example, in 
the case of a single isolated atom of half-life equal 
to 1 hour, there is only a probability that the atom 
will decay in any reasonable number of minutes 
either side of the 1 hour period. In fact, the 
atom might decay in the first second after f = 0 
(when observations are started) or it might decay 
1 day after t — 0. The process of decay is a statis- 
tical one which when applied to large numbers of 
atoms, as is usually the case, allows accurate cal- 
culations of the number of disintegrations which 
will occur in a given time interval. 
It must be obvious that the disintegration con- 
stant X and the half-life T are related to each 
other. Since the half-life was defined earlier as 
the time required for a substance to decay to one 
half of its initial activity, we can solve equation 
(4) for Tin terms of X by substituting N=N0/2 at 
time t—T. Thus: 
f’=iV„<r»' (5) 
On converting to logarithmic form, it follows that 
since: 
In 2 = 0.69 
then: 
(6) 
Any single radioisotope is characterized by a 
certain definite half-life which is constant and may 
often be used to identify it. 
As an example of a simple numerical calculation 
involving the half-life and the disintegration con- 
stant, consider the emission of a-particles from 
radium. Experimentally, the half-life of radium 
is known to be 1590 years. By Eq. (6) the dis- 
integration constant X is equal to 7 
1.59X103 yrs. 
0r 5 *1010 seconds or 13-8X 10~12 sec_1- Since the 
atomic weight of Ra is 226, and since there are 
6.0X1023 atoms in one gram atom of Ra (by 
Avogadro’s law), it follows that 1 gram of radium 
contains 2.6X1021 atoms. From Eq. (3) the 
AN . 
expression is the rate at which an clement 
decays, and for radium this rate for 1 gram is: 
X./V= (13.8X 10~12) (2.6X1021) 
= 3.7 X1010 disintegrations/second. 
This numerical quantity of 3.7X1010 disintegra- 
tions/second is known as the curie and is the 
standard unit used in measuring the activity of a 
radioactive substance. Often smaller units called 
the millicurie, me, (1/1000 curie), and microcurie, 
nc, (1/1,000,000 curie) is used, since the curie is 
such a large unit. Recently a new unit, the 
rutherford, has been introduced. This is defined 
as that activity which is equivalent to 106 dis- 
integrations per second. 
Substances which have extremely long half- 
lives obviously have a low specific activity. The 
specific activity of a substance is the number of 
disintegrations occurring per second per gram. 
For example, the heavy isotope of uranium, 
U238, has a half-life of 4.5X109 years, and 1 gram 
of it emits only about 12,000 a-particles per 
second and this is its specific activity. 
It should be pointed out that the definition of 
the curie, which is based on the number of dis- 
integrations and not on the number of radiations 
emitted, holds equally well for emission of a- 
particles, jS-particles, and y-rays. 
6.07 Radioactive Series 
Earlier it was mentioned that the radioactive 
element 88Ra226 decayed by a-emission with a 
half-life of 1590 years to form radon or as it is 
sometimes known, radium emanation. This 
element (86Rn222) is thus a decay product of radium. 
This reaction is shown schematically in figure 6-5. 
Emission of an a-particle from the nucleus of 
88Ra226 reduces the atomic number of the original 
atom by 2 charges, and the mass by 4 mass units. 
Analagous to the manner in which chemical 
reactions are represented by a reaction equation, 
the decay process can also be described by a 
nuclear reaction equation; 
68 RADIOLOGICAL SAFETY 
RADIUM ATOM 
RADON ATOM 
sgRa226 > gfiRn222-f-2He4-)-(2 (7) 
Just as in chemical equations, there has to be 
some type of a balance made on both sides of the 
equation. It will be noted that the superscripts 
representing the atomic masses add up to the 
same total on each side of the equation, as do 
the subscripts which represent the atomic numbers 
of the isotopes. In fact the equation for natural 
a-emission can be written in a more general form 
which applies to any element of atomic number Z 
and atomic mass A. 
Figure 6-5.—Decay of radium to radon 
Figure 6-6.—The uranium series. 
69 RADIOLOGICAL SAFETY 
z element A-*Z-2 element A 4+2He4-j-$ (8) 
The quantity Q in each equation represents the 
energy which is released. Such energy manifests 
itself in the kinetic energy carried away by the 
high speed a-particle as well as by the recoil of the 
more massive radon atom. 
Now if the radon atom were stable and thus 
did not decay into any other element, all the ra- 
dium atoms would soon (speaking in terms of 
geological time) be converted into stable radon. 
Experiments have shown, however, that radon 
also undergoes disintegration by emitting an 
a-particle to form the decay product polonium, 
84Po218. Radon has a half-life of 3.8 days, and 
polonium, which is also radioactive, decays by 
a-emission with a half-life of 3 months to form a 
radioisotope of lead, namely 82Pb214. Radio lead 
decays by /3-emission with a half-life of about 27 
months to form a radioisotope of bismuth, 83Bi214. 
This latter process is described by the nuclear 
equation: 
82Pb214 * 83Bi214+_xc° + Q (9) 
Thus the emission of a /3-particle increases the 
atomic number by 1 unit but does not affect the 
atomic weight. In such equations the weight of 
the emitted electron is taken equal to zero to 
simplify balancing the equation. More generally 
the decay of any element by /3-emission may be 
described by the following equation: 
z element A->(z+u element A + _iC°TQ (10) 
Radium, radon, polonium, and the other radio- 
elements mentioned thus form a series, which is 
diagramatically illustrated in its entirety in 
figure 6-6. This figure shows that radium is not 
the starting point of the series, nor would one 
expect it to be, for it has a relatively short (on a 
geological time scale) half-life; thus, if it were the 
start of the series, it would have long since van- 
ished from the earth. At the head of the series 
is the heavy isotope of uranium, 92U238, whose 
half-life, 4.5 X109 years, is longer than the geo- 
logical age of the earth, about 2.5 X109 years. 
The end point of the series is the stable lead 
isotope, soPb206. So far as the diagram of the 
series is concerned, an a-emission corresponds to 
a jump of 1 place (actually 4 mass units) to the 
left in the column of the diagram and also a 
descent of 1 place in the row of elements. 
For certain purposes, figure 6-7 provides a 
more lucid presentation of the uranium series than 
does figure 6-6. In figure 6-7, the neutron 
number is plotted against the proton number for 
part of the uranium series. Beta reactions are 
clearly illustrated in this figure by an arrow slant- 
ing to the right. RaO can decay either by 
emitting an a-particle to form RaC", or by 
/3-decay to form RaC'. Such a phenomenon is 
known as branching. Table I lists all the isotopes 
in the uranium series and gives both the modern 
symbols, e.g. 82Pb206, as well as the original terms, 
for the member of the series. Both types of 
terminology are in current usage. 
Two other natural radioactive series similar to 
the one already described are known. One is the 
actinium series, and the other the thorium series. 
The former begins with 92U235 and ends with 
82Pb207, while the latter originates from 90Th232 and 
terminates at 82Pb208. Thus each of the three 
series terminates with a different stable isotope of 
lead. In different parts of the world, where 
uranium and thorium are present in different 
amounts, lead is found with different isotopic 
composition. 
In addition to the three radioactive series, there 
are also a few long-lived light elements which are 
radioactive. Table II lists these radioisotopes. 
These light isotopes must be regarded as singly 
occurring and non-related radioactive elements, 
for there is no evidence to indicate that they are 
members of a transformation series. All the four 
radioisotopes have very weak specific activities 
and are difficult to measure even with extremely 
sensitive equipment. 
6.08 Equilibrium in Radioactive Transformations 
The process by which an element decays has 
already been discussed, but nothing has been said 
about the manner in which the resulting decay 
product builds up. For example, radium decays 
with a half-life of 1,590 years into its immediate 
decay product, radon, which has a half-life of only 
3.8 days. It is obvious that the rate at which 
radon will build up is a function not only of the 
70 RADIOLOGICAL SAFETY 
Figure 6-7.—A neutron-proton plot of the uranium series. 
71 RADIOLOGICAL SAFETY 
Table I.— The Uranium Series 
Element 
Symbols 
Half-life 
Particle emitted 
Type 
Range or energy 
S2U238 (UI) 
4.4X 10° years. _ . _ 
a 
2.67 cm. 
goTh234 (UX4) 
24.5 days . 
0.13 Mev. 
81 Pa234 (UX2) - 
1.14 minutes 
( r 
2.32 Mev. 
1 y 
0.80 Mev. 
Uranium 
92U234 (UII) 
3.4X105 years __ _ . 
3.23 cm. 
Thorium (Ionium) 
soTh230 (lo) 
8.3X104 years _ _ . 
3.2 cm. 
Radium 
88 Ra226 
1,590 years 
| a 
3.39 cm. 
1 y 
0.19 Mev. 
Radon 
86Rn222 
3.825 days _ 
4.08 cm. 
Polonium 
84Po218 (RaA)__ 
3.05 minutes 
4.69 cm. 
Lead 
82Pb214 (RaB) 
26.8 minutes 
f 
0.65 Mev. 
1 y 
f “ 
4.1 cm. 
Bismuth - - 
83Bi214 (RaC) 
19.7 minutes 
3.15 Mev. 
I y 
1.8 Mev. 
Polonium 
84Po214 (RaC') 
10~6seconds 
6 95 cm 
Thallium 
81T1210 (RaC") 
1.32 minutes 
1 80 Mev. 
Lead 
82Pb210 (RaD) 
22 years 
0.0255 Mev. 
1 y 
0.047 Mev. 
Bismuth 
saBi210 (RaE) 
5.0 days 
0- 
1.17 Mev. 
Polonium 
84Po210 (RaF) 
140 days 
1 y 
3.87 cm. 
Lead _ _ 
82Pb206 (RaG) 
Stable . _ 
Table II.— 
-Naturally radioactive light elements 
Element 
Isotope 
Half-life 
Type of 
emitter 
Potassium 
i.K* 
1.42 X 109 years 
P, y 
Rubidium 
37Rb87 
6.3 X 1010 years 
P 
Samarium _ _ 
62Sm148 
1.4 X 1010 years 
a 
Lutecium 
71 Lu176 
7.3 X 1010 years 
p 
-/V2=the number of radon atoms present at 
time t 
Then 
Xi7Vi=the number of radon atoms formed per 
second by decay, 
where 
Xi — decay constant of radium. 
Then 
X2A^2=the number of radon atoms decaying per 
second. 
Let 
AN2—the increase of radon atoms that occurs 
in time interval At. 
rate at which it is produced but also of the rate at 
which it decays. In considering this case, the 
problem is relatively simple, since the decay rate 
of radium is so slow that the number of radium 
atoms present at any time can be considered con- 
stant. Let 
iVi = the number of radium atoms at any time 
t. 
72 RADIOLOGICAL SAFETY 
Then 
AN2= (Ni\i—N2\2)At 
Upon integrating, and setting N2=0 when t=0, it 
follows that: 
the rate of decay of each daughter equals the rate 
of decay of the parent. Thus Eq. (12) can be 
written for the whole series 
\xNi = \2N2 = X3./V3=X4iV4 ... (13) 
Thus Eq. (12) can also be written 
N*_T2 
Nl~Tl (14) 
where T2 and Tx are respectively the half-lives of 
the daughter and parent element. From this 
relation, it is significant that if one knows the ratio 
of any two elements in a radioactive series, such 
as uranium and radium, and in addition if the 
half-life of one element is known, then the half- 
life of the other element can be calculated. For 
example, radium occurs in natural uranium ore 
in the proportion of 1 atom of radium to 2.86X106 
atoms of uranium. Since radium has a half-life 
of 1,590 years, then uranium must have a half-life 
equal to; 
Tv= 1590X2.86X106 years. 
= 4.5X 109 years 
This value is in good agreement with experi- 
mental determinations of the half-life made in 
other ways. In cases where the parent atom is 
short-lived compared with the decay rate of the 
daughter, the calculation is somewhat more com- 
plex. This case is treated in advanced texts 
(Rutherford, Chadwick, and Ellis—“Radiations 
from Radioactive Substances”) to which the 
reader is referred. 
Since the age of the earth is estimated to be 
about 2.5X109 years, all radioactive elements 
which occur in nature must have half-lives of the 
order of 108 years, or they must otherwise be 
decay products of parents having half-lives of 108 
years. On this basis more than one-quarter of 
the U238, with a half-life of 4.5X109 years, has 
disappeared since the earth was created. 
The curie, the unit of intensity for measure- 
ment of radioactivity, has been defined as that 
activity due to 3.7 X1010 disintegrations per 
second. It was originally defined as the activity 
of that amount of radon which was in equilibrium 
with 1 gram of radium. At equilibrium condi- 
tions, both radium and radon decay at the rate of 
Figure 6-8.—Growth curve for a radioisotope 
This equation is plotted in Figure 6—8 to illus- 
trate the way in which the new atoms of radon 
build up to an equilibrium value. This simply 
means that the radon is disintegrating at the same 
rate that it is being formed. Radon, which in a 
more general terminology would be called the 
daughter, is present in a constant ratio to the 
amount of the parent radium present. Equilib- 
rium will be reached for a theoretical value of 
t equal to infinity. This causes the exponential 
term in Eq. (11) to drop out, leaving 
(£) (12) 
Radium is usually used in the form of a salt, 
generally as the chloride or bromide. A radium 
salt, freshly recrystallized to remove its decay 
products, shows little activity, for in its pure initial 
state in which no radon is present it emits only 
a-particles with a half-life of 1,590 years. As illus- 
trated earlier, this would mean that it would be 
emitting only 3.7X1010 a-particles per second. 
When radium is in equilibrium with its decay 
products, it emits four times as many a-particles, 
actually 14.8 X1010 a-particles per second. The 
radon disintegrates- to form a daughter isotope, 
RaA, and the whole series of transmutations fol- 
lows. The relation between radon and RaA is 
similar to that between radium and radon, for 
73 RADIOLOGICAL SAFETY 
3.7X1010 disintegrations per second so that both 
definitions are equivalent. 
In specifying the activity of any substance, it 
is customary to refer to the number of atoms of 
the substance disintegrating per second even 
though it may not bo an a-emitter. 
The roentgen has already been defined as the 
amount of radiation which produces 1 electro- 
static unit of ions in 1 cubic centimeter of air 
under standard conditions of temperature and 
pressure. Thus the roentgen unit is a measure 
of the ionization produced by X- or y-radiation in 
a given sample of air, while the curio is a measure 
of the rate of emission of radiation by a radio- 
active source. 
The roentgen unit applies only to electromag- 
netic radiation, and the curie is only a measure of 
the number of emissions with no reference to the 
energy of the radiations. It is obviously desir- 
able to have a unit which will express both the 
number and the energy of radiated particles or 
quanta. 
It can be shown easily that the definition of the 
roentgen unit is equivalent to requiring that 
1.6 X1012 ion pairs be produced in one gram of air 
under standard conditions. A national extension 
of this definition is the roentgen equivalent physical 
{rep). One rep is that quantity of ionizing radia- 
tion which is capable of producing 1.6 X 1012 ion 
pairs per gram of air. 
Some radiations have an effect on biological 
tissue out of proportion to the amount of ioniza- 
tion produced, and consequently another unit of 
biological effectiveness is introduced. The roentgen 
equivalent man (rem) is that quantity of radiation 
which when absorbed by man produces an effect 
equivalent to the absorption by man of one roent- 
gen of X— or y — radiation. For example if a 
given flux of neutrons resulted in the production 
of 1,6 X 1012 ion pairs per gram but produced a 
biological effect equal to 5 r of gamma rays, 1 rep 
(neutrons) would equal 5 rem. 
6.09 Equivalence of Mass and Energy 
In Section 6.07 several nuclear reaction equa- 
tions were used to describe the emission of 
a-particlcs from nuclei. In each equation, a 
term Q was used to take care of the energy carried 
away by the high speed a-particles and the re- 
coiling nucleus. In the case of an a-particle 
emitted by radium, the a-particle leaves the 
nucleus with 4.79 Mev of kinetic energy. What 
is the source of this exceedingly high energy? 
To answer this question and to prepare the ground 
for the next section on the theory of a-emission, 
this section is devoted to a brief discussion of the 
equivalence of mass and energy. 
Early in this century, Einstein resolved certain 
difficulties which were inherent in classical theories 
of mechanics and electrodynamics by proposing a 
radically new approach to the problems. Einstein 
set forth in his now famous theory of special rela- 
tivity that the mass and energy of any physical 
system arc related by the equation: 
E=mc2 (15) 
where 
E is the energy of the system 
m is its inertial mass 
and 
c is the velocity of light. 
This equation states that any body having an 
inertial mass m also has a total associated energy 
E given by the product of its mass multiplied by 
the square of the velocity of light. On the basis 
of this concept, a 1 gram mass of an element is 
equivalent to an energy of 
E= 1 (aXlO^-OXlO20 ergs 
and since 1 erg = 2.78X 10“14 kilowatt hours 
£'=25,000,000 kilowatt hours. 
On the face of it, this seems absurd for 1 gram of 
an element to be equivalent to 25 million kw. hr., 
for this is truly an enormous amount of energy. 
In thermal units, it is equal to 85 billion b.t.u. or 
2IX1012 calories of heat energy. 
A similar calculation applied to the energy 
content of a single hydrogen atom shows that it is 
equivalent to 931 Mev of energy. However, Eq. 
(15) docs not state that the energy E is releasable; 
all that it states is that if all the mass (m) could be 
somehow converted into energy, then the quantity 
me2 of energy would be released. To appreciate 
the fact that an extremely small change in mass 
of a system produces a very large change in 
energy, consider first the combustion of coal. 
This chemical reaction is written simply as: 
C+02 >CO 2+Q (16) 
where 
$=the thermal energy released. 
74 RADIOLOGICAL SAFETY 
If 1 pound of carbon burns completely to form the 
single end-product carbon dioxide, it is known tha t 
Q=about 4 kilowatt hours of energy (in the form 
of heat); 3.67 pounds of C02 result from the 
chemical reaction, and in comparison with this 
amount of material, the mass equivalent of 4 kw.- 
hr. of energy is exceedingly small, being only 
3.7X 10~10 pounds. Therefore, in order to detect 
the change in mass in this reaction, one would 
have to measure 3.7X10-10 lbs. in a 3.67-pound 
total sample. Weighing to an accuracy of 1 part 
in 1010 is beyond our present means of chemical 
analysis. In fact, the most sensitive micro- 
balance can measure about 1 part in 107, so that 
it is not possible to measure the mass difference 
between the elements on the left-hand side of 
Eq. (16) and that on the right. This statement is 
equally true for any purely chemical reaction, for 
the reaction which has been discussed is an 
extremely energetic chemical reaction. The mass 
change is so small as to be a thousand times too 
slight to detect with even the best micro-balances. 
When nuclear reactions are considered, the 
situation is quite different. The energy released 
is many fold larger than that liberated in a chemi- 
cal reaction. In the chemical burning of 1 atom 
of carbon, about 1 electron volt of energy is 
released, whereas in the emission of an a-particle 
from radium, 4.8 Mev are released. Thus, per 
atom of carbon, nearly 5 million times more 
energy and more mass are released. Now 4.8 
Mev of energy is equivalent to a mass of 8.6X 10~27 
grams. A single radium atom weighs about 
3.6X10~22 grams, so that it should be possible to 
measure the loss in mass that occurs in the reaction 
given by: 
S6Ra226 > S4Rn222-f2He4-f- Q 
The ratio of mass lost to original mass is 1 to 
40,000. Through the use of mass spectrographs, 
mass differences as small as 1 part in 40,000 can 
be measured, and it found that the Einstein mass 
energy relation is verified. 
6.10 Nuclear Binding Energy 
The exact measurement of nuclear masses with 
mass spectrometric equipment makes it possible 
to calculate the energy with which nuclei are 
bound together. Consider any nucleus of mass M 
(accurately measured) which contains N neutrons 
and P protons. Both the mass of the neutron 
(mn) and that of the proton (mP) have been 
accurately measured and are known to be: 
mn= 1.00893 m.u. (atomic mass units) 
mp= 1.00813 m u 
But, by definition, the atomic mass unit is a 
mass equal to 1/16th of the mass of the 8016 
isotope. 1 mass unit equals 1.67X10~24g. Sup- 
pose that one calculates what the mass of this 
nucleus should be if it is simply the sum of the 
masses of the individual neutrons and protons 
inside the nucleus. Let this value to be calcu- 
ated be W then 
W=Nmn+Pmv (17) 
From the Einstein equation, it follows that the 
total energy associated with this mass is obtained 
by multiplying the right hand side of the equation 
by the factor c2. 
To illustrate the application of Eq. (17), let 
N—2 and P=2 so that the value calculated is W; 
i. e., the theoretical mass of the two neutrons and 
two protons which make up an a-particle. 
W=2 (1.00893)+2 (1.00813) 
= 4.03412 mass units. 
The mass spectrographic value for the observed 
mass M of the helium nucleus is 
M=4.00389 mass units 
The difference in mass (AM) between the observed 
and calculated value is 
AM= IF-M= 0.03023 m.u. 
By previous definition, this quantity AM is called 
the mass defect. Since 1 mass unit is the equiva- 
lent of 931 Mev, the mass defect for a helium nu- 
cleus is (0.03023) X (931 Mev) =28.1 Mev. In 
other words, if one were to synthesize a helium 
nucleus by some imaginary process using 2 neu- 
trons and 2 protons, the resulting nucleus would 
be lighter than the total mass of the original 
particles by 0.03 mass units, which has disappeared 
to form 28 Mev. The mass which has been lost 
in the reaction when converted into energy units 
is called the binding energy of the nucleus. Table 
III lists the atomic masses which have been 
measured for some of the lighter elements. Other 
quantities listed are the mass defects, binding 
75 RADIOLOGICAL SAFETY 
energies, and binding energy per nuclear particle. 
A further discussion of the binding energy per 
nuclear particle is postponed to Chapters 7 and 8. 
The fact that 28 Mev of energy is liberated in the 
imaginary fusing together of 2 neutrons and 2 
protons to form a stable helium nucleus implies 
that if this stable assembly of particles is to be 
smashed up into its separate components, then 
energy must be supplied to the nucleus from some 
outside source. The reason why energy must be 
added to a nucleus in order to disrupt it is that 
the neutrons and protons within the nucleus 
stick together, each nucleon being bound to the 
system by an energy which is about 8 Mev for 
most nuclei. What, then, is the physical nature 
of the nuclear forces which bind nucleons together? 
gravitational. Now the gravitational force be- 
tween two particles mn and mv (neutron and proton 
as in the deuterium nucleus) separated by a dis- 
tance r is given by 
F=G7rbprL (18) 
where G is the gravitational constant and is = 6.66 
X10-8 gram-1 cm3 sec-2. Here the force would 
be an attractive one, but for a value of r=10-13 
cms., which is a typical separation for nucleons, 
the force between a neutron and proton is ex- 
tremely small. Actually the force is about 1038 
times less than that required to account for the 
observed binding energy of the deuteron. 
Since neither of these assumptions lead to a 
solution of the problem, it is necessary to assume 
that nuclear forces are of a new type not previously 
found in physics. From experimental data cer- 
tain characteristics of this new type of force are 
known. These are: 
(a) The force is always attractive. 
(b) It does not depend on the nature of the 
nucleon, i. e., whether it is a neutron or 
proton. 
(c) Its range is very short, of the order of 
10-13 cms. 
(d) Nuclear forces show a saturation effect. 
According to the second characteristic, the force 
which binds a neutron to a proton or a proton to 
another proton is about the same in magnitude. 
The force between a neutron and another neutron, 
called the neutron-neutron force, is also about the 
same as the neutron-proton force. The third 
characteristic is perhaps the most striking. Up 
to a distance of about 10-13 cms. the nuclear force 
has a constant value; beyond this critical dis- 
tance, the force drops rapidly in value to zero. 
In this respect, the nuclear force differs from the 
coulomb force, which obeys an inverse square law 
and always has a non-zero value. The last char- 
acteristic of a nuclear force, namely, the satura- 
tion property, is very important. It can be ex- 
plained in terms of a pairing of nucleons within 
the nucleus. That is, each tends to pair off with 
another nucleon, so that it effectively exerts a 
force only within a small group of nucleons. This 
surprising characteristic of a nuclear force ac- 
counts for the fact that no isotope of mass num- 
ber 5 exists in nature. The four nucleons making 
Table III.—Binding energies for light elements 
Stable atom 
Atomic mass 
(in mass units) 
Mass defect 
A M 
Binding 
energy 
B M€T 
Binding 
energy per 
particle 
BEPPMev 
1. 00893 
iH1 
1. 00813 
iH» 
2. 01473 
0. 00233 
2. 17 
2. 17 
2He3 
3. 01698 
. 00821 
7. 72 
2. 58 
2He4 
4. 00389 
. 03022 
28. 1 
7. 03 
3Lifi 
6. 01686 
. 03432 
32. 3 
5. 40 
3lf 
7. 01818 
. 04191 
39. 0 
5. 57 
4Be® 
9. 01504 
. 06213 
58. 6 
6. 51 
5b>» 
10. 01631 
. 06899 
64. 8 
6. 48 
8B“ 
10. 01292 
. 08131 
71. 6 
6. 50 
6C12 
12. 00398 
. 09834 
91. 6 
7. 63 
,C13 
13. 00761 
. 10368 
96. 5 
7. 42 
8o>« 
16. 00000 
. 13642 
127. 0 
7. 94 
ioNe22 
21. 99864 
. 18975 
176. 7 
8. 03 
uNa23 
22. 99680 
. 19971 
185. 9 
8. 08 
,8S33 
32. 98260 
. 29916 
278. 5 
8. 44 
17 Cl35 
34. 98107 
. 31776 
295. 8 
8. 45 
6.11 Nuclear Forces 
On the basis of the laws of physics which have 
been discussed up to now, one might attempt to 
explain nuclear forces in either of two ways. 
First, it might be assumed that the forces are 
coulomb or electric forces. However, such an 
assumption only illustrates that the nucleus should 
not be bound together at all, for the only charged 
particles in the nucleus are protons, and these 
being of like charge and close together would repel 
each other and constitute a disruptive force. 
Second, it might be assumed that the forces are 
76 RADIOLOGICAL SAFETY 
up a helium nucleus form a closed system in 
which each nucleon is fully saturated with respect 
to its interaction with the other three nucleons. 
As a result, these nucleons do not attract an ad- 
ditional neutron or proton to form an isotope of 
mass 5. Isotopes of mass 6 and higher exist be- 
cause these nuclei do not contain a subnuclear 
system having the configuration of a helium 
nucleus. Thus, 3Li6 is not a system composed of 
1 a-particle, 1 neutron and 1 proton. It is, in- 
stead, a system of 3 neutrons and 3 protons, all 
of which interact and exhibit saturation. 
If the nucleons did not exhibit saturation, the 
binding energy of a nucleus would be proportional 
to the square of the total number of nucleons 
within it. This is not the case for 3Li6 nor for 
heavier isotopes. Another way of looking at the 
phenomenon is to point out that the additional 
neutron which one would like to add to the 
2IIe4 nucleus is forbidden from occupying the same 
virtual orbit within the nucleus as the other four 
nucleons because these orbits, analogous to 
electronic orbits, have a definite upper limit to 
the number of occupants they can tolerate. 
Consequently the additional nucleon must go into 
an orbit which is so far removed from the others 
that the short range nuclear force is not effective 
and the nucleon is not bound to the other four 
particles. 
Just as Bohr developed the concept of atomic 
structure, he likewise advanced a model of nuclear 
structure. Basing his ideas on the characteristics 
of nuclear force as they are outlined above and upon 
the fact that only certain ratios of neutrons to 
protons are allowed for stable atoms, Bohr 
proposed that the nucleus could be thought of as 
a compact aggregation of nucleons, all in a constant 
state of motion and yet restricted to motion 
within the confines of a sphere of small radius. 
On this model, the nucleus corresponds to a small 
sphere of liquid, the constituents of which are 
nucleons which are fairly uniformly distributed 
throughout the sphere. For this reason, the Bohr 
model of the nucleus has been called the liquid drop 
model. Since the nucleons move with high speed 
within the nucleus and since this nucleus is extreme- 
ly small in diameter, these particles make many 
collisions per second, and all tend to have the 
same average energy. It is therefore easy to see 
that the nucleus has a uniform density. 
The short range nuclear forces which have been 
introduced into the discussion are known in 
quantum mechanics as resonance or exchange 
forces. These forces are not well understood, and 
much of the current research in physics is directed 
toward understanding the nature of the neutron- 
proton interaction. 
It should be realized that the coulomb forces 
of the protons continue to act even though they 
are in the nucleus. One can picture the process 
as a superposition of the coulomb field on the 
nuclear force field. Thus the presence of a large 
number of protons in a nucleus, as in heavy nuclei, 
presents a repulsive force which tends to disrupt 
the entire nucleus. It is for this reason that the 
heavy stable isotopes have more neutrons than 
protons in their nuclei. The number of neutrons 
which can be added to nuclei is limited by an ex- 
clusion principle which requires that such addi- 
tional particles go into higher nuclear orbits where 
the short-range force of nucleons is not effective. 
These two factors make the shape of the stability 
curve (shown in fig. 5-23) understandable. 
6.12 Nuclear Potential Barriers 
While the foregoing section has involved a dis- 
cussion of nuclear forces, it would have been 
equally suitable to carry out the discussion using 
the concept of potential energy rather than force. 
The forces may be derived from the mutual poten- 
tial energies of particles in a system. (See fig. 
6-9.) 
Figure 6-9.—Potential energy curve for a nucleus. 
77 RADIOLOGICAL SAFETY 
There is sketched a potential energy V curve for 
a nucleus as a function of the distance r from the 
center of the nucleus. At large distances, actu- 
ally for any value of where a is the nuclear 
radius, the potential obeys the usual l/r law. At 
a distance r=a or for any value of r<a, nuclear 
forces are effective, and the potential energy drops 
to a constant value = —K independent of the 
value of r<a. In the sketch this is shown as a 
potential well. For light nuclei, this potential 
well lies so low that it has a negative potential 
energy value. Let Fmax be the potential corres- 
ponding to the height or maximum value of the 
potential harrier. For any two charged particles 
which form a system, the value of Fmax depends on 
the nature of the two particles. For example, for 
two light particles, such as two deuterons, the 
barrier is only a few tenths Mev, whereas for 
heavier nuclei, 7max may be larger than several 
Mev. The concept of a potential barrier may be 
used in considering how two isolated particles will 
interact when brought close together; or it may 
be used in analyzing the resistance of a single 
system to disruption. In chapter 8, the former 
type of reaction will be discussed while the latter 
type of reaction will be described now. 
6.13 The Theory of Alpha Emission 
Figure 6-10 shows the potential energy distribu- 
tion for a radium nucleus. Now consider the 
process by which an a-particle is ejected to form 
the daughter atom radon. If the a-particle were 
at a distance, say, r=h, away from the center 
of the nucleus, then it would be repelled. For r 
equal to the nuclear radius a and for smaller 
values of r, the a-particles will be held within the 
nucleus. Suppose that inside the nucleus, the 
a-particle has a potential energy V~Va as indi- 
cated by the dashed horizontal line. It is obvious 
that while the a-particle is inside, it possesses a 
potential energy which is greater than that at any 
value of c. This statement is true for at any 
value of the a-particle is outside the nucleus 
and is experimentally observed to travel with con- 
siderable kinetic energy. This could only have 
been gained from the potential energy which the 
a-particle had in the nucleus. However, in order 
for the a-particle to escape, it must somehow or 
other get over the potential barrier. 
From the standpoint of classical physics, the 
a-particle is doomed to spend an eternity trapped 
within the potential barrier for there is no means 
by which it can spontaneously acquire enough 
energy to hurdle the potential barrier. Thus 
classical physics offers no explanation of spon- 
taneous or natural emission of a-particles. 
Modern physics, as exemplified by wave me- 
chanics offers a solution to this impasse. It takes 
account of the wave nature of the a-particle and 
shows that there is a small but finite probability 
that the a-particle may leak through the- potential 
barrier. The theory as developed independently 
by Gamow, and by Condon and Gurney, even 
calculates the average time required for the a- 
particle to penetrate a given potential barrier. 
These calculated times are in fair agreement with 
the observed half-lives of a-emitters. The theory 
further states that the time which the a-particle 
will take to leak out through a given barrier 
depends very critically upon the height (Fnjax) of 
the potential barrier. It is beyond the scope of 
this manual to present more detailed treatment of 
the theory of a-emission. Such a treatment may 
be found in Gamow’s “Atomic Nuclei and Nuclear 
Transformations.” One of the notable successes 
of the theory is that it accounts for the extreme 
range of half-lives which are found in nature and 
in fact shows that the disintegration constant of 
an a-emitter is simply related to the range or 
energy of the emitted particle. In 1911, two 
physicists, Geiger and Nuttall found that the 
Figure 6-10.—Potential barrier for radium. 
78 RADIOLOGICAL SAFETY 
range R of an a-particle is related to its dis- 
integration constant X as follows: 
log R=A+B log X (19) 
where A and B are constants. 
According to this relation, a-emitters which have 
the longest half-lives emit a-particles of the 
shortest range. For example, an a-emitter which 
emits a-particles of 1 cm range has a half-life of 
about 2X1011 years. Such an element emits 
particles so infrequently it may almost be re- 
garded as completely stable. On the other hand, 
a-emitters giving off particles of 6 cm range in air 
(about 7 Mev) have half-lives about 10~3 seconds. 
The Geiger-Nuttall relation is plotted in figure 6- 
11 where it is seen that members of each radio- 
active series fall on a straight line. 
the usual range of a-particles in centimeters of 
air, for in general these devices are operated with 
a gas not much different from air and at approxi- 
mately atmospheric pressure. When ranges in 
air are given, it is understood to mean air under 
standard conditions (0° C. and 760 mm. pressure). 
Figure 6-13 shows the experimentally obtained 
relation between the range of a-particles in air 
and the corresponding energy of the particles. 
For low energies, this curve corresponds to a 
Figure 6-12.—Alpha particle tracks in a Wilson cloud 
chamber. 
Figure 6-11.—Geiger-Nuttall relation for the three 
radioactive series. 
6.14 Absorption of Alpha Particles 
Certain rather general properties of a-particles 
have already been mentioned; it remains to de- 
velop a more detailed picture of the interaction of 
a-particles with matter, to discuss the mechanism 
by which a-particles lose energy, and to examine 
in detail some aspects of a-particle spectra. 
(a) Range in air and in tissue.—Wilson cloud 
chamber photographs of a-particles (see fig. 6-12) 
show that for any given a-emitter, the alpha 
tracks observed are usually very straight, heavily 
ionized tracks characterized by a definite range. 
Tracks as seen in a cloud chamber correspond to 
Figure 6-13.—Range vs. Energy curve for alpha particles 
in air. 
79 RADIOLOGICAL SAFETY 
plot of the function R=aE312, where a is a con- 
stant and E is the energy of the a-particle. At 
high energies the range deviates from the 3/2 
power law. From it, a 5 Mev a-particle is seen 
to have a range of 3.5 cms. of air. The range of 
a-particles when given in terms of centimeters of 
air is far greater than the distance these same 
particles would travel in human tissue. As an 
example, consider the range in tissue of a 5 Mev 
a-particle. Now since human tissue has a density 
of about 1, the range in it can be obtained by 
multiplying the range of the particle in air by the 
density of air. This follows from the relation 
R&\r X X Ptlssue 
(20) 
where p refers to the density of the absorber. 
Thus a simpler equation results by taking the 
approximate value of the density of tissue and 
substituting it in Eq. (20). 
#ti8sue=0.00129 R (21) 
Here the symbol R has been substituted for Ralr 
since the two are synonymous, and the density of 
air has been taken as 0.00129 gms/cc. Therefore 
a 5 Mev a-particle has a range in tissue of 
(0.00129) (3.5) = 0.0045 cms. It is customary to 
express this range, since it is so small, in other 
units of length, namely, in microns. A micron 
(n) equals 0.0001 cms (10~4 cms), and thus a 5 
Mev a-particle has a range of 45n in human tis- 
sue. Even the most energetic alphas cannot pene- 
trate more than 70p into tissue. This should not 
be interpreted as meaning that a-particles are inef- 
fective in producing biological changes in tissue. 
On the contrary, since these particles expend all 
of their enormous energy in such a localized section 
of tissue, they may produce very significant bio- 
logical effects. As will be shown in chapter 13, 
the danger from a-particles is acute when a-emit- 
ters are taken into the human body (by ingestion, 
inhalation, or incision). 
(b) Alpha particle spectra.— Just as a mass spec- 
trograph may be used to sort out and identify the 
isotopes of an element, likewise a spectrograph of 
similar design may be used to sort out the a-par- 
ticles emitted from any isotope. When this is 
done, it is found that some a-emitters may give 
off groups of a-particles, each of which has a dis- 
crete range (energy). In general, an a-emitter 
gives off one group of a-particles with greatest 
intensity and emits a low intensity of other groups 
of different energy. ThC", for example, emits 
seven a-particle lines or groups. For a long time, 
polonium was thought to emit monoenergetic al- 
phas of 5.3 Mev, but careful investigation has 
shown that it probably emits at least 12 lines or 
discrete groups. These have, however, very weak 
intensities compared with the principal group, 
which has 5.30 Mev energy, and is emitted with 
intensity about 5,000 times larger than that of 
any other polonium group. The a-particle spec- 
tra are important in that they reveal the existence 
of discrete energy states or levels within the 
nucleus. This point will be amplified in discussing 
the origin of nuclear 7-rays (sec. 6.17). 
(c) The interaction oj alpha particles with mat- 
ter.—Cloud chamber photographs show that 
a-particles produce dense ionization along their 
tracks. As the relatively massive, doubly-charged 
a-particle passes through the atoms of a gas, it 
makes frequent collisions with the outer, loosely 
bound electrons of the gas atoms. The electric 
field of the a-particles sweeps across the outer 
electrons, accelerates them, and pulls many of 
them from their shells. Thus many gas atoms 
are ionized. This process of ionization results 
in a detached electron and an ionized gas atom 
(an ion-pair). In the process of ionization, the 
a-particle has to supply energy to the gas atoms 
to cause an ion pair to be formed. On an aver- 
age, this process requires about 33 electron volts 
per ion pair formed. In addition to energy lost 
by ionization, the a-particle also yields energy 
to neutral gas atoms by excitation. That is, it 
causes electronic transitions which are not suffi- 
cient to allow the electron to escape from its atom. 
By these processes, the a-particle continues to 
lose energy, and thus it is slowed down. As it 
slows down, the a-particle spends more time in 
the vicinity of any gas atom and consequently 
it has a higher probability of ionizing more and 
more atoms. If one defines the number of ion 
pairs formed per centimeter of air as the specific 
ionization, it follows that this quantity should be 
fairly constant when the a-particle is moving 
with high energy, but it should increase as the 
a-particle slows down to low energies. 
By merely counting the separate droplets along 
the track of an a-particle in a cloud chamber 
picture, one may determine the specific ioniza- 
tion of the particle. In figure 6-14, there is 
80 RADIOLOGICAL SAFETY 
point C. Accordingly, it becomes a question as 
to what one should accept as the true range for 
a-particles. This is a question of more concern 
to physicists than it is for practical considerations, 
and the reader is referred to any advanced text 
for a discussion of the problem. 
6.1 5 The Theory of Beta-Decay 
It has already been mentioned that /3-particles 
emitted from nuclei show a continuous energy 
distribution. Such an energy distribution is il- 
lustrated in figure 6-16 for /3-particles emitted by 
Figure 6-14.—Specific ionization vs. distance for alpha 
particles from radium C. 
shown a curve obtained for the specific ionization 
of a particles from RaC as a function of the dis- 
tance along the track of the particle. Within a 
few mms. of the end of its range the specific ioni- 
zation drops very rapidly to zero. 
If a monoenergetic group of a-particles is care- 
fully studied, it will be noticed that while the 
group has a fairly definite range, there will be 
some alphas which have a shorter and others 
longer range than the average range for the 
group. This phenomenon is illustrated in figure 
6-15. Here, it is seen that if all the alpha par- 
ticles had the same range R, the number of alphas 
as a function of range would be constant and then 
break sharply at a value of the range =R‘, in 
other words it would follow the dotted curve at 
A. Actually the curve breaks before the point R, 
bending gradually at B and extending past R to 
Figure 6-16.—Energy distribution of 
beta particles. 
RaE. Other /3-emitters show similar continuous 
spectra, except that each has a characteristic 
value of Emax which is sometimes called the end 
point energy. This is the value usually given in 
tables of /3-particle energies. Experiments have 
shown that /3-decay involves only one /3-particle 
per nuclear disintegration. 
Any attempt to explain the emission of /3- 
particles from the nucleus with a continuous 
energy distribution must satisfactorily explain not 
only the end point energy Em&x but it must also 
account for the half-life of the decay process and 
predict the general form of the energy distribution 
curve. If one were to assume that the process of 
/3-decay is similar to that of a-decay, then one 
would have monoenergetic /3-particles or groups 
of such particles leaving the nuclei. One might 
conceivably argue that such is the case and that 
these monoenergetic particles are converted into 
a continuous spectrum of rays by losing energy 
outside the nucleus by interaction with the orbi- 
tal electrons. However, it can be demonstrated 
Figure 6-15.—Straggling of alpha particles. 
81 RADIOLOGICAL SAFETY 
that such a conversion to a continuous spectrum 
is not possible. 
It is inconsistent with our knowledge of mod- 
ern physics to postulate the existence of electrons 
within the nucleus prior to decay. In the case 
of a-emission, this was not true, for it was shown 
that the saturation character of nuclear forces 
leads to a stable configuration of two neutrons 
and two protons which can be tolerated within 
the nucleus. How then can one reconcile the 
emission of /3-particles from the nucleus, if they 
are not allowed to exist there? One must assume 
that when /8-decay occurs, the electron is created 
and leaves the nucleus. Thus the /3-particles 
would have the same type of virtual existence 
within the nucleus as does the X-ray photon in 
the atom prior to its emission therefrom. 
One conceives of the nuclear process whereby 
/3-particles are created as being a break-up of a 
nuclear neutron into a proton and an electron. 
on1—+ (22) 
Such a creation process is indicated in the sub- 
nuclear reaction equation. In such a reaction 
the electron is assumed to have negligible mass. 
Since this reaction leaves the resulting nucleus 
with an additional +1 charge, it satisfies the 
requirement that /3-decay changes the parent 
nucleus into a daughter with an increased nuclear 
charge of 1. 
Even with such a creation process, there is still 
the difficulty of explaining the continuous energy 
spectrum of the /3-particles. The assumption 
that the /3-particle originates from the sub- 
nuclear conversion of a neutron into a proton 
explains the existence of the electron but fails to 
endow it with a continouus energy distribution. 
Supposing that a /3-particle of any energy Ex is 
emitted by a nucleus whose /3-particle upper 
energy limit is Em&x. This is illustrated dia- 
gramatically in figure 6-17. Then the /3-particle 
carries away from the nucleus energy equal to Ex. 
It must be assumed that each /3-decay process 
releases energy equal to Em&x and therefore it is 
clear that an amount of energy E=Em&x — El is 
unexplained. Now one can perhaps question 
whether or not both energy and momentum are 
conserved in the process of /3-decay, but the con- 
servation laws are so all embracing in their range 
of validity that it is difficult to assume that the 
Figure 6-17.—Energy relations in beta emission. 
laws do not apply here. As an alternative 
hypothesis, the theoretical physicist, Pauli, sug- 
gested that a new type of particle, the neutrino, is 
involved in the /3-decay mechanism. He assumed 
that the neutrino is a fundamental particle of 
very small mass and electrically neutral. When 
the /3-particle is created, a neutrino is simulta- 
neously produced and carries away the energy 
AE which is not given to the /3-particle. Thus 
the creation equation, Eq. (22) should be rewrit- 
ten as: 
oW1—>ip]Tie°-f-o*?° (23) 
where 0r]° is the symbol for the neutrino. 
By virtue of its peculiar properties, no charge 
and practically zero mass, the neutrino is an 
extremely elusive particle, and the chief evidence 
for its existence is theoretical in nature.1 
Two theories of /3-decay have received most 
attention from the scientific world. One was 
proposed by Enrico Fermi and the other by 
Konopinski and Uhlenbeck. Both theories pre- 
dict continuous /3-particle spectra which agree 
lairly well with observations. Fermi has deduced 
that the maximum energy Fmax emitted in /3- 
decay is related to the decay constant by the 
following equation: 
\=kE*„ (24) 
where the constant k has slightly different values 
for different nuclei. This equation is often called 
the Fermi relation. Sargent had found the same 
relation empirically prior to its deduction on a 
theoretical basis. A plot of log£’max against 
1 Certain experiments have been reported which give about the best 
experimental indication for the existence of neutrinos. The reader is referred 
to a paper by H. R. Crane and J. Halpern, “Physical Review” S3,789 (1938). 
82 RADIOLOGICAL SAFETY 
log X where X is the disintegration constant for 
p-dec&y, is called a Sargent diagram and is 
shown in figure 6-18. 
versus energy curves, it is advantageous to discuss 
the mechanism by which electrons are slowed 
down in passing through matter. 
When a high energy electron passes close to a 
nucleus and interacts with the nuclear field, it 
undergoes acceleration. The laws of electro- 
dynamics require that an electric charge radiate 
energy when it is accelerated. Thus when the 
electron makes such a “virtual” collision with a 
nucleus, it radiates a quantum of energy. This 
quantum will be emitted with a frequency which 
depends upon the energy of the incident /3-particles 
and upon the closeness of the collision. Such 
processes are known as radiative collisions and also 
as hremsstrahlung processes. The latter term is a 
German word meaning “braking radiation.” 
When a /3-particle makes a similar collision with 
an orbital electron, it does not undergo a similar 
reaction. However, at much higher energies 
(>107ev.) /3-particles do react with orbital elec- 
trons in directed collisions and transfer most of 
their energy into what are called knock-on elec- 
trons. Such processes need not enter into con- 
sideration here. 
For lower energies, the /S-particle loses energy 
by the conventional process of ionization (collision 
loss). In this process, as was the case for a-par- 
ticle ionization, the electric field of the /3-particle 
pulls electrons from their shells, thus causing 
ionization. It can be shown that the ionization 
loss which atoms suffer in this way depends upon 
the square of the charge which the incident 
particle carries. Thus an a-particle has four 
times the ionizing power of a /3-particle of the same 
velocity. 
In general, radiative losses suffered by electrons 
arc less than ordinary collision losses. For higher 
energies and heavier elements, the radiative proc- 
ess becomes more important in absorbing electrons. 
The deflection or elastic scattering of electrons 
is important for many nuclear experiments. It is 
found that in traversing a thickness t of an element 
of atomic number Z, the angle through which the 
electron is deflected away from its original path 
varies as the square root of t, and for any scatter- 
ing angle, the intensity is proportional to Z2. 
Elastic scattering occurs as a result of /3-particles 
interacting with nuclei as well as with orbital 
electrons. In materials of very low atomic 
number, elastic scattering is roughly the same for 
Figure 6-18.—A Sargent diagram. 
6.16 The Absorption of /3-Porticlcs 
Beta particles are far more penetrating than 
a-particles. WThile our discussion of a-particle ab- 
sorption was limited principally to gases, the 
following discussion will be concerned both with 
gases and solids. Whereas an a-particle of several 
Mev energy has a specific ionization of several 
thousand ion pairs per centimeter of air, a /3-par- 
ticle of the same energy produces only a few ion 
pairs per cm. One reason for this is that for the 
same energy, say 3 Mev, a /3-particle travels with 
about 99 percent the speed of light c, while an 
a-particle of the same energy has a velocity of 
only 4 or 5 percent of c. It is therefore necessary 
to examine phenomena of /3-particle absorption in 
detail just as was done in the case of a-particle 
absorption. 
(a) Interaction of /3-particles with matter.—In 
dealing with the absorption of /3-radiation from a 
pure /3-emitter where a continuous spectrum is in- 
volved, it is apparent that the problem of relating 
range to energy will not be as simple as it was for 
a-particles. Furthermore, cloud chamber pictures 
of /3-particles show they do not travel in straight 
lines as do alphas but rather they are subject 
to many deflections and as a result, the /3-particles 
may pursue a more or less tortuous, random path. 
When combined these effects yield an absorption 
curve which looks somewhat like an exponential 
curve (see subsec. (6)), Before presenting range 
83 
7746H9 O - 48 7 RADIOLOGICAL SAFETY 
both processes, whereas for heavy elements 
nuclear scattering is by far the more important 
process, often 100 times as large. Elastic 
scattering should not be confused with the radi- 
ative collision process which is an inelastic scatter- 
ing taking place at high energy. 
(6) Range of (3-particles in matter.—The range 
in air of (3-particles may be plotted as a function 
of energy, just as was done for a-particles. Such 
a plot is given in figure 6-19. 
Figure 6-20.—Range vs. Energy plot for beta particles 
Figure 6-19.—Range vs. Energy plot for beta particles 
in air. 
Thus a (8-particle having an energy of 2 Mev has 
a range of over 8 meters in normal air. Since 
/3-particle absorption is independent of the mate- 
rial of the absorber, it is customary to express the 
range in grams/cm2 of the absorbent. Figure 
6-20 gives the range-energy plot where the range 
is expressed in gm/cm2. At low energies the 
ionization losses and elastic scattering are very 
large, and the curve departs from the linearity 
which is exhibited at higher energies. 
A typical absorption curve for primary (3-emis- 
sion is given in figure 6-21. The word primary 
will be used for (3-particles of continuous energy 
distribution. The intensity falls off sharply for 
small thicknesses of absorber, since the low energy 
(3-particles are rapidly absorbed. Thereafter, the 
Figure 6-21.—A typical absorption curve for primary beta 
particles. 
curve is fairly well represented by the exponential 
where p is the linear absorption 
coefficient. If the absorber has a density—p 
then the quantity is called the mass 
absorption coefficient. This coefficient pm is 
roughly independent of the atomic number Z 
of the absorbing element. Actually pm increases 
slightly with larger values of Z, but for practical 
84 RADIOLOGICAL SAFETY 
purposes it may be regarded as a constant. The 
point on the abscissa of figure 6-21 corresponding 
to zero intensity is called the maximum range of 
the /3-particle and is an important experimental 
quantity. A rough estimate of the absorbing 
thickness or range of /3-particles in any material 
may be obtained from the formula: 
tp=R=0.54Em-0.16 
where t is the thickness of the absorbing material 
in centimeters, p the density of the substance in 
grams per cubic centimeter, and Em the maximum 
energy of the /3-particles in Mev. These units 
yield the range R in grams per square centimeter. 
For a situation where /3-particles of two energies 
exist, we may treat each group as having its own 
maximum energy and add the results, or even 
obtain a practical average by treating the particles 
as if they had one maximum which is the average 
energy of the two most energetic groups. 
(c) /3-particle spectra.—The general form of the 
continuous or pure /3-particle spectrum has 
already been discussed in section 6.15. However, 
there are, in addition to the primary /3-particles, 
discrete /3-particles which are emitted from elec- 
tronic shells of atoms, the nuclei of which emit 
7-rays. These secondary j8-particles thus consti- 
tute the line-spectra. In some atoms which 
emit primary and discrete /3-particles, the number 
of secondary rays is small compared with the 
primaries. There are, on the other hand, some 
isotopes which give off more secondary than 
primary /3-particles. Since the secondary /3- 
particles derive their energy from a photoelectric 
process, their energies are characteristic of the 
atoms from which they are emitted. 
6.17 Nuclear Gamma Rays 
(a) The origin of gamma rays.—In the case of 
line spectra in the optical region, it was shown 
that the existence of discrete emission line spectra 
implied that the atom itself contained discrete 
energy levels, transitions between which gave 
rise to photons of energy equal to the difference 
in energy between the levels. For the case of 
the nuclear system, two different line spectra are 
known to be emitted; the a-particle and the 
7-ray spectra. 
When a-particle spectra were discussed, no men- 
tion was made of the explanation for the existence 
of groups of a-particles having discrete energies. 
This subject is discussed at this point in order to 
show the relation between a-particle and 7-ray line 
spectra. Assume that an a-emitting nucleus gives 
off several discrete groups of a-particles, called 
oq, ai, a2, and so forth. These correspond to dis- 
crete energy levels within the nucleus. Such levels 
are diagrammatically illustrated in figure 6-22 
where they are superposed on a potential energy 
curve for the nucleus. 
Figure 6-22.—Nuclear energy level picture. 
When an a-particle is emitted from a nucleus, it 
need not necessarily leave that nucleus (which is 
now the daughter) in its ground state. Instead 
it may leave it in an excited state. The daughter 
nucleus may then drop down to its ground state 
by emitting a 7-ray. Another possibility exists— 
the daughter nucleus may jump directly from its 
excited state by emitting an extra high energy 
a-particle and going to the ground state of its 
daughter (this would be the granddaughter of the 
original parent). In this case, where there are two 
possible processes, a competition occurs, and that 
with the shortest mean life will predominate. 
Nuclei will decay by two different schemes, for 
example, RaC', ThC', and AcC' (see fig. 6-6). 
These are called isomers, and the phenomenon is 
85 RADIOLOGICAL SAFETY 
itself called nuclear isomerism. These two proc- 
esses can be stated as follows: Let 
Ea be the energy of the emitted a-particle. 
Ed be the normal energy for the disintegra- 
tion process. 
Case I; J£’a>E: In this case the a-particle has 
extra energy which must be attributed to the 
parent nucleus having been left in an excited state 
when it was formed. As an example, /8 decay of 
RaC leaves RaC' in an excited state. In the 
subsequent transition by a decay to RaD, the a 
carries away this extra energy. 
Case II; £’«<£': Here the a-particle has less 
than normal energy, which must be due to the 
product nucleus (daughter) being left in an excited 
state. Thus in the transition from ThC to 
ThC", a-particlcs are emitted to take the excited 
ThC" nucleus to its ground state. Figure 6-23 
shows an energy level scheme for ThB, ThC, 
ThC', ThC", and ThD as well as the a, /3, and 
7-transitions which take place between these 
levels. For the purpose of this discussion, the 
lowest level of ThD is taken equal to zero energy. 
All other energy levels are plotted on a linear scale 
above this zero level. Not all conceivable transi- 
tions are shown on this diagram. The reason for 
this is that certain transitions are forbidden by 
quantum mechanics. There are operative within 
the nucleus a set of selection rules which determine 
whether or not a given transition will occur. A 
discussion of this subject involves factors other 
than those which will be considered in this simpli- 
fied treatment of nuclear physics. 
(b) Gamma ray spectra.—One might wonder 
how line spectra of 7-rays could be obtained 
experimentally, for the rays themselves are not 
subject to deflection in an electric or a magnetic 
field. 7-rays energies may be measured by 
measuring internally converted electrons for low 
energy 7-rays and by observing Compton elec- 
trons and photo-electrons for higher energy 
gammas. 
It will be seen from figure 6-23 that 7-ray spectra 
are associated with both a and /3 emission. As a 
general rule, 7-rays are more often associated 
with /8-particles—these gammas are usually also 
harder than those found accompanying a-e mission 
A radioactive isotope which emits /3-particles 
unaccompanied by 7-rays is called a pure /3-emitter. 
(c) Absorption of y-rays.—The mechanism of 
the interaction between gamma quanta and matter 
has already been discussed for X-ray quanta and 
it need not be repeated here. A 7-ray photon 
differs from both /3- and a-particles in that it does 
not produce an ion track such as could be photo- 
graphed in a Wilson Cloud chamber. 
Two types of absorption coefficients for 7-rays 
have been introduced thus far, namely, the linear 
absorption coefficient n, and the mass absorption 
coefficient /u„,=m/p- It is instructive to introduce 
two more coefficients, that is, the atomic absorp- 
tion coefficient, Ma and the electronic absorption 
coefficient, ne. 
jna=-- relative absorption per atom (since 
N— number of atoms per gm) 
ne relative absorption per electron (since 
' there are Z electrons per atom) 
In table IV, values of these four coefficients 
have been tabulated for representative elements. 
These coefficients all refer to a 7-ray energy of 1.3 
Mev. 
Table IV 
Element 
(cm*1) 
(cm2/gm) 
Ht=p/pN 
(cm2/gm/atom) 
*, = p/pNZ 
(cm2/gm/elec- 
tron) 
0.12 
0.06 
1.2X10-a 
2.0X10-25 
. 16 
.06 
2.6X10'24 
2.0X10-25 
.46 
.06 
5.3X10-M 
2.1X10-25 
.51 
.06 
6.1X10-M 
2.1X10-25 
Tin 
.35 
.06 
1.2X10-22 
2.4X10-25 
Lead 
.80 
.07 
2.5X10-22 
3.0X10-25 
On the assumption that the 7-rays interact only 
with electrons, it might be thought that for 7-rays 
of the same energy the quantity He would be the 
same for all elements. The fact that He (column 4 
in the table) increases for lead to a value 50 per- 
cent higher than that for the light elements demon- 
strates that the binding energy of the electron 
comes into consideration. Thus more tightly 
bound electrons, which are present in heavier ele- 
ments, absorb relatively more energy per electron 
than do the more loosely bound ones. 
86 RADIOLOGICAL SAFETY 
« particle transition ■*— x ray transitions 
/3 particle transition 
_ength of arrow is proportional to energy of the radiation 
Figure 6—23.—Energy level scheme for thorium B, C, C1, Cu, and D. 
87 RADIOLOGICAL SAFETY 
Chapter 7 
NUCLEAR REACTIONS 
7.01 Nuclear Bombardment 
It is well known that two nuclear particles 
strongly resist any effort made to bring them close 
together. Because of the high potential barriers 
which exist in nuclei, an incident particle must 
have a very high velocity before it can overcome 
the potential barriers. This is the reason why 
nuclear reactions, more properly designated as 
induced reactions, are so rare under ordinary cir- 
cumstances. For example, molecules of air at 
room temperature have an average energy of 
about 1/30 e. v., and atoms involved in chemical 
reactions rarely exchange more than a few e. v. of 
energy. Since such energies are small compared 
with the heights of nuclear potential barriers, the 
particles never come close enough to cause a 
nuclear reaction to be induced. 
In describing experiments in which induced 
nuclear disintegrations occur as the result of 
nuclear bombardment, it is customary to use the 
heavier of the two participating nuclei as the tar- 
get, and to use the lighter particle as the missile 
which is projected at the target. Nuclear missiles 
commonly used include all elementary particles, 
which can be accelerated to high velocity by some 
device called an accelerator. A few of the more 
generally used particle accelerators will be de- 
scribed in the following sections. 
Since natural radioactivity furnishes a simple 
source of high-energy particles, it is quite under- 
standable that the earliest experiments in the field 
of induced radioactivity were performed with this 
source. Shortly after Rutherford’s early work in 
this field, physicists took advantage of another 
natural source of high-velocity particles, namely 
the cosmic radiation, to observe new types of 
reactions. Cockroft and Walton then demon- 
strated that protons could be artificially accel- 
erated, and a new type of nuclear research was 
born. This field led to the development of the huge 
particle accelerators, such as the cyclotrons, beta- 
trons, and Van de Graf accelerators, which are in 
vogue today. 
Researches in the field of induced radioactivity 
have led to the discovery of many artificially pro- 
duced radioisotopes and have produced a very 
large number of new types of nuclear reactions. 
What is more important from the standpoint of 
atomic energy, the experiments in nuclear dis- 
integration have resulted in the discovery of a 
new particle called the neutron. 
7.02 Rutherford’s Alpha Particle Bombardment 
Lord Rutherford first showed in the year 1919 
that bombardment of nuclei with a-particles could 
produce nuclear disintegrations. The apparatus 
which he used to observe this important phenome- 
non is sketched in figure 7-1. 
Figure 7-1. Rutherford’s alpha particle bombardment 
experiment. 
In this experiment a RaC' source is used. It is 
mounted on a moveable platform and placed with- 
in a gas-tight container, one end of which supports 
a zinc sulphide screen. Zinc sulphide has the 
property of giving off scintillations of visible light 
when bombarded by heavy, charged particles. An 
observer who has thoroughly adapted his eyes to a 
darkened room can use a microscope and observe 
the scintillations on the screen. When the source 
is at a distance x, less than the range of RaC' 
a-particles, the ZnS screen is illuminated with many 
scintillations. However, with the chamber of the 
apparatus filled with nitrogen, Rutherford and 
Chadwick found that some scintillations were ob- 
servable on the screen even when the source was at 
a distance much greater than 7 cms. (the range of 
RaC' a-particles). It was felt that these scintil- 
lations were caused by long range protons pro- 
duced as a result of the disintegration of nitrogen 
nuclei. The protons were attributed to a nuclear 
reaction given by the equation: 
7N14-f2He4 ♦ g017+1H1 (1) 
89 RADIOLOGICAL SAFETY 
height of the potential barrier and therefore no 
disintegrations should occur. This difficulty is 
solved by the wave mechanical theory, which 
allows for a penetration or “tunneling” through 
the potential barrier. It is for this reason that 
nuclear reactions can be initiated at energies 
which may be much lower than the potential 
barrier maximum. 
7.03 Nuclear Cross Sections 
In the process of passing through matter a 
high speed a-particle may actually traverse about 
105 atoms before it is absorbed. From Ruther- 
ford’s experiments, it can be shown that only 
about 1 a-particle in every 105 emitted causes a 
nuclear transmutation. Thus only about 1 colli- 
sion in 1010 results in an (a, p) reaction. At best, 
then, these reactions are very improbable. 
Obviously, some consistent manner of expressing 
the probability for the occurrence of a given 
reaction is needed. In other words, there is 
required a means of expressing this probability in 
numerical form. One way to approach this 
problem is to imagine a uniform beam of particles 
striking a target, as shown in figure 7-3. Let 
Many years later, cloud chamber pictures were 
taken which demonstrate graphically how the 
reaction takes place. Figure 7-2 shows a diagram 
of a single 7N14 disintegration under a-particle 
bombardment. 
Figure 7-2.—Nitrogen disintegration by alpha 
bombardment. 
The short track corresponding to 8017 is usually 
called a recoil track, and the 8017 is in this case a 
recoil nucleus. By the application of the conserva- 
tion laws of energy and momentum, the angles 
which the disintegration products make with the 
direction of the incident particle may be easily 
calculated and coincide with observed values. 
Further studies by Rutherford and others showed 
that protons produced by the transmutations of 
nitrogen are emitted uniformly in all directions. 
Furthermore, other elements which were ex- 
amined for transmutation were observed to emit 
protons. Most of the light elements disintegrate 
under a-bombardment, yielding protons. Of 
these, aluminum, nitrogen, and boron exhibit the 
highest probability for reactions of this (a, p) type. 
This terminology (a, p), is quite generally used; 
the incident particle is always the first within the 
parentheses and the resulting emitted particle is 
second. 
In the case of a-emission from nuclei, it was 
pointed out that classical concepts did not allow 
a-particles to escape from the confines of the 
nuclear potential barrier. Just as the potential 
barrier (on the classical picture) trapped particles 
within the nucleus, in the same way particles 
bombarding nuclei arc forbidden entrance into 
these nuclei unless they have kinetic energy 
sufficient to pass over the potential barrier. An 
analysis of the problem of a-bombardment of 
certain light nuclei shows that the energy of the 
natural a-particles from, say, RaC' is less than the 
Figure 7-3.—The concept of nuclear cross section 
N0=number of incident particles per sec. 
per cm2 of target area. 
Ns=number of atoms per cm2 of target 
area. 
N„ —number of reacting particles per sec. 
per cm2 of target area. 
Sigma (<r) = a quantity, cross section expressing the 
probability for a specific reaction to 
occur. 
90 RADIOLOGICAL SAFETY 
Thus: 
(Cm-2) (Sec—) 
NoN. (Cm-2) (Sec-1) (Cm-2) 
be maximal. In this way, high energy protons 
are produced in the paraffin by neutron impact. 
The reaction equation for neutron production is 
written: 
4Be9+2He4 * 6C12+<pd + £ (3) 
Since the masses of Be, He, and C are known, 
and since the initial energy of the a-particle is 
also known, the measurment of the “Q” of the 
reaction allows for a measurement of the mass of 
the neutron to be made. Measuring the “Q” of 
the reaction requires that the energies carried off 
by the disintegration products, 6C12 and 0n\ 
must be evaluated. This can be done experi- 
mentally. For a precise measurement of the 
neutron mass, another type of reaction is prefer- 
able. This reaction, the photo-disintegration of 
the deuteron nucleus, will be described in section 
7.12. 
Neutrons may also be produced by the a-bom- 
bardment of other light elements, but the a-par- 
ticle bombardment of beryllium is one of the 
reactions yielding neutrons in greatest abundance. 
Three types of such sources are generally used: 
1. Ra-Be source—2. Rn-Be source.—The 
radium beryllium and radon beryllium sources 
yield about 10 to 15X106 neutrons/sec for 
each curie of a-radiation in the source. 
Recently, powdered radium beryllium mix- 
tures have been prepared in a pressed form 
which yield 1.7 X107 neutrons/sec/gm Ra for 
high Be to Ra mass ratios. 
3. Po-Be source.—This source yields about 
2.8X106 neutrons/sec/curie. 
The energies carried off by neutrons from any 
of these sources vary, but fpr the Ra-Be mixture, 
neutrons are emitted with energies up to 13 Mev. 
Such neutrons are called fast neutrons. 
7.05 Artificial Radioactivity 
Joliot and Curie investigated the alpha induced 
neutron emission in a number of light elements, 
and discovered that some of these elements were 
made radioactive by the bombardment with 
a-particles. That is to say, the elements con- 
tinued to undergo disintegration long after they 
had been removed from the vicinity of the a-par- 
ticle source. Prior to their work, all nuclear 
reactions which had been produced in the labora- 
tory had been instantaneous and ceased just as 
soon as the bombardment was stopped. 
Thus it is as though each atom on the target pre- 
sented an area a, to the bombarding particle for 
the given reaction to occur. It will be shown that 
there are many types of nuclear disintegrations, 
and for some of these the cross section is rather 
high—in some cases as large as 1CT20 cm2. Other 
reactions are very improbable and yield cross 
sections as low as 10~32 cm2. In fact, the varia- 
tion in cross section is so extreme that it is some- 
times difficult to visualize it in comparison with 
the physical cross sectional area of a nucleus, i. e., 
3X10~24 to 3X10-25 cm2. A convenient unit for 
measuring cross section is the barn (10~24 cm2). 
7.04 The Discovery of the Neutron 
The alpha bombardment of light elements also 
showed that short wave electromagnetic radiation 
is produced and has the same properties as do 
the y-rays emitted by naturally radioactive sub- 
stances. When the element beryllium was bom- 
barded with a-particles, a strange unexplained ef- 
fect took place. Instead of protons, a very pene- 
trating radiation was emitted which was thought 
to be a very short wave length 7-ray. Absorption 
measurements made by Bothe indicated these 
rays had absorption coefficients corresponding to 
energies in the neighborhood of 15 Mev. 
What was most unusual about this penetrating 
radiation was that when it was allowed to fall 
upon a paraffin slab, it apparently produced a new 
type of radiation having a very long range, i. e., 
over 20 cms. of air. The English physicist Chad- 
wick first showed that the penetrating rays emitted 
by the Ra-Be source could not be y-rays. Chad- 
wick investigated the particles ejected from the 
paraffin and proved that they were protons. He 
then showed that the rays emitted by the Ra-Be 
source must be neutral particles having about the 
same mass as protons. These particles he called 
neutrons. 
It is easy to see that neutrons should transfer a 
maximum amount of energy to protons in passing 
through a hydrogen-rich material such as paraffin. 
In any elastic collision, if the colliding substances 
are of about equal mass, the energy transferred 
from the incident object to the recoil object will 
91 RADIOLOGICAL SAFETY 
Elements such as Al, Si, and P were found to 
decay by emitting positrons. The process can 
be best understood by considering the produc- 
tion of radiophosphorous which was the first 
artificial radioisotope made by Curie and Joliot 
in 1934. The two step reaction is: 
the emitted a-particles. The nuclear reaction 
initiated by the 0.15 Mev protons is: 
aLi7—|— 1K1 > 22He4+$ (6) 
This would be the reaction occuring in the more 
abundant isotope of lithium. Since the energy of 
the protons is quite exactly known, the energy 
imparted to the pair of helium nuclei can be 
calculated as follows: 
3Li7=7. 01818 
00813 
-f-K. E. of 00016 (0.15 Mev=0.00016 m.u.) 
Initial mass=8. 02647 
2X2He4=8.00778 (2X4.00389) 
+K. E. of 2He4= Q 
Final mass=8. 00778 + $ 
Equating; 
8.00778+ $=8.02647 
$=0.1869 m.u. excess energy 
$=17.4 Mev. 
The reaction thus leads to two products which 
have less mass than that of the original particles. 
The $ to this reaction is +17.4 Mev which appears 
in the form of kinetic energy of the two a-particles. 
Each a-particle will carry off 8.7 Mev energy and 
will have a range in air of over 8 cms. These 
predictions are verified experimentally and show 
that the above system of mass-energy accounting 
is a valid one. 
In solving the above example, the values used 
for nuclear masses are actually atomic mass 
values, but this does not affect the validity of the 
results. The reason why this can be done is that 
the same number of electrons are present on both 
sides of the equation and thus balance out. This 
method works for all reactions excepting positron 
emission, where the decaying isotope loses not 
only a positron but also an orbital electron. This 
is taken into account by adding two electron 
masses (or 1.02 Mev) to the mass of the disin- 
tegration product. 
Now a particle emitted by a natural radioiso- 
tope with, say, an energy of 5 Mev, should be 
identical with a particle of the same type which is 
accelerated to an energy of 5 Mev by some ma- 
chine. Therefore, the remarkable aspect of the 
Cockroft-W alton experiment is not that laboratory 
13AF+2He4 > 15P30+0n1 (4) 
isP HSi30+,c° (5) 
The first equation describes the usual neutron 
production reaction. Here i5P30 is a disintegra- 
tion product which is unstable and decays with a 
half life of 2.3 minutes into 14Si30 and a positron. 
Positrons, as emitted by radioisotopes, are exactly 
the same as the cosmic ray particles, bearing 
+ 1 charge and having a mass equal to that of 
the ordinary negative electron. Absorption ex- 
periments showed that the positrons are stopped 
in matter in the same manner as ordinary /3-par- 
ticles. 
As a general rule, it can be stated that the cross 
section for producing an artificial radioisotope 
varies inversely as the half life of the isotope. 
In effect, this means that it is easier (requires 
fewer bombarding particles) to induce artificial 
radioactivity having a short half life than it is 
to do so for isotopes of longer half life. Today 
every element in the periodic system has at least 
one radioisotope and about 450 induced radio- 
activities are known. Some of these, such as 
C14, P32, and I131, are well known for their applica- 
tion to medical research and therapy. 
It is now known that artificial radioactivity can 
be induced by many reactions other than those 
produced by alpha bombardment. The use of 
natural radioisotopes, such as RaC and Po, seri- 
ously limits the experimenter to alpha, beta, and 
gamma-rays of rather limited energy and inten- 
sity. It was for this reason that Cockcroft and 
Walton’s experiment with the acceleration of 
protons is of such significance for it opens up a 
whole new field of nuclear physics to investigation. 
7.06 The Cockcroft-Walton Experiment 
In 1932, Cockcroft and Walton managed to 
produce an artificially accelerated beam of protons 
with an energy of about 150,000 ev. They 
directed this beam at a lithium target and observed 
92 RADIOLOGICAL SAFETY 
accelerated particles could initiate nuclear dis- 
integrations, but that these particles could cause 
such reactions at such low energies as 150,000 e.v. 
These findings prompted physicists the world 
over to try to devise new types of accelerators or 
atom smashers which would accelerate other types 
of particles to even higher energies. The original 
equipment built by Cockroft and Walton con- 
sisted of an accelerating tube with a hydrogen arc 
source. To this tube they applied a high potential 
which was obtained through a high voltage trans- 
former and a special arrangement of rectifiers and 
condensers which served to “double” the trans- 
former output voltage. The protons produced in 
the hydrogen arc were accelerated down the tube 
and directed against a target assembly where the 
nuclear reactions took place. 
High voltages can be produced by: 
Impulse generators (charging condensers in 
parallel and discharging in series)—3 Mev. 
Electrostatic generators (Van de Graaf ma- 
chihes)—5 Mev. 
Voltage multiplier circuits (arrangements of 
condensers and rectifiers designed to multiply 
a transformer output voltage)—2 Mev. 
Cascade transformers (use of a series of in- 
sulated transformers yields 1 Mev.) 
Resonant transformers (involves a Tesla- 
type design and can be used up to 2 Mev) 
Coils of a transformer are tuned to resonance 
at a relatively high frequency. 
Linear resonance accelerators (Sloane-Law- 
rence type use of cylindrical segments aligned 
in a tube, each segment being of such length 
that the application of high frequency high 
voltage to segments gives continual acceler- 
ation down the tube. Voltages are limited 
only by length of tube and ability to main- 
tain a beam. 
Magnetic resonance accelerators (cyclotron, 
betatron, and synchrotron). 
7.07 Particle Accelerators 
Three of the various types of accelerators will 
be discussed briefly. 
Simple accelerator.—A very simple accelerating 
device consists of an insulating tube inside of 
which are arranged cylindrical metal tubes as 
illustrated in figure 7-4. At one end an arc or 
filament source S produces ions (protons) which 
are injected into the main acceleration tube T 
by means of a focussing system F. Once in- 
jected into the chamber, the ions are gradually 
accelerated in successive jumps by high voltages 
which are placed upon the inner metal cylinders. 
Figure 7—4.—The linear accelerator. 
On each of the metal cylinders there is imposed a 
progressively higher voltage from a direct current 
external supply. These cylinders are insulated 
from each other by segments of the external glass or 
porcelain tube. The whole system is maintained 
under a high vacuum (10~s mm. Hg) by high- 
speed pumps. With the high vacuum the particles 
being accelerated do not suffer energy loss by 
collisions with gas molecules, and a gas discharge 
inside the accelerating tube is prevented. The 
use of many separate acceleration cylinders and 
corona discharge rings allows a uniform poten- 
tial gradient over the length of the tube. Thus the 
ions are focussed into a narrow beam of several 
Mev energy and directed against a target assem- 
bly (not shown) where they give rise to nuclear 
reactions. 
The cyclotron.—In 1932, Lawrence developed a 
very novel technique for accelerating particles to 
high energies without using very high DC 
voltage sources. This device, called a cyclotron, 
operates on the following principles. Figure 7-5 
shows a diagram of the essential components of a 
cyclotron. The acceleration chamber is a hollow 
metal pillbox consisting of two semicylindrical dees 
which are insulated from each other. The dee sys- 
tem is attached to a vacuum pump and kept under 
a high vacuum and is sandwiched between the 
poles of a large electromagnet. To each of the dees 
there is applied a high frequency voltage of about 
10 megacycles/sec. 
At the center of the dee system is an arc source 
for producing positive ions. These ions are 
accelerated into one of the dees, say D2, by the 
potential difference existing between Dt and D2. 
93 RADIOLOGICAL SAFETY 
For proper acceleration in the cyclotron, the 
frequency of the electric field must be adjusted so 
that as the particles leave the dees they are in 
phase with the electric field and are accelerated 
across the space between the dees. This condition 
is met by making the angular velocity of the high 
frequency field equal to the angular velocity of the 
ions. Thus: 
j=2*f 0) 
Substituting the value of v/r from Eq. (8), it is 
found that 
'-ss <10> 
where / is the frequency of the oscillator in cycles/ 
sec. 
Actually, the time which any particle spends in 
a dee is independent of the radius of the circular 
path it follows. It is easily shown that the 
energy of an ion traveling at radius r in field of 
value H is given by: 
e=*L(&)2 (I1) 
where E is given in Mev. 
As an example, protons running on a 16 cm. 
radius in a magnetic field of 13,000 oersteds attain 
an energy of 2 Mev. Insertion of a deflecting 
plate allows the particles to be brought out of the 
chamber through a thin window. This deflecting 
plate carries a high voltage in order to pull the 
particles from their paths. Once the beam leaves 
the dees and the magnetic field, it travels in a 
straight line away from the cyclotron. Bombard- 
ments of targets are often carried on inside the 
vacuum chamber or with the outside beam. 
At Berkeley, the most recently constructed 
cyclotron is a frequency-modulated type which 
overcomes the fact that the particles being accel- 
erated increase in mass because of their high 
velocity and get out of phase with an ordinary type 
of high frequency acceleration. The new machine 
has accelerated deuterons to 200 Mev using this 
type of modulation. 
The betatron.—-One might think that a cyclotron 
could be used to accelerate electrons as well as 
heavy particles. However, the electrons increase 
in mass much more quickly and would get out of 
phase between the dees. This difficulty was over- 
Figure 7-5.—Principal components of a cyclotron 
This potential difference arises from the fact that 
Di is at a positive peak while D2 is at a negative 
peak of the voltage cycle. Thus the ions are 
accelerated into D\ where they enter into a field 
free space since the electric field exists only 
between the dees. However, the effect of the 
uniform magnetic field is to cause the ions to 
move in circles. As the ions make a 180° trip 
through D2, they again enter the space between 
the dees where they are accelerated once more. 
This time when they enter the ions have more 
kinetic energy and hence are less affected by the 
magnetic field. Therefore, as the ions make more 
complete circles in the dees, they spiral out into 
circles of larger radii. Since the centripetal force 
on the particle must equal the force of the mag- 
netic field, 
(7) 
where 
IT= magnetic field in oersteds 
e=charge of particle being accelerated 
v= velocity of the particle 
m=mass of the particle 
r—radius of the particle path 
Thus the radius in which the particle will move is: 
mv 
r=m <8> 
94 RADIOLOGICAL SAFETY 
come with remarkable success by Kerst in 1941. 
He devised an electron induction accelerator which 
is better known as a betatron. In place of a high 
frequency electric field to accelerate the particles, 
the betatron uses a varying magnetic flux, which 
induces an accelerating electric field. The accel- 
erated beam impinges upon an internal target and 
a beam of X-rays is emitted. These high energy 
quanta are much more penetrating than any 
gamma rays artificially produced. A 300 Mev 
betatron is being built at the University of Illinois. 
7.08 Nuclear Reactions 
The accelerators just described offer the possi- 
bility of producing almost any type of high energy 
particle for bombardment purposes. The com- 
monly used accelerated particles are: electrons, 
protons, deuterons, and alpha particles. By al- 
lowing them to impinge on suitable targets, in- 
tense beams of neutrons, X-rays, and gamma rays 
can be obtained. There are about 280 stable 
nuclei in nature, any of which can be used as a 
target for any of the missiles mentioned above. 
Furthermore, for any single type of bombarding 
missile there may be more than one type of 
reaction which occurs. It is therefore readily 
appreciated that it would be impossible to describe 
even a small fraction of all reactions which are 
known. 
Because certain of the reactions throw new light 
on nuclear structure a few of these will be dis- 
cussed. Later in the chapter, the various nuclear 
reactions for producing neutrons will be described 
and this will furnish an indication of the variety 
of reactions which may occur. Nuclear disin- 
tegrations can be grouped in the following general 
categories which are set up on the basis of the 
nature of the disintegration products. 
(a) Simple excitation oj the nucleus.—In this 
case, the collision puts the nucleus in a higher 
state of excitation and subsequently a 7-ray is 
emitted, bringing the nucleus back to its ground 
state. Such reactions are easily induced by heavy 
particle bombardment of light elements. 
Example: Alpha-gamma reaction.■—The general 
case of gamma emission by alpha-particle bom- 
bardment of a nucleus with simple excitation is: 
ZA+2Hei-**ZA+iHei 
*ZA^A+hv 
(6) Simple capture (radiative capture).—Here 
the collision results in capture of the incident 
particle and in the production of a new isotrope. 
Often this simple capture process is detected by 
gamma emission or by the artifiicial radioactivity 
of the new nucleus. Two examples of this reaction 
are discussed in section 7.13. 
(c) Two particles as end products.—In this case, 
the incident particle is captured with the simul- 
taneous emission of a different particle from the 
resulting nucleus. As an example, consider the 
so-called D on D or D-D reaction. Here deute- 
rons are used to bombard a deuterium target with 
the following result: 
1D*+,D*-»1H1+1H8+Q (12) 
This reaction yields a proton of 14.3 cm. range and 
a triton (a tritium nucleus) of 1.6 cm. range. From 
this, the Q of the reaction turns out to be 4 Mev. 
This reaction is of great interest since all the 
particles involved are isotopes of hydrogen. Tri- 
tium is the heaviest isotope and it is now known 
to be j8-active, emitting very weak /3-particles 
with a half life of about 30 years. The reaction 
is one of the most accurately measured and 
permits a mass measurement of the tritium isotope. 
(id) More than two particles as end products.— 
Here capture of the bombarding particle results 
in a disintegration where three or more end prod- 
ucts are formed. An interesting example of this 
type of reaction is the emission of three a-particles 
as a result of deuteron bombardment of B10: 
(13) 
The “Q” of this reaction amounts to about 10 Mev 
and the energy is shared by the three a-particles 
with resulting ranges of about 4, 8, and 14 cms. 
The same reaction can be induced by proton bom- 
bardment of the more abundant 5Bn isotope, but 
it yields about 1 Mev less energy. 
7.09 Energetics of Nuclear Reactions 
Suppose that a copper target is placed m a cyclo- 
tron beam and bombarded with deuterons. Sev- 
eral nuclear reactions might be expected from 
bombardment of the most abundant 29CU63 iso- 
tope. 
Except for the id, d) reaction which may be 
regarded as simple scattering, all of the above re- 
actions are bona fide reactions which have been 
•An excited state of the nucleus 
95 RADIOLOGICAL SAFETY 
of the same mass and charge but having different 
decay schemes. For example, 30Zn65 may decay 
by any of the following schemes: 
3oZn64+0wl (d,n) 
30Zn63+2onl (d,2n) 
r29Cu6*+lHi (,d,p) 
‘28Cum+,Z>2 (</,rf) 
'mCu92-!-,//3 (rf,<) 
,28Ni61 +2#<d (rf,«) 
29Cu63+,Z)2- 
29Cu65-(-+iC0 (Positron emission) 
3lGa65-f .je0 (/3-decay) 
29Cu65—_!C° (K-electron capture) 
(14) 
soZn65 
The significance of the negative sign in the last 
equation is that the electron is not emitted but is 
absorbed. The absorption or capture of a K shell 
electron into the nucleus produces the same prod- 
uct nucleus (example 29C1165) as would result if 
positron emission occurred. 
It is clear that a bombarding particle can cause 
a variety of nuclear reactions to take place. The 
extent to which any one reaction occurs depends 
upon the energy of the bombarding particle. 
7.10 Positron Emission and K-Electron Capture 
In general if the number of neutrons in a disin- 
tegration product is too small in comparison to 
the number of protons, the nucleus will reduce its 
charge by one unit by positron emission. Positron 
emission occurs only if the energy difference be- 
tween the original and product nucleus (due to 
difference in mass) is greater than 2w,)C2. Here 
m0 is the rest mass of the electron so that the 
available energy in order to realize positron emis- 
sion must be greater than 1 Mev. If the available 
energy is- less than 1 Mev positron emission will 
not occur. Therefore in positron emission, the 
positron will always have 1 Mev less kinetic 
energy than if /3-decay had occurred. In other 
words, if the available energy between parent and 
product nuclei is 3 Mev, then for positron emis- 
sion, a positron with 2 Mev energy will be emitted. 
If the disintegration would make available less 
than 1 Mev energy, the reaction can still gc, but 
it will take place in a different way. The parent 
nucleus will capture an electron from the K shell 
(K electron capture) and subsequently emit a 
quantum of energy hv in order to rid itself of 
excess energy. The nucleus might pull into itself 
an L shell electron, but a K electron capture is 
much more probable. The general reaction is 
given by: 
ZA+-x#-*{Z-l)A+hv (18) 
Since the process leaves a vacancy in the K shell, 
another orbital electron will drop down into the 
observed. Now the question arises: For a given 
bombardment, which of the reactions will occur? 
The cyclotron can be adjusted so that it pro- 
duces a fairly monoenergetic beam of deuterons of 
any energy. It is found, for example, that the 
d-2n reaction is absent at low energies but becomes 
significant for 10 Mev deuterons. There is thus, 
what is called a threshold energy which must be 
reached before certain of the above reactions will 
go. It is possible to predict which of the above 
reactions will go; in other words, the threshold 
energy can be calculated from an evaluation of the 
energetics of the process. 
Of the heavy disintegration products listed 
above, three exhibit artificial radioactivity and 
decay by /3— or /3+ emission or by K electron 
capture. Both 30Zn63 and 29Cu62 are positron- 
emitters. The decay for 29Cu62 is: 
29Cu62-^->2gNi62++,e°+2.6 Mev (15) 
Here the figures 10.5 m. (minutes), written above 
the arrow, denote the half life for positron emis- 
sion. The tritium produced in forming 29Cu62 is 
also radioactive, so this reaction yields two arti- 
ficially radioactive end products. 
In addition, the disintegration product 29Cu64 is 
artificially radioactive and is remarkable in that 
it may decay either by /3+ emission, by /3— emis- 
sion, or by K electron capture. Such an isotope is 
known as an isomer. Although the nuclear disin- 
tegrations which have been discussed for Eq. (14) 
are all instantaneous, it is also known that delayed 
radioactivity (artificial) is observed for the 
reaction: 
65 (16) 
This isotope also exhibits isomerism. About 40 
pairs of nuclear isomers are known, i. e., isotopes RADIOLOGICAL SAFETY 
K shell thus emitting a K X-ray quantum. 
Furthermore, if the nucleus is left in an excited 
state, it may emit a gamma ray from the nucleus. 
Thus K electron capture may involve the emission 
of two photons—one from the nucleus and one 
from the atom. It should be pointed out that the 
X-ray emitted will be characteristic of the product 
atom. 
The absorption of positrons leads to annihila- 
tion of matter, in that the positron unites with an 
ordinary electron to produce gamma radiations. 
Thus the annihilation process is the inverse of pair 
production. Theoretically it is not possible for 
an annihilation to yield a single quantum of 1 
Mev energy, if only an electron and positron are 
involved. In this case, two photons of 0.5 Mev 
energy are emitted, thus satisfying the laws of 
conservation of momentum and energy. If, how- 
ever, the combination of an electron and positron 
takes place near the nuclear field, the massive 
nucleus can enter into the reaction by absorbing 
a small amount of energy. In such an event, a 
single photon of 1 Mev can be emitted. Both 
types of radiation, the 0.5 and the 1.0 Mev photons 
are observed experimentally. The reaction can 
be written as: 
>27(0.5 Mev) 
or (19) 
P+-\-e~-*y(l.O Mev) 
7.11 Theory of Nuclear Reactions 
The nature of the mechanism of nuclear reac- 
tions may be understood from a consideration of 
the following: 
(а) The Bohr model of the nucleus. 
(б) The concept of nuclear potential barriers. 
(c) The application of the conservation laws. 
(d) The application of wave mechanics. 
(e) The concept of nuclear cross sections. 
Bohr conceived of a nuclear reaction as a two-step 
process: 
First, the incident particle and the target 
nucleus amalgamate to form an intermediate 
nucleus. 
Second, this intermediate or compound 
nucleus disintegrates into the reaction 
products. 
On a time scale, the first step takes only about 
10“21 seconds, whereas the disintegration (this 
does not apply to the decay of artificial radio- 
isotopes but only to other nuclear reactions) takes 
about 10~12 seconds. In the compound nucleus, 
the excess energy must be assumed to be tem- 
porarily shared by all nucleons. That,this must 
be true is clear from the comparatively long life 
(10~12 seconds is long in nuclear time units) of 
the compound nucleus, for in 10~12 seconds all the 
nucleons make many collisions with each other 
and split up the excess energy among themselves. 
Furthermore, Bohr’s conception of this process 
assumes that the disintegration of the compound 
nucleus is an event which is not directly connected 
with the original amalgamation process. The 
way in which the compound nucleus disintegrates 
depends upon a competition between the various 
reactions which are energetically possible. In 
fact, it is expected and observed that the specific 
reaction which requires the least energy will take 
place first. However, it is no exaggeration to 
state that practically any nuclear reaction can be 
realized if it is energetically possible. The re- 
action may go with extremely low yield or effi- 
ciency but it will go. 
Compound nuclei are relatively stable in the 
sense that they hold together for a much longer 
time than it takes the neutron to traverse the 
nucleus. The latter time is equal to a nuclear 
diameter (10~12 cms.) divided by the neutron 
velocity (109 cm./sec.) which is about 10“21 
seconds. Since the compound nucleus exists 
for about 10“14 secs., this is 107 times greater than 
the neutron traversal time. In general, the 
emission of a particle from the compound nucleus 
depends upon the probability that any one nucleon 
will receive sufficient energy to escape from the 
nucleus. 
It will be shown that most neutron capture 
reactions have highest cross section at low veloci- 
ties. This is understandable on the basis that 
slow neutrons spend more time in the vicinity 
of the nucleus and are thus more apt to be ab- 
sorbed. In fact, for a neutron traveling with a 
velocity v, the probability for absorption is 
proportional to the time that the neutron remains 
in the vicinity of the nucleus; this is merely a time 
equal to l/v. This law, called the 1/v law, applies 
to slow neutrons but it is sometimes also valid 
for higher energies. Neutrons are also often 
absorbed by resonance capture. In such cases, 
neutrons must have an energy which is the same 
97 RADIOLOGICAL SAFETY 
discussed in section (7.08). This was an example 
of a d-p reaction. There is in addition, with the 
D on D reaction, a very important d-n reaction 
which goes: 
1D2+1D2-^2He3+0^1 + 3.2 Mev (21) 
Due to the mass difference of 0.0034 m.u. a 0 
of 3.2 Mev is imparted to the neutron and the 
rare isotope of helium. This reaction goes with 
deuterons of only 100 Kev and yields 1 neutron 
for every 106 deuterons. The D on D reaction 
is a relatively efficient one for producing neutrons. 
Cyclotrons running with a 10 microampere beam 
bombarding a target of heavy ice yield about 108 
neutrons/second. This corresponds to a yield of 
about 1 neutron for 105 deuterons. 
(b) The p-n reaction.—As an example of the 
production of neutrons by proton bombardment 
consider 3Li7 as a target element. Then: 
3Li7+iH1-^>4Be7+onl + $ (22) 
Because of the fact that 4Be7 has only 3 neutrons 
and 4 protons, it is to be expected that it will try 
to overcome this neutron deficit by positron 
emission. This actually is observed, and therefore 
1 Mev of energy must be supplied by the proton 
for this effect. In addition, the neutron is heavier 
in mass than the proton by about 0.8 Mev so 
that the total Q of the above reaction is —1.8 
Mev. The negative sign means that 1.8 Mev of 
energy has to be supplied by the proton for the 
reaction to start. This further means that for 
1.8 Mev incident protons, the neutrons are 
produced with very little energy. Experimentally 
a threshold value of 1.86 Mev has been measured 
for this reaction, thus confirming the validity of 
the prediction. This reaction furnishes a very 
convenient means of producing mono-energetic 
neutrons of any energy, simply by varying the 
energy of the incident protons. 
(c) The 7-n reaction.—Bombardment of deu- 
terium and 4Be9 with gamma rays, yields what is 
termed the photoelectric production of neutrons. 
While the process, in common with most gamma- 
ray bombardments, has a very low yield, it is 
important because it permits an accurate evalua- 
tion of the mass of the neutron. Consider the 
reaction with deuterium. 
iD2 + Ar —> + Q (23) 
as that of certain energy levels of the nucleus. 
For example, the neutron capture cross section 
curve of uranium as a function of energy exhibits 
sharp peaks at low energies. These are called 
resonance peaks. Breit and Wigner have developed 
a theory of the resonance structure of nuclei on 
the basis of assuming a certain structure to the 
nuclear energy levels. 
An interesting concept of nuclear reactions is 
involved in thinking of the compound nucleus as 
an aggregate of nucleons having an effective 
nuclear temperature. On the liquid drop model 
of the nucleus, all of the nucleons are in a con- 
stant state of collision and have an average 
kinetic energy which can be translated into a 
nuclear temperature by the equation: 
(20) 
where k is the Boltzmann constant and T is the 
absolute temperature. The addition of a neutron 
to a nucleus by the capture process gives the com- 
pound nucleus the kinetic energy of the neutron 
plus the binding energy (8 Mev) of the neutron. 
This additional energy makes itself manifest in 
increased motion of the nucleons and raises the 
nuclear temperature. Bohr has estimated that 
the capture of a 10 Mev neutron by a heavy nu- 
cleus raises the temperature to about 1010 °C. At 
this high temperature the emission of a neutron 
can be thought of as a boiling ojf process. When 
a neutron is boiled off, it carries its binding energy 
as well as kinetic energy. Thereupon the result 
ing nucleus drops in temperature. This boiling- 
off analogy is valid for heavy nuclei and high exci- 
tation energies C>8 Mev) where the nuclear 
energy levels fall close together. For low excita- 
tion energies, the energy levels are far apart 
(100,000 e.v.) whereas for 8 Mev (the binding 
energy of one neutron) the level spacings are much 
closer, being separated by 10 to 100 e.v. At still 
higher energies C>10 Mev) the energy level spac- 
ings are only 1 e.v. or less apart, thus forming a 
continuum of levels. 
7.12 The Production of Neutrons 
The production of neutrons by the a-n reaction 
has already been discussed. Examples will be 
given of the d-n, p-n, and y-n reactions. 
(a) The d-n reaction.—The D on D reaction was 
98 RADIOLOGICAL SAFETY 
If 7 rays of 2.62 Mev from ThC" are used and if 
the proton ranges are accurately measured, the 
Q of the reaction will be: 
2.62-2Ep=-Q and EP=0A5 Mev 
since the energy carried off by the neutron will be 
almost equal to that of the proton. This yields 
Q=—2.2 Mev and means that the neutron is 
bound to the deuteron with 2.2 Mev binding 
energy. Writing Eq. (23) in terms of the masses 
involved and using 1 m.u. as equal to 931 Mev, 
the mass of the neutron can be accurately ob- 
tained. 
2 fi2 0 4 s; 
2.01473+—-j = 1.00813 
Mn= 1.00893 m.u. 
7.13 Neutron Induced Reactions 
Although the neutron is an uncharged particle, 
its energy can be expressed simply in electron 
volts. It is a matter of common practice to 
classify neutrons as thermal, slow, or fast accord- 
ing to the following schedule: 
Even before discussing the specific neutron in- 
duced reactions, the above data indicate that neu- 
trons exhibit unusual properties for reaction at 
extremely low energies. This remarkable prop- 
erty is due to the fact that neutrons, being 
uncharged, do not have to penetrate a potential 
barrier in order to enter the nucleus. Some 
elements, such as cadmium, exhibit truly enormous 
cross sections of several thousand barns for ther- 
mal neutron capture. 
In general, neutrons induce a very large number 
of reactions. Only a few examples will be given 
for each of the following reactions (n, 7), (n, p) 
(n, a), (n, n) and (n, 2„). A discussion of the most 
unusual neutron induced reaction, namely fission, 
will be given in the next chapter. 
(a) The n-7 reaction or “neutron capture”.— 
When a neutron strikes a nucleus, it may enter it 
and be captured. This process increases the mass 
of the original nucleus by -f 1 and forms an isotope 
of it. The new isotope may be stable or it may 
be radioactive. If stable, it will show no gamma 
ray emission except for the instantaneous radia- 
tion produced in the capture process whereas the 
unstable isotope will decay. The gamma rays 
emitted in the capture process are called capture 
gammas. Since the n to p ratio in the product 
nucleus increases as a result of neutron capture, 
the radioactive products decay by /3-emission. 
Example of simple non-radioactive capture: 
48Cd113+ >48Cd ni+hv (24) 
It is known that 48Cd114 is stable. There are three 
remarkable features of the neutron capture by 
cadmium. First, cadmium has a cross section of 
about 4,000 barns; thus it virtually soaks up slow 
neutrons. In fact, in the neutron reactions to be 
described in the next chapter, rods are plated with 
a coat of cadmium to allow for control of the reac- 
tor. Recent experiments show a second remark- 
able feature of the reaction. Figure 7—6 shows 
a mass spectrum of cadmium which has been irra- 
diated very strongly with thermal neutrons. It 
is easily seen that the Cd113 isotope is depleted and 
Cd114 is enhanced in abundance, thus proving that 
Cd113 is the only isotope of six cadmium isotopes 
to absorb the neutrons strongly. Finally, Cd113 
shows this enormous capture cross section only for 
neutrons of thermal (1/30 ev) energy. At other 
higher energies it is a relatively poor absorber. 
Neutron group 
Energy in e.v. 
Thermal 
0.03 e.v. 
1 e.v.-100 e.v. 
100 e.v.—1 Mev. 
Over 1 Mev. 
Slow - * 
Intermediate. 
Fast 
Thermal neutrons are those which have an average 
energy of e.v., corresponding to the energy of 
a neutron in equilibrium with air at room temper- 
ature. Since these thermal neutrons are strongly 
absorbed by cadmium they are sometimes called 
“C” neutrons. Rhodium also strongly absorbs 
neutrons of slightly higher energy; other elements 
are listed in the following table in order of in- 
creasing neutron energy. 
Neutron group 
Absorbing element 
Resonance 
energy (e.v.) 
9 
Cadmium 
0. 2 
1. 0 
1. 4 
5. 0 
“D” 
Rhodium 
((jyy 
Indium _ 
“A” 
Silver 
99 RADIOLOGICAL SAFETY 
may take place at still higher energies, but in 
general the cross sections become larger as the 
neutron energies are progressively lowered. The 
cross section for neutron capture in cadmium is 
plotted in figure 7-7 
Figure 7-6.—Mass spectrum of irradiated cadmium. 
Photograph by Prof. A. J. Dempster 
Example of radiative capture: 
uRh^+on1 >45Rh104+7 (25) 
45Rh104 _> 46Pd104+-,e°+2.3 Mev. 
This is a very common reaction which has been 
observed in many other cases, totaling over 100 
reactions. The cross section of rhodium for 
neutron capture may be obtained from a measure- 
ment of the captured gamma rays or by observing 
the intensity of the /3-decay of Rh104. 
All elements except helium are known to capture 
thermal neutrons. Since the emission of a charged 
particle after capture involves additional energy, 
a competition usually exists between neutron re- 
emission (scattering) and y-ray emission (radia- 
tive neutron capture). In general, the probability 
that capture will occur follows a l/» law, that is, 
the cross section varies as the reciprocal of the 
neutron velocity. Boron, for example, follows 
this law even to quite high neutron energies. On 
the other hand, cadmium, gadolinium, and 
dysprosium have thermal absorption cross sections 
which do not follow the l/v law. The reason for 
this is that these isotopes have excited states 
such that when capture occurs at certain energies 
corresponding to these states, resonance absorp- 
tion takes place. Resonance absorption takes 
place in the thermal region for a few isotopes and 
others exhibit resonance for slow neutrons, 
usually below 100 c.v. energy. This phenomenon 
Figure 7-7.—Cross section for neutron capture by cad- 
mium as a function of energy. 
(b) The n-p reaction.—While the neutron can 
slip into a nucleus without being affected by the 
potential barrier, the n-p reaction still involves a 
consideration of the potential barrier, because a 
charged particle, the proton, has to escape through 
it. Thus one might expect that neutrons of higher 
energy will produce greater yields in the n-p 
reaction, since the proton will have a better chance 
to leak through or surmount the barrier. As an 
example, consider the absorption of a neutron into 
an Al27 nucleus: 
13 Al27+o^1—>12Mg27 -f iHl + Q (26) 
In effect, the mass of the original nucleus remains 
unchanged. All that has happened is that 13 Al27 
has exchanged a proton (emitted) for a neutron 
(absorbed). 
The masses on the left hand side 
of the equation =27. 0988 
The masses on the right hand side 
of the equation =27. 1009 
-0. 0021 m.u. 
Therefore the neutron has to supply (0.0021) (931) 
100 Mev=2 Mev to the nucleus before the reaction 
will go. This means that the n-p reaction is a fast 
neutron reaction. Measurement of the cross 
section for the n-p reaction in Al27 gives a curve 
as shown in figure 7-8. 
RADIOLOGICAL SAFETY 
trons. Consider the neutron induced reaction in 
5B10 (the less abundant of the two boron isotopes): 
5B10+0nl—>3Li7 4- 2He4 4- Q (27) 
This reaction has a thermal cross section of 3,800 
barns for the B10 isotope and theoretically releases 
3 Mev of energy. However, Li7 is often left in 
an excited state which reduces the kinetic energy 
imparted to the a-particle. A 2.5 Mev a-particle 
is extremely useful, especially when it is pro- 
duced by such an efficient absorption process, for 
it means that the alpha can be counted and serve 
as a measure of the neutron flux. This is ac- 
complished in an ionization chamber or counter 
filled with BF3, boron trifluoride, or lined with a 
boron compound. The separation of 5B10 from 
the more abundant but poorer absorber SBU al- 
lows these devices to be made even more efficient. 
Boron which is depleted in 5Bn and thus enhanced 
in 5B10 is known as enriched boron. Some 40 
n-a reactions are known, and as was the case for 
the n-p reaction, these are limited to elements 
with Z<C40. 
(d) The n-n reaction {or inelastic neutron scatter- 
ing).—In such reactions, there is usually no change 
in the target nucleus except perhaps for the 
excitation of the nucleus to a higher energy state 
with the subsequent emission of a photon. The 
reaction for any element of mass number Z is 
given by; 
ZA+0nl-*ZA+cn'+Q (28) 
where it is understood that the product nucleus 
ZA is in an excited state. Experimentally it is 
observed that the Q for the reaction is negative, 
indicating that the incident neutron has more 
energy than the ejected neutron. For the incident 
neutron to lose kinetic energy in the collision, it 
must form an intermediate nucleus with the 
bombarded nucleus. Cross sections for this n-n 
or more properly n-n+ 7 reaction are about equal 
to the physical cross sectional area of the nucleus, 
and this fact provides a measure of the nuclear 
radius. Only a few reactions of this type are 
known which result in a radioactive product. 
Strictly speaking, a pure n-n reaction would 
be merely elastic neutron scattering with no 
energy being lost by the incident neutron. Elastic 
neutron scattering is thought of as a process in 
which the incident neutron shoots through the 
Figure 7-8.—Cross section as a function of energy for n-p 
reaction in Al27. 
The threshold energy comes at 2.7 Mev instead 
of the 2 Mev as predicted by consideration of the 
energetics of the reaction. What has been 
neglected in the prediction is that no account has 
been taken of the energy for the proton to escape 
the potential barrier. When this is included in the 
calculation the threshold energy is compatible 
with our analysis. As the energy of the incident 
neutrons increases, the protons find it increasingly 
easier to escape from the nucleus until the neutrons 
reach a saturation cross section (<r8) at an energy 
of 5.9 Mev. After that, the potential barrier does 
not interfere with proton escape from the nucleus. 
It should be clear from figure 7-8 that such cross 
section curves tell a great deal about the structure 
of the potential barrier. Since many of the 
product nuclei formed by the n-p reaction are 
/3-emitters, subsequent /3-decay causes the pro- 
duct nucleus to revert to the original form that 
it had before the transmutation. Over 50 n-p 
reactions are now known, but most of these re- 
actions are confined to elements with Z<40, for 
the heavier elements present too high a potential 
barrier for proton emission. 
(c) The n-a reaction.— This reaction is of very 
practical value when applied to boron, for it 
makes possible an easy means of detecting neu- 
101 RADIOLOGICAL SAFETY 
nucleus too quickly to undergo interaction with 
the nucleus and suffer energy loss. As such, this 
type of scattering leaves the nucleus unexcited. 
Because elastic collisions are so important in 
understanding how neutrons are slowed down, the 
subject will be treated more extensively in section 
7.14. 
(e) The n-2n reaction.—To remove a neutron 
from a nucleus requires that energy equal to that 
of the binding energy for the neutron be supplied 
to the nucleus. Earlier it was noted that the 
binding energy for a single neutron averages 
about 8 or 9 Mev. Therefore, if a very fast (say, 
10 Mev) neutron were to collide with a nucleus, it 
might be expected that two neutrons would be 
ejected.. Furthermore, for the lighter elements, 
the loss of a neutron would lower the NjP ratio 
and make positron emission the probable decay 
scheme for the product nucleus. As before, this 
would mean an additional I Mev would be required, 
making the total energy to be supplied by the 
neutron about 10 Mev. 
Such reactions are commonly observed when 
neutrons from a cyclotron bombardment of 
deuterons on lithium are used. A typical reaction, 
that for potassium, is illustrated by: 
19K39 + o'^1~>I9K38 + o^1'Tott'1 -\-Q (29) 
As expected, K38 is a positron emitter, decaying 
with a half life of 7.7 min. by emitting a positron 
of 2.3 Mev. 
Over 100 n-2n reactions have been observed, 
most of which result in product nuclei which are 
/3-emitters. It is understandable that this decay 
scheme is feasible, since for larger numbers of 
nucleons in a nucleus, the depletion of the neutrons 
by one does not so seriously upset the delicate 
balance as it does in lighter nuclei. 
Using the same line of reasoning that the detach- 
ment of 1 neutron requires 10 Mev, it might be 
indicated that three neutrons could be ejected by 
using 20 Mev neutrons. A few reactions of this 
type have been observed but it is found that a 
n-2n-\-p reaction also occurs in addition to the 
n-Sn reaction. 
7,14 Energy Release From Nuclear Reactions. 
In the foregoing sections, thermal neutrons have 
been indicated as being important in many neu- 
tron-induced reactions. However no mention was 
made of the mechanism by which neutrons ac- 
quired thermal velocities. Actually thermal neu- 
trons are produced by slowing down fast neutrons 
through elastic collisions with atoms. It is rather 
paradoxical that after it has frittered away all but 
a fraction of an electron volt of energy, the neutron 
should be so effective in inducing nuclear reactions. 
Of the reactions which have been discussed in 
this chapter, none have appeared to produce high 
yields so that they could be used for any practical 
application nor were any mechanisms apparent 
which would allow an exoergic reaction to per- 
petuate itself. However for certain reactions in 
the light elements, say, the p-2a reaction in 
lithium it is apparent that per nuclear disintegra- 
tion enormous energy is liberated. Starting with 
8.02631 gms., the reaction yields products of 
8.00778 gms, thereby losing 0.01853 for a gram 
atom. Thus the complete conversion of 7 gms. of 
3Li7 would yield a total of 400,000 kwhr. of energy. 
Per atom, the reaction would release 17.3 Mev 
energy. It is a far cry from disintegrating a single 
3Li7 atom to completely converting 7 gms. of 
3Li7 by proton bombardment. Only 1 in about 
105 protons results in a disintegration and if the 
a-particles produced by the reaction were energetic 
enough to cause an a-p reaction the yield would 
be very small. There would thus be no possibility 
of this reaction perpetuating itself. However, per 
nucleon in the 3Li7 atom, about 2% Mev of energy 
is released. This is a very sizeable amount of 
energy per nucleon as contrasted with 200 Mev re- 
leased in the fission of uranium. The latter 
released only —- or less than 1 Mev per nucleon 
but it has the enormous advantage of being a self 
perpetuating reaction. 
7.15 Cosmic Radiation 
All of the reactions discussed so far have in- 
volved radiation of less than 20 Mev. In cosmic 
radiation, however, energies of a quite different 
order of magnitude are present. 
The words the cosmic ray are so frequently 
used that the layman believes that there is only 
one type of cosmic ray and he is disappointed 
when no simple description of this ray can be 
given. Actually there are several different kinds 
of cosmic rays. However, two general types of 
cosmic rays may be defined. 
102 RADIOLOGICAL SAFETY 
Primaries.—This category includes protons 
which come from some cosmic origin beyond our 
own galaxy. There may also be a small percent- 
age of electromagnetic radiation or high energy 
electrons. Due to the effect of the earth’s mag- 
netic field only the highest energy O109 e. v.) 
protons are able to enter the atmosphere at the 
equator. On the other hand protons of all en- 
ergies are allowed to come in at the poles. When 
they strike the top of the earth’s atmosphere, the 
protons interact with the nitrogen nuclei to form 
secondary particles. 
Secondaries.—The primary particles produce 
new sub-nuclear particles called mesons or meso- 
trons. Mesotrons are particles which have a mass 
about 200 times that of the electron and may 
carry a single positive or a single negative charge. 
Created high in the atmosphere, the mesotrons 
travel down toward the earth with high velocity 
and great penetrating power. As a particle, the 
mesotron is most unusual for it is unstable and 
decays in about 2 microseconds to form an elec- 
tron and a neutrino. In addition high energy 
secondary electrons and photons are found in the 
cosmic radiation. Due to the fact that these par- 
ticles have enormous energies from 107 to 1015 
e. v. they interact strongly with matter and pro- 
duce other tertiary cosmic rays such as neutrons 
and alpha particles. 
The cosmic ray intensity shows considerable 
variation with altitude and geomagnetic latitude. 
Examples of this are given in figure 7-9. It will 
be noted that the primaries produce great num- 
bers of secondaries as is evident from the maximum 
in the curves. Even at high altitudes the cos- 
mic radiation intensity is only about 1 milliro- 
entgen/day. 
Figure 7-9.—Total cosmic ray intensity as a function of 
altitude. 
103 RADIOLOGICAL SAFETY 
Chapter 8 
NEUTRON PHYSICS AND FISSION 
8.01 The Discovery of Nuclear Fission 
Soon after Chadwick had announced the dis- 
covery of the neutron, Enrico Fermi and his 
collaborators in Italy began bombarding uranium 
with these new particles. Upon irradiating ura- 
nium with neutrons from a Ra-Be source, they found 
that several activities were induced in the element, 
and they were puzzled by the fact that these 
activities did not correspond to those which might 
be expected, i. e. elements with atomic numbers 
86-92. It was then believed (and this is now 
known to have been fallacious) that these induced 
activities were due to elements of atomic number 
higher than 92. Such elements are called trans- 
uranium elements. Fermi’s work stimulated re- 
search in other countries, and in 1938 Curie and 
Savitch performed chemical separations on neu- 
tron-irradiated uranium and discovered that an 
element with a 3.5 hour half life was precipitated 
out with lanthanum. The investigators attributed 
the 3.5 hour activity to a transuranium element 
because lanthanum was not known to have a radio- 
activity of that half life. 
In the same year, Hahn and Strassman, repeat- 
ing the Curie-Savitch experiment, proved that the 
3.5 hour activity was due to barium, whose dis- 
integration product was lanthanum. They thus 
proved that the neutron induces in uranium a 
reaction which causes the nucleus to split up into 
two heavy fragments. This splitting up process 
they termed fission. Curie and Savitch had in- 
deed observed the phenomenon of fission, but they 
did not recognize it as such. 
The discovery of fission stimulated great activ- 
ity in the United States. This activity, begun in 
1939 with the investigation of fission phenomena 
in almost every nuclear physics laboratory, con- 
tinued at an ever increasing pace and culminated 
in the large scale release of nuclear energy. 
Prior to the war the private researches of labora- 
tories all over the world had revealed many new 
facts about these phenomena. A brief summary 
of the prewar status of nuclear fission is given in 
the next section. 
By the process of the splitting up of uranium, 
two smaller fragments are produced which to- 
gether weigh considerably less than the original 
mass of the uranium nucleus. This disparity in 
mass is a real one and means that the considerable 
quantity of energy, roughly 200 Mev, is liberated 
in the fission process. It was therefore of the 
greatest interest to understand, on a theoretical 
basis, what heavy isotopes were capable of being 
fissioned (called fissionable materials) and why 
these isotopes fissioned. 
Meitner and Frisch pointed out the analogy 
between the fission process and the division of a 
small liquid sphere into smaller drops as a result 
of a physical deformation of the drop. They noted 
that the mutual repulsion of protons in very heavy 
nuclei is able to predominate to a great extent over 
the forces holding the nucleus together. Thus a 
small amount of energy added to a uranium nucleus 
may produce such a deformation that the short 
range nuclear forces are no longer able to compete 
with the longer range repulsive forces and the 
nucleus tears itself into two parts. Each of these 
fission fragments then carries off very high kinetic 
energy, the exact value of which depends on its 
specific mass. 
In 1939, Bohr and Wheeler published their 
paper “The Mechanism of Nuclear Fission” in 
which they discuss the theoretical basis for fission. 
Their calculations predicted that the fission of 
uranium under the slow neutron bombardment was 
due to the U235 isotope rather than that of the more 
abundant U238 isotope. Less than a year later, a 
group of investigators separated a very small 
quantity of U235 from U238 and proved that it was 
responsible for the fission. It was recognized at 
the time that the fission process gave rise to extra 
neutrons which might be used for further produc- 
ing more fissions in a chain reaction. 
Five years after it was shown that U235 fissioned 
under thermal neutron bombardment, an atomic 
bomb was successfully detonated in New Mexico. 
The term atomic bomb is a misnomer which 
persists through popular usage; actually it should 
be called a nuclear bomb, since it depends upon 
the release of nuclear energy. 
105 RADIOLOGICAL SAFETY 
8.02 Fission Phenomena 
required conditions could be achieved, but many scientists 
had clear ideas as to the problems involved and the direc- 
tions in which solutions might be sought. 
8.03 The Energy Released in Fission 
Elements with atomic mass number less than 
100 are energetically stable, and only the heavier 
elements are energetically disposed to the fission 
process. The following table of typical values for 
energy available, from a given parent nucleus and 
corresponding product nuclei illustrates how 
fission energy increases with increasing atomic 
number: 
In June of 1940, many fundamental aspects of 
nuclear fission had been investigated and published 
in the scientific periodicals. It is of interest to 
summarize the state of knowledge in this new 
expanding field as was done by H. D. Smyth in 
his report “Atomic Energy for Military Purposes.”1 
All of the following information was generally 
known in June 1940, both here and abroad: 
(a) That three elements—uranium, thorium, and pro- 
tactinium—when bombarded by neutrons sometimes 
split into approximately equal fragments, and that these 
fragments were isotopes of elements in the middle of the 
periodic table, ranging from selenium (Z = 34) to lan- 
thanum (Z = 57). 
(b) That most of these fission fragments were unstable, 
decaying radioactively by successive emission of /8-particles 
through a series of elements to various stable forms. 
(c) That these fission fragments had very great kinetic 
energy. 
(d) That fission of thorium and protoactinium was 
caused only by fast neutrons (velocities of the order of 
thousands of miles per second). 
(e) That fission of uranium could be produced by fast or 
slow (so-called thermal velocity) neutrons; specifically, that 
thermal neutrons caused fission in one isotope, U-235, but 
not in the other, U-238, and that fast neutrons had a 
lower probability of causing fission in U-235 than thermal 
neutrons. 
(/) That at certain neutron speeds there was a large 
capture cross section in U-238 producing U-239 but not 
fission. 
(g) That the energy released per fission of a uranium 
nucleus was approximately 200 million electron volts. 
(h) That high-speed neutrons were emitted in the process 
of fission. 
(?') That the average number of neutrons released per 
fission was somewhere between one and three. 
O') That high-speed neutrons could lose energy by in- 
elastic collison with uranium nuclei without any nuclear 
reaction taking place. 
(k) That most of this information was consistent with 
the semi-empirical theory of nuclear structure worked out 
by Bohr and Wheeler and others; this suggested that pre- 
dictions based on this theory had a fair chance of success. 
Looking back on the year 1940, we see that all the pre- 
requisites to a serious attack on the problem of producing 
atomic bombs and controlling atomic power were at hand. 
It had been proved that mass and energy were equivalent. 
It had been proved that the neutrons initiating fission of 
uranium reproduced themselves in the process and that 
therefore a multiplying chain reaction might occur with 
explosive force. To be sure, no one knew whether the 
Table I 
Parent nuclei 
Product nuclei 
Available fls- 
sion energy 
Mev 
28Ni61 
nSi30 + uSi31 
-11 
soSn117 
25Mn58 + 25Mn59 
+ 10 
68Er‘67 
34Se83 + 34Se84 
+ 94 
82Pb205 
41Nb,03+«Nb103 
+ 120 
92U239 
46Pd1I9 + 46Pd120 
+ 200 
In this and the following sections, the parent 
nucleus for fission will always be taken as the 
compound nucleus which includes the mass of the 
neutron producing fission. Thus in speaking of 
the fission of 92t/235, the compound nucleus 92C/236 
will be used when considering mass relations of the 
product nuclei. Only a few heavy isotopes, all 
with an atomic weight greater than 220, are known 
to undergo fission. If one wishes to understand 
why fission occurs only for these heavy isotopes, 
it is clear that one must be able to present a 
qualitative or perhaps a semiquantitive picture 
of the fission mechanism. This picture must 
include everything which is known about the 
interaction of nucleons within the nucleus. One 
of the most revealing things which is known about 
the nucleus is the measure of its mass defect, for 
this immediately yields a value for the average 
binding energy per nucleon. Figure 8-1 shows 
a smoothed curve for the average binding energy 
per nucleon as a function of the atomic weight. 
The total binding energy per nucleus is equal to the 
product of the binding energy per nucleon and the 
number of nucleons. 
A possible fission reaction is: 
1 The official report on the Development of the Atomic Bomb under the 
Auspices of the United States Government, 1940-45. By Henry De Wolf 
Smyth, chairman, Department of Physics, Princeton University, Consult- 
ant, Manhattan District, U. S. Corps of Engineers. 
92U235 + o^^(92U236)->46Pd118 + 46Pd118 + Q (1) 
106 RADIOLOGICAL SAFETY 
so that the mass of any nucleus may be calculated 
from it: 
M—m„( A — Z) + mrZ—a, A uAn + 
t t t t + 
Term a bed e 
i*-ty 
®4 M (4) 
-/I /Jv 
/ 9 
Whore M is the exact mass of an isotope of charge 
Z and mass number A which would result from 
building up the nucleus from Z protons and A — Z 
neutrons, taking into account the observed de- 
creases in mass of the proton and neutron due to 
binding. This rather formidable equation, con- 
sisting of 7 terms each of which is a function of A 
and/or Z, will not be derived here. The signifi- 
cance of each term is as follows: 
Term a = \mn{A—Z)\ is simply the product of 
the mass of the free neutron (mn) and the total 
number of neutrons in the nucleus. 
Term b = [mpZ\ is similarly the product of the 
mass of the free proton (mp) and the total number 
of protons in the nucleus. 
Terms c through g all make up the binding 
energy which is released when the free neutrons 
and protons are brought together to form the 
nucleus under consideration. This is equivalent 
to expressing analytically the empirical fact that 
nuclei have uniform density. This means that the 
volume occupied by a nucleus is proportional to the 
number of nucleons and consequently the radius 
is proportional to A+ 
Term c: The term (cqH) expresses the fact that 
the nucelons are held together by the attractive 
nuclear force, and therefore work was done and 
energy lost when the particles were fused. The 
constant of proportionality ax is numerically 
+ 0.00504. 
Term d: (a2A%) is a term which takes into ac- 
count the fact that the surface of the nucleus con- 
tains nucleons which are not subject to the same 
interaction with other nucleons as are those in 
the interior. Surface nucleons are less tightly 
bound. It is for this reason that light nuclei 
have binding energies per nucleon less than those 
for medium heavy nuclei, since light nuclei have 
relatively greater surface area per unit volume. 
Figure 8-1.—Average binding energy per nucleon. 
This equation is balanced with respect to both 
charge and mass. The energy released is equal to 
the binding energy of the product minus the bind- 
ing energy of the parent. Thus for Eq. (1) 
Ef= 118.S118+ 118i?U8—236Z?238 (2) 
where 7? is the binding energy per nucleon for the 
nucleus indicated by the subscript. From figure 
8-1 the binding energy per nucleon for the palla- 
dium nucleus is 8.5 Mev and for 92f/236 it is 7.5 Mev. 
Thus 
£>=236(8.5-7.5)-236 Mev. (3) 
Considering the errors in the values for B, this is 
in fair agreement with what is actually measured 
for the fission energy. 
8.04 The Binding Energy Equation 
In the foregoing section, the use of binding 
energies allowed a very direct calculation of the 
total energy released in fission. The next section 
will show that if certain critical amounts of energy 
(excitation energies) are added to a uranium 
nucleus, it will undergo fission. The addition of 
such energy can come about as the binding of an 
additional neutron to the L7235 nucleus. However, 
the nuclei will be shown to have different excita- 
tion energies, and it is therefore of the greatest 
importance to calculate the amount of energy with 
which a neutron binds itself to a nucleus. To do 
this, an equation may be derived semi-empirically 
107 RADIOLOGICAL SAFETY 
Since the nuclear surface area is proportional to r2 
and since r is proportional to A,/j, this effect will 
be proportional to A2'J. Empirically, a2 is a con- 
stant= -f 0.014. 
Term e: ( «'3 ) expresses the repulsive effect of 
the protons within the nucleus. For this 
coulomb repulsion of the protons increases suf- 
ficiently to offset the attractive forces. It can be 
3e2Z2 
shown to be equal to — 
The constant a3—0.000627. 
r (z-at\ 
Termj: I u4 \ 2/ takes account of the em- 
L 3 - 
pirical fact that the number of protons in any 
nucleus tends to be equal to one half the total 
number of nucleons. This tendency may not 
seem apparent in heavy nuclei, where the number 
of neutrons is greater than the number of protons, 
but the two would be equal were it not for the 
electrostatic repulsion of the protons. Inside the 
nucleus there are neutron-proton, neutron-neutron, 
and proton-proton interactions. These interac- 
tions are of the same order of magnitude and ac- 
count for the fact that nuclei tend to contain the 
same number of protons and neutrons. a4, the 
constant of proportionality, is equal to 0.083. 
Termg: Delta (5) is a correction term which ad- 
justs for small changes in energy due to the pa iring 
of nucleons in the nucleus. This term may be: 
5 = -\-k if A is even but Z is odd 
5 = 0 if A is odd 
5=—k if A is even and Z is even 
, 7 0.036 
&n d. k 
It thus takes into account the fact that nuclei 
with odd numbers and even numbers for Z and A 
are more or less stable according to table II. 
Abundance of stable isotopes according to odd- 
ness—evenness of Z and A-Z. 
It should be understood that the relative 
abundance of naturally occurring isotopes is a 
measure of their stability. For example s016, an 
even-even isotope, is very abundant whereas 
8017, an even-odd isotope is less common. Further- 
more only four odd-odd isotopes occur in nature. 
By simplifying Eq. (4) and substituting the 
constants ax a2, a3, a4, the following equation is 
obtained: 
M = 0.99389/1 — 0.0081 Z-j- 0.014yl2/3 -f- 
0.00627+0.083 /z--V+J (S) 
Table II 
\ 
\ . 
A-7, \ 
\ 
\ 
\ 
Even 
Odd 
Even 
Most abundant . 
Moderately abun- 
dant. 
Odd 
Moderately abun- 
dant. 
Least abundant. 
It will be noted that this is a semiempirical 
equation into which has been put the contribution 
of all factors which are empirically known to 
effect binding energy. As such it is an approxi- 
mate equation and gives a fairly reliable evalua- 
tion of nuclear masses for all but low values of A. 
Suppose now that the binding energy of a 
neutron to a U235 nucleus be calculated: 
Mass of U235 from Eq. 5 m.u. 
Mass of the added neutron—> 1.00893 
Mass of (U235+n) —>236.12133 
Mass of U236 from Eq. 5 -^236.11401 
Difference in mass —> .00732 m.u = 
6.81 Mev 
Similarly, the binding energy of a neutron to 
U238 can be found to be 5.31 Mev. The factor in 
Eq. 5 which yields a difference of 1.5 Mev in the 
binding energies for a neutron to U235 and U238 is 
the delta-term. In the next section, it will be 
seen that this difference of 1.5 Mev is sufficient 
to explain why U235 fissions with thermal neutrons 
but U238 does not. 
8.05 The Theory of Fission—Energetics 
From the results of the last section, the energy 
which will be given up to a compound nucleus 
by a captured neutron is now determined. It 
remains to be shown why this energy causes a 
fission reaction in certain heavy nuclei. Only a 
few isotopes undergo fission with thermal neutrons 
because there exists a threshold energy which 
must be supplied to the nucleus before fission will 
108 occur. This threshold energy may be termed the 
activation energy. Perhaps this is best visualized 
as being the difference between Ee and Ef where 
Ec is the coulomb repulsive energy and Ef is the 
energy for symmetric fission; i. e., fission products 
of equal mass. Curves for Ec and Ef are plotted 
in Figure 8-2 as a function of the mass number. 
In this figure Ec—Ef for .4 = 235 is about 6 Mev. 
This means that a 6 Mev potential barrier exists 
for the two fission fragments which are trying to 
RADIOLOGICAL SAFETY 
Figure 8-3.—Energy of a nucleus as a function of distance 
between two fission fragments. 
in figure 8-4 where the curve given in figure 8-3 is 
presented again with three curves extending from 
r—0 to r—2R. 
Figure 8-2.—Coulomb and fission energy vs. Atomic mass 
number. 
escape. Once the fission energy curve crosses the 
coulomb energy curve, which it does at .4=250, 
no stable isotope should exist. 
Suppose that the energy of the two fission frag- 
ments (or of the compound nucleus) be considered 
as a function of the distance separating the two 
fragments. When the fragments are still in the 
nucleus (r=2R where R is the fragment radius) 
the energy in the compound nucleus must be 200 
Mev. When the fragments are very far apart 
(r= oo) the energy must be zero. In between 
these two extremes only the coulomb forces will 
act and the curve can be represented as in figure 
8-3. At distances equal to the fragment diameter 
(r=2R), the coulomb force no longer is effective 
and is indicated as abruptly ending at a finite 
value. It is the finite value which is important 
in considering fission, for the difference between 
it and the fission energy is the height of the poten- 
tial barrier for fission. Accordingly, the problem 
of determining whether fission will occur can be 
divided into three categories. These are illustrated 
Figure 8-4.—Potential barrier for fission. 
Let the coulomb energy at r—2R be equal to 
E2R. Then three cases are important 
109 RADIOLOGICAL SAFETY 
Case 1: E2R<Ef or E2R—Ef is negative. 
Such nuclei would be spontaneously unstable 
and would not exist in nature. 
Case 2: E2R^>Ef or E2R—E{~§ Mev. 
Nuclei such as uranium, thorium, and trans- 
uranium elements (plutonium) fall in this 
category. The fission barrier for these ma- 
terials is about 6 Mev. 
Case 3: E or E2R—Ej^>50 Mev. 
Light nuclei with A <+100 come in this cate- 
gory and are very stable with regard to fission. 
The nuclei considered under Case 2 are of great- 
est interest, for the excitation energy is of the same 
magnitude as can be supplied by neutron absorp- 
tion or by bombardment with light charged par- 
ticles. Of the various means of inducing fission, 
the neutron absorption process is of most impor- 
tance to this discussion. 
Bohr and Wheeler calculated that the excitation 
energy for fission of U235 was 5.2 Mev and for U238 
was 5.9 Mev. A slow neutron will add only 5.3 
Mev to U238 and no fission will occur, but it will 
add 6.8 Mev to U235 and fission should occur. 
Thus, the bombardment of U235 with thermal 
neutrons suffices to excite the compound nucleus 
to a level greater than the excitation energy, thus 
overcoming the potential barrier and causing 
fission. If more energetic neutrons, say 2 Mev 
neutrons, are used to bombard U238, the added 
kinetic energy will suffice to cause fission. This 
fast fission reaction in U238 cannot be used in the 
atomic bomb because other processes (see sec. 8.11) 
are more probable. 
One might imagine that there might be a small 
probability for fission fragments to leak through 
the fission barrier analogous to alpha emission. 
This actually happens in the U238 nucleus but the 
half-life for the process is exceedingly long, about 
1017 years. This phenomenon is called spon- 
taneous fission and produces about 20 fissions per 
hour in a gram of uranium. 
8.06 The Theory of Fission—Mechanics 
It is not enough that the excitation energy for 
fission be exceeded in a nucleus because of the 
competition of nuclear processes. Thus, merely 
adding a certain quantity of energy to a nucleus 
does not insure that fission will occur, for other 
processes, such as the emission of light particles, 
might be more probable. If, however, the excita- 
tion energy is concentrated in the proper modes of 
oscillation of the nucleus, then fission will occur. 
The mechanics of the fission process (fig. 8-5) is 
pictured as consisting of a deformation of the 
otherwise spherical nucleus A into a nonspherical 
nucleus B. This nucleus deforms further produc- 
ing a constriction in the middle C. Then the con- 
striction narrows D producing a highly deformed 
product. Finally the constriction snaps, yielding 
two separate fission fragments or products E. 
Figure 8-5.— Mechanics of fission process. 
The fission process does not often yield fission 
products of equal mass and because of this, it is 
said to be asymmetric. Just why this asymmetry 
exists in not well understood. When the fission 
fragments appear, neutrons, /3-particles, gamma 
quanta, and sometimes high energy a-particles 
are emitted. Furthermore, the fission products 
are themselves radioactive and emit /3-particles as 
well as 7-rays. All of these radiations carry away 
some fraction of the total fission energy. The 
division of energy among the various products 
can be made between two equations: 
Fission lAr , .Gamma /Ax 
Nucleus Neutrons+ rays (6> 
200 Mev 160 Mev 15 Mev 5 Mev 
Kinetic 
Radioactive decay of 
Fission fragments (7) 
(+20 Mev) 
This energy balance is only approximate, but it 
serves to illustrate where the total fission energy 
goes in the reaction. 
Two types of neutrons produced by the fission 
process can be distinguished. Prompt neutrons 
are emitted instantaneously while delayed neutrons 
are emitted over a period of seconds after fission 
has occurred. The prompt neutrons comprise 
over 99 percent of all the neutrons emitted and 
apparently have their origin in the fission prod- 
ucts. One might expect the prompt neutrons to 
be emitted by the compound nucleus, but it would 
appear that they are emitted from highly excited 
fission fragments within 10~12 seconds after fission. 
110 RADIOLOGICAL SAFETY 
The number of neutrons produced per fission 
averages between one and three. As they are 
emitted from the fission fragment, these neutrons 
have very high energy. As might be expected, 
where highly excited nuclei are involved, the fission 
gamma radiation is extremely penetrating. 
8.07 Types of Fission and Cross Sections 
Fission of U235 by thermal neutrons has already 
been discussed, and fast neutron fission of the 
same isotope has also been mentioned. In gen- 
eral the cross section for fission of U235 varies with 
the energy of the incident neutron. This cross 
section approximates a l/v law. Other isotopes 
which are fissionable by neutrons are discussed in 
sections 8.11 and 8.14. For the present, only the 
fission of uranium will be discussed. 
Protons and deuterons may also be used to in- 
duce fission in uranium. These processes are 
written as (p, /) and (d, j) reactions. In general, 
cross sections for these reactions are rather low. 
Another type of fission process, called photo- 
fission, is known. In this reaction, the fission is 
induced by the nucleus absorbing a very high 
energy photon. From these reactions, some vari- 
ations in the fission mechanism may be expected 
to produce slightly different fission fragments 
than those produced by neutrons. 
Only three isotopes are classed as fissionable 
materials namely 92U233, 92U235, 94Pu239, although 
almost any isotope of atomic number greater 
than 90 can be fissioned by some means. The 
term, fissionable material, as it is used today, re- 
fers to isotopes which undergo fission by neutrons 
with a high cross section such that the materials 
can be used as atomic explosives. U233 and Pu239 
are not naturally occurring isotopes but must be 
manufactured by a neutron bombardment. 
Ordinary uranium consists of three isotopes 
234, 235, and 238, and is chiefly U238 with the 
other isotopes being present as follows: 
Figure 8-6.— Uranium mass spectrum. 
Photograph by Prof. A. J. Dempster 
Figure 8-6 shows the first mass spectrogram 
taken of uranium by Dempster in 1935. Here 
the 235 isotope is faintly visible but U-234 is not 
apparent on the photograph. The fissionable 
U-235 isotope can be separated from U-238 by 
physical methods. Uranium from which U-238 
has been removed is said to be enriched uranium. 
Through the use of electromagnetic separation 
and diffusion processes, this enrichment can be 
carried out until any desired U235 content is 
reached. These separation processes are ex- 
tremely difficult and costly operations and dur- 
ing the last war were carried out at Oak Ridge, 
Tenn. No detailed discussion of these processes 
is given here. In the following sections when the 
term pure U-235 is used it will mean U-235 which 
has been completely separated from U-238. 
8.08 Fission Products and Radioactivity 
Consider a symmetric fission of the 92U236 
compound nucleus into two fragments of equal 
mass. This process is diagrammatically illustrated 
in figure 8-7. 
TABLE IV 
Figure 8-7.—Nuclear constituents of fission products 
Uranium 
isotope 
Relative abun- 
dance 
Percentage abun- 
dance 
238 
1 
99. 28 
235 
1/239 
. 710 
234 
1/17, 000 
. 006 
--- 
100 
Each fragment will then have mass 118 which 
will be comprised of 46 protons and 72 neutrons 
(a palladium nucleus). There will be an instan- 
taneous emission of two neutrons (on an average), 
and the resultant fission products will be 46Pd117. 
Now natural palladium has the majority of its 
isotopes bunched around mass 107 and its heaviest 
111 RADIOLOGICAL SAFETY 
isotope is 46Pd110. Therefore these super-heavy 
46Pd117 atoms formed in fission must be unstable. 
It is therefore logical to suppose that the isotope 
117 would reach stability by /3-emission, thus mak- 
ing up the proton deficiency of the nucleus. This 
can be easily visualized by referring to the stability 
curve given in figure 8-8. On the curve, A rep- 
age of any fission isotope to the total number of 
atoms fissioned. Except for their extreme neu- 
tron/proton ratios, the fission product isotopes are 
no different from radioisotopes produced by other 
means. Many of them are identical with radio- 
isotopes produced artificially, and in fact many of 
the fission products were first identified by their 
characteristic half-lives. 
In addition to the /3-particles and 7-rays which 
are emitted by the fission products, neutrons are 
also known to be emitted for as long as several 
seconds after fission has occurred. These arc 
spoken of as delayed neutrons in contrast to the 
prompt neutrons which are emitted within 10~12 
seconds after fission. Delayed neutrons make up 
only 6/10 of 1 percent of the total neutrons emitted 
and fall in several groups having different half- 
lives. Most of these delayed neutrons are emit- 
ted within 0.2 seconds after fission but a few 
(0.02 percent of the total) have a half-life of about 
1 minute. It is not too difficult for neutron 
emission to occur in these nuclei which have an 
abundance of neutrons. In fact, the energy re- 
leased by beta decay is sometimes comparable to 
the binding energy of a neutron to moderately 
heavy nuclei in the fission product region. While 
these delayed neutrons are of great practical im- 
portance in atomic power, they constitute such a 
small fraction of the fission neutrons that further 
discussions will not deal with them. From the 
standpoint of atomic energy the number of fission 
neutrons emitted per neutron absorbed is of enor- 
mous importance. While the exact value for this 
number is still secret, the figure averages some- 
where between 1 and 3 neutrons per fission. The 
number is given the symbol 77. 
8.09 The Chain Reaction for Fast Neutrons 
Suppose one has available a small sphere of 
pure U-235. Now since each fission of a U-235 
nucleus produces at least two neutrons, it might 
be imagined that these fission neutrons would 
strike other U-235 nuclei and cause them to fission. 
Such being the case, it is entirely possible that 
this process may multiply itself very rapidly and 
fission a great many of the nuclei before the heat 
generated by the fission products would blow the 
sphere apart. This multiplication process is 
called a “chain reaction,” and is illustrated in 
Figure 8-10. Some neutrons will be lost from 
P igure 8-8.—Fission products and the stability curve. 
resents the U236 compound nucleus. B represents 
the 4ePdm nuclei as they are formed in fission. 
These fission products lie far off the stability curve 
and to reach it they must emit on an average of 
from 3 to 4 /3-particles as indicated by the short 
arrows in figure 8—8. The processes whereby a 
fission fragment undergoes successive beta disin- 
tegration and produces a series of new fission prod- 
ucts are known as a fission chain. 
The various isotopes found among the fission 
products are listed in Appendix L—“Nuclei 
Formed in Fission: Decay Characteristics, Fission 
Yields and Chain Relationship.” Figure 8-9 
shows the yield of fission products as a function 
of mass. Two groups of fission products are 
formed. A heavy group has a maximum at about 
mass 139, and a light group a maximum of mass 
95. The term fission yield refers to the percent- 
112 RADIOLOGICAL SAFETY 
0 « Ctrtoln Mott 
0* Unctrtoln Mott 
Figure 8-9.—Mass distribution of fission products. 
113 RADIOLOGICAL SAFETY 
Figure 8-10.—A diagram of chain reaction in U235 (fast fission) 
114 RADIOLOGICAL SAFETY 
the system so the reaction will be self-perpetuating 
only if the number of neutrons produced by fission 
is greater than the sum of the neutrons producing 
the fission and those lost. One loss can be mini- 
mized by using very pure U-235 so that no non- 
fissionable elements capture neutrons. A second 
loss depends on the size of the system. For a 
sphere, the production of neutrons will be pro- 
portional to the number of atoms in it, and 
therefore to its volume and mass. The escape 
of neutrons, on the other hand, will be proportional 
to the surface area. As the size of the sphere is 
increased, the escape of neutrons becomes rela- 
tively less important until a certain critical mass 
is reached at which the reaction is just self-per- 
petuating. Smaller masses than this are called 
subcritical and larger ovcrcritical. Once the 
critical size is exceeded, the number of neutrons 
will multiply very rapidly and an explosion will 
result if this occurs under the proper conditions. 
If, however, the system should be just over- 
critical and there were no restraining forces keeping 
it in a small volume, it would create a flash of 
neutrons, heating up the mass until it expanded 
to a new size. This would be subcritical, and the 
reaction would cease. 
It should be emphasized that the ultimate 
source of energy, whether released in bomb-form 
or in a power plant, lies in the kinetic energy of the 
fission fragments. These fragments flying apart 
with high velocity constitute a heat source of high 
temperature, measured in millions of degrees. It 
is this thermal energy that accounts for the explo- 
sive effects of an atomic bomb, just as it is also 
the reason why atomic power is produced. This 
concept is very simple and it should be clear that 
there is nothing mysterious about atomic energy. 
The essential difference between an atomic bomb 
and an atomic power plant is that in the former 
the energy is uncontrolled and released in an 
extremely short time, whereas in the latter, the 
energy is controlled and released over a period of 
years. 
8.10 The Atomic Bomb 
A logical way to assemble an atomic bomb might 
be to take two hemispheres, each of which is sub- 
critical, and bring them together very quickly. 
A mechanism which would accomplish this is 
illustrated in figure 8-11. One hemisphere of 
Figure 8-11.—An atomic bomb. 
pure U-235 is imbedded in a large mass of material 
(tamper) placed at the target end of the gun barrel. 
At the other end might be a hemisphere to serve 
as a projectile. Separated by the length of the 
barrel, each subcritical mass would be safe, but 
by firing the projectile down the barrel it would 
attain high velocity and weld itself together with 
the target into an over-critical mass. The heavy 
tamper together with the inertia of the projectile 
would serve to keep the over-critical assembly 
together until a large number of atoms were fis- 
sioned. This would insure a high efficiency in the 
reaction. When talking of the efficiency of an 
atomic bomb, the term means the percentage of 
the fissionable material which is fissioned in the 
explosion. The explosive force of an atomic bomb 
has been publicly stated to be equivalent to about 
20,000 tons of high explosive. From this fact the 
number of curies associated with an atomic ex- 
plosion can be readily and directly calculated. 
The radioactivity is thus found to be equivalent to 
that of thousands of tons of radium. Such is the 
truly fantastic radioactivity associated with atomic 
bomb detonations. Furthermore, the neutrons 
produced by the fission may escape and add to this 
radioactivity either by inducing an (n, 7) or 
similar reaction in surrounding material, or by 
directly passing through material and causing 
ionization from proton recoils. 
If instead of considering the radioactivity asso- 
ciated with this hypothetical bomb, one investi- 
gates the power output from it, the figures ob- 
tained are equally astronomical. This figure may 
be obtained by multiplying the number of fissions 
by the energy released per fission. About 2X109 
kilowatt hours of energy would be liberated. 
Furthermore, this energy would be liberated 
extremely fast and thus magnify the explosive 
effect. The effect of releasing such enormous 
energy in such a short time interval is that the 
115 
774689 O 48 - 9 RADIOLOGICAL SAFETY 
relatively small amount of material is converted 
into a gas at a temperature of several million 
degrees. By virtue of its temperature, the gas 
expands rapidly as a ball of fire producing a blast 
or shock wave which moves with supersonic 
velocity. 
8.11 Resonance Capture in U238 
Besides releasing energy with explosive violence, 
nuclear reactions can be carried out under con- 
trolled conditions in order to be useful for power. 
In the course of the foregoing sections, there has 
been no real explanation why fast fission cannot be 
used to start a chain reaction in natural uranium 
or, in other words, in U238. The reason is that 
while fast fission does occur in U238, there is also a 
competing absorption process which captures fast 
and other neutrons. This capture robs the system 
of neutrons and effectively prevents realizing a 
chain reaction in pure U238. For this reason U238 
is not classed among the three fissionable materials. 
Even though natural uranium contains only a 
small amount of U235, this amount is significant 
because of the relatively high fission cross section 
of U235 for slow neutrons. One might therefore 
hope that this small fraction of fissionable material 
would permit natural uranium to be used in a 
thermal fission chain reaction. The advantage to 
this scheme would be that while it would not lend 
itself to a bomb-type application, it might be 
useful for power production or as an intense 
neutron source to produce radioisotopes. If it 
had been possible to produce U285 economically 
and in large quantities in 1943, the Manhattan 
Project would never have attempted to build the 
large thermal reactors (chain reacting-controlled 
systems) which were constructed at Oak Ridge, 
Tennessee and Hanford, Washington. 
The reason why these large reactors, tech- 
nically called piles, were built was that there was 
no assurance that Oak Ridge could produce pure 
U235 in time to be of military use in the war. A 
part of the Manhattan Project, was assigned the 
mission of building piles for the purpose of 
utilizing the resonance capture phenomenon in 
U238 and thus producing a new transuranium 
element which might be used in place of U235. 
The resonance capture process for U238 can be 
written as: 
92U238 4- o^[92U-]^3 93Np239 4- 
(8) 
The transuranium element 93 is called nep- 
tunium. It is produced by the beta-decay of the 
compound nucleus 92U239 which has a half-life of 
23 minutes. Neptunium is itself unstable and 
undergoes beta-decay with a half-life of 2.3 days to 
form element 94—plutonium. This reaction is: 
njNp239 -^-►..Pu2* 
(9) 
From small-scale experiments carried out with 
microscopic quantities of Pu239 produced by cyclo- 
tron bombardment of uranium with deuterons, 
it was shown that plutonium is a fissionable ma- 
terial just as U235 is fissionable. Since this new 
element has a different chemistry from uranium, 
it is possible to separate it from bombarded ura- 
nium by chemical treatment—a process vastly 
simpler than trying to separate U235 from U238 by 
physical means. 
8.12 The Slowing Down of Neutrons 
In order for the chain reaction to occur in a 
natural uranium system it is necessary that some 
of the neutrons be slowed down to thermal 
energy. However, the resonance capture *by 
U238 has to be partially circumvented in order to 
obtain thermal neutrons. Furthermore, any im- 
purities in the system, such as boron and other 
neutron absorbers, have to be eliminated in order 
to obtain thermal neutrons once the resonance 
capture by U238 has been overcome. 
To accomplish this objective, Fermi suggested 
that a lattice of natural uranium and some light 
element be used for the reacting system. Certain 
light elements, such as carbon, beryllium, and 
heavy water, have the property of not readily 
absorbing neutrons by capture, but they do un- 
dergo elastic collisions with neutrons. These sub- 
stances are known as moderators. Suppose elastic 
collisions between a fast neutron and a large num- 
ber of carbon atoms be considered. This process 
is illustrated in figure 8-12. 
A fast neutron, such as is produced in fission, 
comes in at the top of the diagram and is elas- 
tically scattered by the carbon nuclei. It under- 
goes 6 collisions and then is scattered out of the 
field of view. On the scale of the diagram, only 
116 a few of the carbon atoms are shown and are 
greatly magnified. The distance between each 
collision is between 2 and 3 cms.; thus, it is ob- 
vious that the carbon is practically transparent to 
neutrons. At each collision, the neutron loses 
about )eth of its energy. Thus to convert fast 
neutrons (>1 Mev) to thermal neutrons (1/30 ev) 
requires that the neutrons make about 100 elastic 
collisions with the carbon nuclei. Furthermore, 
during the course of these collisions the neutron 
must not be absorbed either by U238 or by im- 
purities in the carbon. 
RADIOLOGICAL SAFETY 
and shape of these materials is a problem that in- 
volves many factors, some of which are discussed 
in the next section. 
Figure 8-12.—The slowing down of neutrons by carbon 
atoms. 
Figure 8-13.—Diagram of chain reaction using a 
moderator. 
Since the purpose of slowing down the neutrons 
is to take advantage of the slow fission in U236, there 
must be some arrangement of uranium and car- 
bon which will permit the reaction to go. How- 
ever, the problem is not so simple, for it must be 
remembered that the fissions are only desired in 
order to produce neutrons to manufacture Pu239 by 
the resonance capture process. Therefore, a bal- 
ance must be struck in which so many neutrons 
are reserved for thermal fission, so many for 
resonance absorption, and a certain number are 
allowed for loss. The loss may be either by escape 
from the system, by absorption in impurities in 
the uranium, or by capture by impurities in the 
carbon. Figure 8-13, schematically illustrates 
these processes. 
So far as the fission process is concerned, a pile 
consists of a critical mass of a mixture of a fission- 
able material and a moderator. The exact size 
8.13 Piles 
Two piles will be considered. The first is the 
pile designed to produce plutonium, and the second 
is the type designed to produce power. Of the 
first type, the carbon-natural uranium pile will be 
considered. 
(a) Plutonium production pile.—Thermal neu- 
tron reactors were constructed at Hanford, Wash- 
ington for the purpose of producing plutonium. 
Details of construction for these units are still 
classified, as is the power level of operation; how- 
ever, the principle may be seen as illustrated in 
figure 8-14. In this diagram, the uranium is 
shown in the form of lumps imbedded in graphite 
blocks which are stacked together to form a critical 
assembly. 
Two cadmium-plated control rods are shown 
running vertically into the pile. With these rods 
117 RADIOLOGICAL SAFETY 
unit would be about 4X1010 neutrons/cm2 per 
second. This would mean that about 4X1016 
atoms are being fissioned every second. The fission 
product activity would be equal to about 2.0X106 
curies! Two million curies is a fantastic amount of 
radioactivity, and for this reason piles operating 
at high power levels require thick shields (not 
shown in diagram) to prevent the neutrons and 
gamma rays from injuring personnel working in 
the vicinity. 
If 4X1016 atoms are fissioned per second, then 
IX1016 atoms of plutonium will be formed every 
second. In 1 day, 86,400X1016 Pu atoms will be 
formed-—this would be equivalent to about 0.3 
grams of plutonium per day. These figures are 
all hypothetical and are without factual basis; 
they are used only to illustrate the order of magni- 
tude of pile reactions. 
The actual plants at Hanford use the uranium in 
the form of aluminium jacketed slugs which can 
be easily removed from the pile. Once the neu- 
tron irradiation of each slug has proceeded to a 
point where there are significant quantities of 
plutonium in it, the slug is removed from the pile, 
allowed to decay for some time so that its radio- 
activity decreases, and it then undergoes the chem- 
ical processing. Even for long neutron irradia- 
tions, the relative proportion of Pu239 in the 
uranium slug is small and has to be recovered by 
special techniques. 
Every thermal pile, whether it is designed for 
plutonium production or for power production, 
has certain basic requirements which can be 
summarized as follows: 
(1) Critical size must be attained. 
(2) An efficient moderator must be used. 
(3) Pile controls must be suitably designed. 
(4) Provision must be made for adequate 
cooling. 
(5) The fissionable material must be replace- 
able. 
(6) Proper shielding is necessary. 
(6) Power pile.—Figure 8-15 shows a diagram 
of the Daniels power pile which is to be built at 
Oak Ridge. It differs from the pile described 
above in that it is a high temperature reactor from 
which heat is extracted to run a conventional 
power source. Much has been said about atomic 
power and many misconceptions are current. 
Figube 8-14.—Scheme of a uranium carbon pile. 
all the way in the pile, the cadmium absorbs the 
thermal neutrons and the pile will not operate. 
As the control rod is removed, the pile will reach 
the critical mass stage and will operate. Thus the 
pile is an extremely simple machine, for it has no 
moving parts other than the control rod which is 
used to start up the pile. Further removal of the 
control rod increases the neutron flux within the 
pile and thus increases the power level of operation. 
As the power level increases, the increased fission 
rate boosts the thermal energy generated, and un- 
less this excess heat were removed, the pile would 
soon become dangerously hot. To do this, alumi- 
num tubes are placed inside the reactor and cool- 
ing water is circulated. 
If the pile were operated at a power level of 
100 kilowatts the thermal neutron flux in the 
118 RADIOLOGICAL SAFETY 
Figure 8-15.—Daniels atomic power plant. 
119 RADIOLOGICAL SAFETY 
Rather than discuss the Daniel’s pile in detail, the 
following facts about atomic power are summar- 
ized; 
(1) The highest temperature at which a power 
pile may be operated is determined by the proper- 
ties of pile materials. 
(2) A power pile cannot be operated indefinitely 
without recharging the unit with fresh fissionable 
material to replenish that which has been depleted 
by fission. 
(3) The process by which the heat energy gen- 
erated in the pile is converted into useful power 
is exactly the same as in an ordinary power plant. 
Conventional heat exchangers, condensers, and 
blowers are used just as illustrated in figure 8-15. 
(4) Every atomic power plant will produce 
radioactivity in proportion to the power output 
of the machine. For this reason, special shielding 
and health precautions are absolutely essential for 
pile operation. 
(5) No atomic power plant can operate unless 
it contains a certain critical mass of fissionable 
material. Because of this fact, together with the 
fact that many tons of shielding and conventional 
power equipment are needed, atomic power plants 
will not be readily adaptable for anything except 
fixed or large mobile installations such as naval 
vessels. 
supplant existing power resources during the next 
several decades. 
8.14 The Transuranium Elements 
Both the transuranium elements neptunium 
239 and plutonium 239 have already been men- 
tioned. Plutonium is an alpha emitter with a 
half life of 24,000 years, and is of prime impor- 
tance because it fissions with slow neutrons just 
as does U-235. Other isotopes of these two ele- 
ments can be produced by artificially accelerating 
light particles and bombarding uranium with 
them. 
In addition, isotopes of elements 95 and 96 
have recently been announced. Element 95 is 
called americium and is abbreviated Am. Its 
single isotope is at mass 241, is an alpha emitter, 
and has a half life of 500 years. Element 96 has 
been named curium (Cm) and to date has two 
isotopes, one of mass 240 and another of mass 242. 
Both are alpha emitters and have half lives of 1 
and 5 months respectively. 
The transuranium isotopes are shown in table V. 
In this table, the symbol with the half-life 
figure denotes the type of decay scheme for each 
isotope. K indicates decay by K electron cap- 
ture. Not indicated in this chart is the U-233 
isotope which is produced by neutron absorption 
in thorium 232. This reaction leads to two sub- 
Table V 
Mass number 
234 
235 
236 
237 
238 
239 
240 
241 
242 
Chemical 
symbol 
Curium_ 
1 mo a 
5 mo a 
Cm 
Americium 
500 y 
a 
Am 
Plutonium . 
50 y a 
24,000 y 
a 
Pu 
Neptunium _ 
4.4 d 
K 
8 mo. 
K 
20 hr 
P 
2 X 106y 
2d p 
2.3 d p 
Np 
Uranium 
2.7 X 105y 
a 
7 X 108y 
a 
6.8 d p 
4.5 X 10« 
y « 
23 m p 
U 
(After Seaborg Science 104, 379 (1946) 
(6) Until these new type power units have been 
built and successfully operated for considerable 
periods of time, no evaluation of the relative cost 
of atomic power to ordinary power can be made. 
The immediate prospects are not such as to en- 
courage one to believe that atomic power will 
sequent beta decays forming 92U233, which is an 
important isotope by virtue of the fact that it 
undergoes slow fission. 
There are thus three fissionable isotopes which 
are important for power or military application— 
92U233, 92U235, and 94Pu239. 
120 RADIOLOGICAL SAFETY 
Chapter 9 
INSTRUMENTATION AND PHOTOGRAPHIC DOSIMETRY 
9.01 Introduction 
The detection and measurement of high energy 
radiation depends entirely upon the proper use of 
suitably constructed instruments since nature has 
not seen fit to provide man with senses capable 
of responding to it. Without instruments even 
intense radiation fields will not be recognized 
until irreparable damage has been done. It is 
therefore of utmost importance that all persons 
making radiation measurements have a thorough 
understanding of the principles of operation and 
the limitations of the available instruments. 
Furthermore, in making radiation measurements 
an individual must interpret meter readings in 
terms of the characteristics of the specific instru- 
ment, and serious and dangerous errors can easily 
be made without a knowledge of the basic prin- 
ciples behind the instrument design. This chapter 
aims to present briefly the underlying principles, 
design characteristics, and limitations of the types 
of instruments at present available. 
9.02 Ionization of Gases 
If photographic film and a few special meth- 
ods are excepted, all detecting devices are based 
upon the ionization produced in gases by the 
incident radiation. When an ionizing agent, such 
as an alpha particle or a photon of electro-mag- 
netic radiation, enters a gas, it may act on a 
neutral atom or molecule with a force large enough 
to remove one or more electrons from the atom. 
It is most probable that two ions will be formed, 
and so it is customary to speak of the formation of 
ion pairs. This process must be carefully dis- 
tinguished from pair production, where an elec- 
tron and a positron are born out of annihilation 
of a high energy gamma ray (ch. 5, sec. 5.10). 
When the total energy of an ionizing radiation 
is known and the total number of resultant ion 
pairs is determined, it is found that the energy 
lost per ion pair is considerably greater than the 
ionization energy. This is due to the fact that 
some collisions occur without ionization but with 
an energy loss to the ionizing agent. Moreover 
in some collisions a more tightly bound inner 
electron will be removed, and this will require 
more energy than the ionization energy, which 
refers to the most loosely bound electron. The 
average energy loss per ion pair in air is about 
33 electron volts. Hence an incident particle 
having an energy of 1.5 Mev will produce in air 
1.5X106/33 or 4.5X104 ion pairs. The total 
number of ions produced will be twice this figure. 
The production of ionization by a high-speed 
particle has been used in the Wilson cloud chamber 
to make visible the path of the particle. The cloud 
chamber is an invaluable tool in nuclear research 
and as such merits a brief description even though 
its use is confined to physics laboratories. The 
cloud chamber utilizes the fact that water vapor 
will not readily condense to form visible rain drop- 
lets unless there is a nucleus of some sort to collect 
around. Charged particles or ions are very accept- 
able nuclei for droplet formation. In the chamber 
water vapor is produced in a cylinder closed at the 
top with a glass plate for viewing and at the bot- 
tom with a tight-fitting piston. A small amount of 
water is put on top of the piston. If the piston is 
suddenly withdrawn, the gas will expand and 
cool. It will be supersaturated, that is it will 
contain more water than it can hold at the re- 
duced temperature. Conditions are therefore 
favorable for droplet formation with a subsequent 
raining down of the droplets into the excess water 
on the top of the piston. If ions are present along 
the path of an incident particle, the water droplets 
will form about these ions and will be visible as a 
series of tiny beads of water. This is the only 
available method by which particle tracks in air 
can be made visible, and it has yielded a wealth 
of valuable information. Space does not permit a 
full description of its many applications to nuclear 
research, but some typical tracks in a chamber are 
shown in figure 9-1. 
9.03 ionization Currents 
If ions are formed in a gas subject to an electric 
field, they will move in opposite directions, the 
negative ions toward the positively charged anode 
and the positives toward the negatively charged 
cathode. The speed attained by the ions depends 
on the voltage applied to the electrodes, the nature 
121 RADIOLOGICAL SAFETY 
Figure 9-1.—Visible path of nuclear particles in Wilson cloud chamber. 
Courtesy Carnegie Institute of Washington, Department of Terrestrial Magnetism 
of the ions, and the gas pressure. If the electrodes 
are connected to a battery, the ions reaching the 
electrodes will give up their charge and become 
neutral again at the expense of removing charge 
from the battery. This results in a current flow 
through the battery and the external circuit. In 
general this current flow will be extremely small, 
and special measuring devices are required to 
detect it. As an example consider the ions pro- 
duced by the 1.5 Mev particle previously dis- 
cussed. This particle left a trail of 4.5 X104 ion 
pairs, each ion having a charge of 1.6X10-19 
coulombs. For each ionizing particle the charge 
that has been separated will be 4.5X104X1.6X 
10~19=7.2X 10~15 coulombs. Assuming 100 such 
a-particles entering the gas per second, the total 
charge flowing will be 100X7.2X 10“15 coulombs 
per second or 7.2 X10~13 amperes. Portable 
122 microammeters can scarcely detect currents 
smaller than 10“6 amperes, and the best labora- 
tory galvanometers are sensitive to about 10“10 
amperes. Thus ordinary current measuring in- 
struments are obviously inadequate for work with 
such ion currents. 
RADIOLOGICAL SAFETY 
this voltage will not affect the current readings. 
This is particularly important in portable instru- 
ments where it is not possible to incorporate 
elaborate voltage regulating circuits and where 
battery voltages will change with use. 
An ion will move with an increasing velocity 
and energy until neutralization occurs or until it 
loses energy through collisions with gas molecules. 
If the mean free path (chap. 2, sec. 2.07) is small 
and the collecting voltage is not too high, the 
ion will gain only a small amount of energy 
between collisions. At each collision it will share 
its kinetic energy with the struck gas molecule in 
such a way that both kinetic energy and momen- 
tum are conserved. Such collisions are called 
elastic and are analogous to the collisions of billiard 
balls. 
If the mean free path is increased and if the 
applied voltage is high, the ion will gain a greater 
energy between collisions. When an ion has an 
energy greater than the ionization energy of the 
gas molecule, it may produce secondary ions upon 
collision. The total kinetic energy after the col- 
lision will be less than the total kinetic energy 
before by the amount of energy expended in pro- 
ducing the ion. In this type of collision kinetic 
energy is not conserved, and the process is called 
inelastic. 
The secondary ions formed by inelastic col- 
lisions will in turn be accelerated by the electric 
field and may produce further ionization. This 
cumulative effect is known as Townsend or 
avalanche ionization. If a total of A ion pairs 
results from one original pair, the process is said 
to have a gas amplification factor of A. In 
practice A varies from about 10 in gas-fil]ed 
photoelectric cells to 108 in some Geiger-Mueller 
counter tubes. Avalanche ionization is discussed 
in greater detail later in this chapter. 
9.04 Electroscopes and Electrometers 
Instruments for measuring the amount of elec- 
tric charge collected in an ionization chamber are 
known as electroscopes and electrometers. It is 
sometimes difficult to classify an instrument as 
one type or the other, but for present purposes 
an electroscope will denote an instrument which 
does not require a continuous external voltage for 
its operation. 
The Lauritsen electroscope is one of the most 
Figure 9-2.—Variation of ion current with potential 
applied to collecting electrodes. 
When a constant amount of ionization is pro- 
duced, as by a constant intensity X-ray beam, and 
when the ionization current is measured for 
various voltages applied to the collecting elec- 
trodes, a relation similar to that shown in figure 
9-2 is obtained. With low collecting voltages the 
ion velocities are low, and considerable time is 
required for them to reach the electrodes. Be- 
cause of the mutual attraction of oppositely 
charged particles there is always a tendency for 
ions to recombine and form neutral atoms. Any 
ions which recombine do not contribute to the 
externally measured ion current since they are 
neutralized before they reach the electrodes. 
The chance of recombination is greater the longer 
the time before the ions reach the electrodes. 
Thus with low collecting voltages there is a sub- 
stantial amount of recombination, and many of the 
ions are lost before they can contribute to the ion 
current. The fraction lost decreases with increas- 
ing voltage, and eventually all of the ions are 
collected so there is no further increase in current. 
This condition is known as saturation, and the 
maximum current is called the saturation current. 
It is obviously desirable to work with saturation 
currents whenever possible. This condition will 
yield the maximum current that can be obtained 
from a given amount of ionization. Furthermore 
in the saturation region the current is independent 
of the electrode voltage, and hence fluctuations in 
123 RADIOLOGICAL SAFETY 
Figure 9-3.—Schematic diagram of a Lauritsen electroscope 
generally useful instruments for radiation measure- 
ments. In this instrument a wire is bent into 
the form of an L and mounted on the electroscope 
case through an insulating bead of quartz or amber 
(fig. 9-3). The moving system is a quartz fiber 
about 5 microns in diameter, made conducting 
with a thin metal coating and cemented to one arm 
of the L. To make this fiber visible in the micro- 
scope a second quartz fiber is fused to the free end 
of the first, and at right angles to it to form a T. 
The microscope is focussed on the head of the T 
using light admitted through a small window in 
the end of the electroscope case. The L and the 
conducting fiber form a single conductor which 
is charged by moving a wire from a battery into 
contact with one arm of the L. The mutual 
repulsion causes the quartz fiber to deflect from 
the side of the L. Ions formed inside the case 
will neutralize the charge and the fiber will return 
toward its uncharged position. As in other 
electroscopes the deflection is not linear with 
charge and deflections must always be taken over 
the same scale range. 
Another useful quartz fiber instrument is the 
pencil type electroscope, or dosimeter (fig. 9-4). 
This is essentially a Lauritsen electroscope modi- 
fied so that the entire instrument is about the 
size of a large fountain pen. The conducting 
system in the dosimeter consists of two quartz 
fibers each bent into a U. The two fibers are 
fused together at the ends of the U, and the 
mircoscope is focussed on the end of one fiber. A 
charge placed on the fiber system causes the fibers 
to diverge by mutual repulsion. The protective 
cap on the end of the pencil meter has a small 
window for illuminating the fiber and the scale. 
When the cap is removed, a contact is exposed for 
charging the fiber system from an external battery. 
Instruments of this type can be made sufficiently 
rugged to withstand the shocks of normal human 
activity, are small enough to be worn comfortably, 
and are very useful for measuring integrated 
exposures. They can be made with a sensitivity 
such that 0.1 roentgen will produce about one half 
of full scale deflection. 
Electrometers also measure electric charge 
through the action of electrostatic forces on a fiber 
or a light conducting vane. By applying an exter- 
nal potential to auxiliary electrodes, a somewhat 
greater sensitivity can be attained than is usual for 
electroscopes. Many types of electrometers have 
been developed but it is not possible to discuss 
them here in detail. They are essentially labora- 
tory instruments and are particularly suitable for 
measuring low energy beta or alpha particles. 
Before leaving the discussion of electroscopes 
and electrometers a few general considerations of 
use and operation should be mentioned. In the 
124 RADIOLOGICAL SAFETY 
A Insulating ring 
B Charging rod ihollow to admit light from window) 
C - Fixed heavy metal coated quartz fiber 
D Movable fine metal coated quartz fiber 
E Metal cylinder 
F ■ Transparent scale 
G • Metal support for fibers 
Side view 
showing arrangement 
of fixed and 
movable fibers 
Figure 9-4.—Pocket dosimeter electroscope 
construction and use of these instruments the 
utmost care must be taken to maintain a high 
electrical resistance in all insulators. Only the 
very best insulators, such as amber, quartz, sul- 
phur, or polystyrene, are suitable, and these must 
be kept free from dust, moisture, and handling if 
satisfactory operation is to be obtained. This 
maintenance of high insulation is vital because 
the quantities of electricity involved in most 
ionization measurements are extremely small. 
The minuteness of the electrical quantities in- 
volved can be realized from the following con- 
siderations: An electroscope can be considered as 
a condenser with a capacitance C charged to a 
potential V. The charge Q will be given by the 
relation: 
Q=CV (1) 
A reasonable capacitance for an electroscope is 
10 nn f (10 e.s.u.). If it is charged to 300 volts 
(1 e.s.u.), the charge will be 10 statcoulombs or 
3.3X10-9 coulombs or 2X1010 electrons. 
In the absence of ionizing radiation a good 
electroscope should maintain its charge for many 
hours. Assuming 100 hours as a reasonable dis- 
charge time, the maximum allowable leakage 
current through the insulators can be calculated 
from the relation, 
I=T <2> 
to be 0.9X10-14 amperes. By Ohm’s law the re- 
sistence must be at least 3.3X1016 ohms. Some 
simplifying assumptions have been made in the 
above calculations, but they give the order of 
magnitude of the resistance required in an elec- 
troscope to prevent the minute charges usually 
measured by the instrument from leaking away 
through the resistance. Anyone who has worked 
with high resistances will appreciate the difficulty 
of maintaining these values, particularly under 
field conditions. 
Insulator soak-in is a phenomenon regularly 
encountered in the operation of electroscopes and 
electrometers. When an instrument has been 
out of use for some time and is charged, a rather 
rapid discharge will be noted. This is due to the 
penetration of part of the charge into the insula- 
tor. It is not leakage in the ordinary sense be- 
cause it practically disappears if the instrument 
is kept charged for a day or so. To eliminate this 
the instrument should be charged a day or more 
before it is used. 
It will be noted that the moving part of most 
electroscopes is a quartz fiber. Quartz is very 
strong, particularly in small diameters, has a low 
coefficient of thermal expansion, and has desirable 
elastic properties so that the fiber will always 
return to the same zero point. These character- 
istics make quartz an outstanding material for 
sensitive measuring instruments. 
125 RADIOLOGICAL SAFETY 
9.05 Ionization Chamber Instruments 
Ionization chamber instruments vary widely 
depending on the particular type of radiation to 
be detected. Short range radiation is admitted 
to the chamber through a suitable window. If 
alpha particles are to be measured, the window 
must be exceedingly thin to allow them to enter 
the chamber. Because of their short range, how- 
ever, it is certain that once inside the chamber 
they will expend all of their remaining energy in 
ionizing the gas. Very few windows are thin 
enough to admit a-particles, but thin mica or 
stretched nylon film about 0.0001 inch thick is 
satisfactory. 
If beta particles are to be measured, the win- 
dows need not be so thin, and the path of the par- 
ticle inside may be so long that it is not completely 
absorbed by the gas and loses a portion of its 
energy striking the chamber wall. To obtain the 
greatest possible number of ion pairs, the /3-par- 
ticle should expend its entire energy in the gas. 
If the chamber is filled with a heavy gas, such as 
argon under pressure, all but the most energetic 
/3-particles will be absorbed completely in the gas. 
Quite different considerations enter into the 
design of an ionization chamber for measuring very 
penetrating radiations such as X-rays or 7-rays. 
When a photon enters the ion chamber and is ab- 
sorbed by air, high speed electrons are produced. 
These electrons travel through the gas in the 
chamber producing ions until their kinetic energy 
is spent. All of the ions produced must be col- 
lected to fulfill the conditions of the definition of 
the roentgen, and this means that the ionization 
chamber must be so large that every primary 
electron loses all its energy before striking the 
walls. For 0.2 Mev X-rays this requires a cham- 
ber about 20 centimeters in diameter. With 
higher energy radiations the electrons will have 
higher energies, and the ionization chambers must 
be made still larger. Such chambers are out of the 
question for field use, and it is necessary to con- 
struct chambers which are much smaller but which 
are equivalent to the large standard units. 
To be equivalent, the small portable chamber 
should have the same absorption for X- and 7-rays 
as the air in the standard chamber and should also 
have the equivalent of the long air paths for the 
absorption of the high energy electrons. Since 
the absorption of X- and 7-radiation depends 
primarily on the atomic number of the absorbing 
material, it is reasonably satisfactory to choose for 
the walls of the ionization chamber a material 
having an atomic number close to 7 or 8, the values 
for nitrogen and oxygen. Carbon with an atomic 
number 6 is reasonably close, and chamber walls 
are regularly made of bakelite or plastics which 
contain a high percentage of carbon atoms. A thin 
wall of such material will be equivalent to a large 
amount of air because the solid has a much greater 
density and thus has an equal number of atoms 
packed into a smaller space. Since human tissue 
is composed chiefly of carbon, oxygen, nitrogen 
and hydrogen, such an instrument will simulate 
absorption by the body. 
The wall thickness will be a compromise because 
the optimum thickness depends on the energy of 
the radiation. Low energy radiation will produce 
low energy electrons which lose a large fraction of 
their energy in the walls and hence do not contrib- 
ute fully to the ionization in the gas. Very high 
energy radiation on the other hand may produce 
high energy electrons that leave the chamber and 
so produce in the gas only a fraction of the ioni- 
zation of which they are capable. In practice it 
is possible to build chambers which are satisfac- 
tory for X-rays of energies between about 0.08 
and 0.25 Mev. These chambers can also be used 
to measure 7-rays if they are calibrated against 
suitable standards. Ionization chambers designed 
on these considerations are known as thimble 
chambers. They are usually made of a bakelite 
shell with a thin graphite coating on the inner 
surface to make it conducting and a well insulated 
central electrode. 
One successful thimble chamber instrument is 
the condenser r meter shown in figures 9-5 and 9-6. 
In this instrument the ionization chambers fit into 
a bayonet type socket and make connection with 
the fiber electroscope and charging mechanism. 
The position of the fiber is read with a microscope 
and scale illuminated by an internal bulb and 
battery. With the chamber in position the sys- 
tem is charged by a frictional electricity generator 
until the fiber is at zero on the scale. The charged 
chamber can then be removed from the meter and 
the insulation protected from dust by a metal cap. 
The chamber may be placed in a desired location 
or carried by a workman and read at a later date 
126 RADIOLOGICAL SAFETY 
Figure 9-5.—Condenser r meter. 
A ■ Movable fine quartz fiber G Conductor between bow and plate placing L and A at the same potential 
B Bow to supply tension for fiber A H Scale 
C Supports insulating bow B and plate L from case I One disc of electrostatic generator grounded to case 
0 and E Terminals which make contact when detachable J switch 
tube is inserted in instrument K Light to illuminate scale 
F Ionization chamber L Plate 
M Insulators 
Figure 9-6—Condenser r meter, cut-away view. 
127 RADIOLOGICAL SAFETY 
by reinserting the end of the partially discharged 
chamber into the meter socket. The scale is 
graduated directly in roentgen units with appro- 
priate multiplying factors for the various sized 
chambers. These are available in sizes from 0.25 
to 100 roentgens. The scale reading after exposure 
will be the total exposure since charging; if the 
time between readings is known, the average 
exposure rate can be calculated. 
The condenser r meter has been used for 
measuring neutron intensities as well as X- and 
7-rays. Neutrons will penetrate the chamber 
walls, produce ionizing recoil nuclei and discharge 
the chamber. This meter was used to measure 
neutron intensities until better methods were 
developed. An arbitrary unit of neutron inten- 
sity, termed the n unit, was defined in terms of 
this meter. The definition of an n unit is: If an 
r meter ionization chamber is exposed to a neutron 
flux and an r reading is obtained on the scale, that 
reading will be numerically equal to the number 
of n units of neutron intensity. This unit is un- 
satisfactory because of the dependence of ioniza- 
tion on the velocity of the neutrons but is still 
used to some extent. 
9.06 Ionization Chamber—Amplifier Instruments 
Although the condenser r meter is a very useful 
instrument, it is not entirely satisfactory for sur- 
vey purposes since it does not read radiation in- 
tensities directly. The chambers must be charged, 
left in the radiation field for an appropriate time, 
and then read with the meter. This is quite 
satisfactory if it is desired to determine the total 
integrated exposure of an individual whose work 
requires him to move about in radiation fields of 
varying intensity, but if a large contaminated 
area is to be surveyed the number of chambers 
required becomes exorbitant. This type of work 
requires an instrument which will give a steady 
deflection that is proportional to the amount of 
radiation striking the chamber. 
If very sensitive current measuring instruments 
were available, it would be possible to put one 
of these in series with the ionization chamber 
and the battery and measure the current directly. 
Unfortunately ionization currents are too small 
to be measured with portable meters, and it is 
necessary to use other means. If a resistance is 
put in series with the ion chamber and the bat- 
tery, there will be a voltage drop across it, which 
by Ohm’s law will be proportional to the ioniza- 
tion current. For example, if the ionization cur- 
rent is 10~12 amperes and R is 109 ohms, U=109X 
10“12= 10“3 volts. It is perfectly feasible to measure 
voltages of this order with suitable vacuum tube 
circuits. 
If the resistor in the ionization chamber circuit 
is incorporated into the grid circuit of a vacuum 
tube (fig. 9-7), any voltage developed across the 
resistor will be impressed on the grid and will 
produce changes in the plate current. 
It is possible to obtain vacuum tubes such that 
a grid voltage change of 1 volt will produce a 
plate current change of 2,500 microamperes. If a 
voltage of 10~3, produced by the 10~12 ampere 
current flowing through 109 ohms, is put on the 
grid of such a tube, the change in plate current 
will be 2,500 X 10~3 = 2.5 microamperes or 2.5 X 
10~6 amperes. The tube, therefore, has amplified 
a current of 10~12 amperes to 2.5X10-6 amperes, a 
gain of a factor of 2.5 million. Since this current 
is flowing in the plate circuit of the tube which will 
have a resistance of 106 ohms or less, it is no longer 
necessary to maintain the extremely high insula- 
tion resistances demanded in the ionization circuit. 
Only ordinary insulation values are needed in the 
plate circuit of the vacuum tube or in any succeed- 
ing circuits. 
It is necessary, however, to choose the vacuum 
tube rather carefully if satisfactory operation is 
to be obtained. In the ordinary vacuum tube 
there is a small grid current which flows even when 
the grid is made negative. This grid current is 
due to several factors, one of which is residual gas 
becoming ionized in the electron stream. In the 
average tube this grid current is perhaps 10~10 
amperes which is negligible for most applications. 
When the tube is connected to an ionization cham- 
ber, this grid current has the effect of shunting 
the series resistance and thus reducing the sensi- 
tivity. Special tubes, known as electrometer 
tubes, have been constructed for this use. In 
these tubes it has been possible, by special design 
and construction, to reduce the grid current to 
about 10~15 amperes which permits quite satis- 
factory operation with ionization chambers. 
In many cases the amplification obtained from 
a single tube is not sufficient to operate a rugged 
indicating meter, and further amplification is 
128 RADIOLOGICAL SAFETY 
tube. To eliminate this variable, instruments are 
frequently supplied with a voltmeter and an 
adjusting rheostat so the voltage can be set to the 
value it had at calibration. 
In general, ionization chamber instruments, 
particularly those designed for field use, do not 
have the sensitivity .that can be attained by 
Geiger-Mueller counters. Ionization chamber in- 
struments for field use will detect 7-ray intensities 
of 0.1 roentgen per 24 hours but are not sensitive 
much below this. They are more satisfactory for 
high intensities and can readily be designed for 
intensities of several hundred roentgens per day. 
They can be made so the scale reading is reason- 
ably linear with radiation intensity, and the 
sensitivity range can be altered by changing the 
size of the ion chamber or by changing the value 
of the series resistor. If the ion chamber and the 
electrometer tube are put into sealed units, there 
will be no sensitive insulation exposed to dust 
and moisture, and hence these instruments are 
quite reliable under adverse conditions. 
Ion chambers can be used to detect a-particles 
if the chamber is equipped with a very thin 
window. An a-particle once inside the chamber 
may produce as many as 105 ion pairs over a very 
short path while a /8-particle will produce only 103 
ions in traversing the entire chamber. In a very 
thin chamber the beta ionization may be still 
further reduced without a corresponding reduction 
in tfie a-particle ionization. The pulse passed on 
to the amplifier will therefore be much greater 
for an a-particle. With this arrangement it is 
possible to detect a-particles in the presence of a 
considerable amount of beta and gamma radia- 
tion. If measurements of alpha activity are not 
desired, a thicker window is used which will 
exclude the a-particles. A still thicker window will 
exclude the /3-particles as well, and only gamma 
radiation will be measured. 
9.07 Geigcr-Muellcr Counters 
Geiger-Mueller (G-M) counters take advantage 
of the gas amplification that can be obtained when 
high accelerating voltages are applied to an ioniza- 
tion chamber. Ion chambers are usually operated 
at atmospheric pressure or even under a positive 
pressure. Because of the small mean free path 
at these pressures excessive voltages are required 
to produce avalanche ionization, and G-M tubes 
Figure 9-7.—Ionization chamber with single stage 
amplifier circuit. 
necessary. In the preceding example the final 
plate current change was only 2.5 microamperes 
which is too low to operate portable meters. If a 
resistance is placed in the plate circuit of the 
electrometer tube, variations in ion current will 
produce voltage fluctuations across the resistance. 
These variations in voltage can be impressed on 
the grid of a second tube for further amplification. 
With no ion current in the chamber there will be 
a steady plate current in both tubes. In the 
second tube this steady plate current will produce a 
steady meter deflection on which the current 
changes due to amplified ion currents will be super- 
imposed. It is highly desirable to have a meter 
reading of zero when there is no current (or only 
that due to background) in the ionization chamber. 
To accomplish this the auxiliary circuit shown in 
figure 9-8 can be used. This circuit sends a 
current through the meter in the opposite direction 
to the steady plate current and can be adjusted so 
that the combined currents are exactly zero. 
If this adjustment is made with the ionization 
chamber disconnected, the meter will read zero 
until an ionization current flows. The meter 
readings will then be proportional to the ionization 
current. 
The calibration of an ionization chamber-ampli- 
fier instrument depends on the amount of ampli- 
fication obtained from the tubes, and hence it is 
necessary to maintain the amplification as constant 
as possible. One factor which will affect the 
amplification is the battery voltage which is ap- 
plied to the ionization chamber and the amplifier 
129 RADIOLOGICAL SAFETY 
Figure 9-8.—Ion chamber with zero current bucking amplifier circuit. 
are seldom operated at atmospheric pressure. If 
the pressure in an ionization chamber is reduced 
to about 10 centimeters of mercury, the mean free 
path will be increased, and gas amplification can 
be obtained at voltages of 250-1,500 volts depend- 
ing on the gas and the tube dimensions. * 
Ion chambers are made in many shapes and 
sizes, but successful G-M counters usually have a 
cylindrical cathode from 1 to 10 centimeters in 
diameter with a length from 2 to 10 times the 
diameter. The anode consists typically of an 
insulated axial wire 0.001-inch to 0.005-inch in 
diameter. Future discussions will therefore be 
confined to cylindrical structures. 
To simplify the discussion assume such an 
ionization chamber filled with gas to an absolute 
pressure of 10 centimeters of mercury and exposed 
to a constant amount of radiation, each ionizing 
particle or photon having the same energy. Each 
ionizing particle entering the chamber will pro- 
duce a definite number of ion pairs in the gas, and 
these ions will proceed to the collecting electrodes 
where they will be neutralized and will produce a 
pulse of current in the external circuit. If there 
are a large number of pulses per second, they will 
appear on the meter as a steady current. 
Assume for the moment that there arc few 
pulses and that the size of each pulse can be meas- 
ured. If now the size of the pulse is plotted 
against the voltage applied to the electrodes, a 
curve similar to that of figure 9-9 will be obtained. 
Regions A and B represent the normal ionization 
chamber working conditions where the only ions 
contributing to the pulse are those produced by 
the original radiation. Over region C there is 
some gas amplification occurring very close to the 
central wire. The electric field (volts per centi- 
meter) is not uniform as is the case between two 
parallel plates, but increases near the central 
wire. Hence an ion near the central wire will 
receive a greater acceleration in one mean free 
path than will a similar ion near the outer cylinder. 
In this region the gaseous amplification is quite 
stable for any given voltage and does not depend 
on the number of initial ions present. Thus if the 
voltage is adjusted to a value such that the gas 
amplification factor is 103 and an incident /3-particle 
produces 100 ion pairs, the pulse received at the 
130 RADIOLOGICAL SAFETY 
gradually changes to region E where ail propor- 
tionality ceases. Here a single ion pair is suffi- 
cient to produce an amplified pulse of the same 
size as that obtained from a large number of 
primary ions. This is known as the Geiger region 
and is characterized by gas amplification factors 
of the order of 108. This is the portion of the 
tube characteristic commonly used for counting 
beta and gamma radiation. 
Except in very special circumstances /S-particles 
have a wide range of energies and consequently a 
wide range of ionizing power. In counting them, 
however, it is usually desirable to know the total 
number of particles with no discrimination against 
those of low energy. The Geiger region is ideally* 
suited for this type of detection since here all ion- 
izing events result in equal pulse sizes. The same 
situation exists for gamma radiation since this is 
detected through the ionization produced by elec- 
trons ejected from the walls of the tube by the 
gamma rays. 
The Geiger region usually extends ovdr a range 
of about 200 volts. When still higher voltages 
are used, the region of continuous discharge, F, is 
reached. In this region the tube is too unstable 
for useful operation, and care must always be 
taken to keep the tube voltages below the con- 
tinuous discharge value. Actually the tube does 
not go into continuous discharge but rather pro- 
duces a series of closely spaced pulses from one 
initial ionizing event. Although G-M tubes are 
never operated in the continuous discharge region, 
the mechanism producing this instability is im- 
portant in the Geiger region also, and so warrants 
some discussion. Because the phenomena in- 
volved in the mechanism at the discharge of a 
G-M counter are extremely complicated, this 
discussion will be simplified and incomplete. 
It has already been pointed out that avalanche 
ionization is most likely to take place in the vicin- 
ity of the central wire, since here the electric field 
is high and each electron, on its way to the central 
wire, can acquire enough energy for further ioni- 
zation in each mean free path. Near the central 
wire therefore a large number of electrons and 
positive ions will be formed in the first avalanche. 
The electrons have a small mass and are already 
close to the central wire so they will move toward 
it with high velocities and will be completely 
collected by the wire in 10'6 seconds or less. The 
Figure 9-9.—Ion chamber pulse size versus voltage. 
electrode will be 100X103=105 ions. Under the 
same voltage conditions an a-particle producing 
105 primary ion pairs will yield a pulse of 105X 
103=108 ions. Because of the rather strict pro- 
portionality between the amounts of initial and 
total ionization this portion of the curve is known 
as the region of proportionality, and a counting 
tube operating in this region is called a propor- 
tional counter. As will be described later a pro- 
portional counter can be used to measure a-par- 
ticles or neutrons in the presence of strong beta and 
gamma radiation. With typical designs the pro- 
portional region will extend to gas amplification 
factors of about 104. 
If the voltage is raised still further, the gas 
amplification factor will continue to increase, but 
in region D the amplified pulses are no longer 
proportional to the number of primary ions. A 
sort of saturation effect begins to enter at this 
point and consequently a few primary ions will 
produce nearly as many total ions as are obtained 
from a large number of primaries. There is still 
some difference in final pulse sizes however, so 
this region is known as the region of limited pro- 
portionality. 
The gas amplification continues to increase 
with further increases in voltage, and region D 
131 
774689 0 - 48 - 10 RADIOLOGICAL SAFETY 
positive ions, on the other hand, have to travel 
out to the negatively charged cylinder. Since they 
have comparatively large masses, they move much 
slower than the electrons. The positive ion cloud 
will reach the cylinder in perhaps 10~3 seconds, 
long after the electrons have been collected at the 
wire. 
As a positive ion approaches very close to the 
cylinder, it will pull an electron from the cylinder 
and become a neutral molecule. In general the 
electron will go into one of the upper energy levels 
so the molecule, although neutral, will be in an 
excited state (ch. 5, sec. 5.07). The molecule will, 
however, promptly return to the ground state and 
in so doing will radiate a characteristic series of 
spectral lines. Some of these lines will be in the 
ultra-violet region of the spectrum and conse- 
quently will have sufficient energy to liberate 
photoelectrons from the metal cylinder. With 
high tube voltages a single photoelectron will be 
sufficient to start a second avalanche and thus 
the entire process will be repeated over and over 
again. 
A second type of characteristic curve is helpful 
in understanding the operation of ionization 
chambers, particularly in the Geiger region. For 
obtaining this curve assume the tube to be ex- 
posed to a constant radiation intensity but with 
the incident particles or photons having unequal 
energies. Pulses per second when plotted against 
the applied voltage yield a curve similar to 
figure 9-10. 
recorded. As the voltage is raised and the gas 
amplification becomes appreciable, the most 
energetic particles will be counted, but the weak 
ones will be lost. This is the region of propor- 
tional counting AB. As the gas amplification 
continues to increase with voltage, more of the 
less energetic particles will be counted until 
point C is reached. C is the threshold of the 
Geiger region CD, and here practically every par- 
ticle entering the tube is counted. D is the 
threshold of the continuous discharge region, 
which has no practical application. 
The Geiger region CD is known as the plateau, 
and it is obviously desirable for a tube to have a 
long, flat plateau since here the counting rate 
does not depend strongly on the applied voltage. 
The plateau always has a slight upward slope, 
but it is quite possible to make tubes which show 
a change in counts of only 1 percent for a change 
of 100 volts. The length and slope of the plateau 
depend on several variables. To obtain desir- 
able plateau characteristics the filling gas and 
pressure must be carefully chosen, and the central 
wire must be free from dust, sharp points or die- 
marks. Oxygen and water vapor are particularly 
undesirable and must be completely removed 
before filling. 
It is evident from the above that if a G-M 
tube is to be used quantitatively, the voltage 
applied to it must be carefully adjusted to obtain 
the desired characteristics. Portable instruments 
are necessarily restricted to batteries for the high 
voltage supply, and this makes tubes operating 
on low voltages particularly desirable. With 
special filling gases the center of the plateau may 
occur at about 250 volts instead of the usual 
values of 800-1,200 volts. 
Fixed laboratory instruments are usually 
operated from the power lines instead of from 
batteries and special regulating circuits are used 
to maintain constant voltage. For laboratory 
operation it is not necessary to have low voltages, 
and high-voltage, long-plateau tubes are usually 
used. The voltage setting for proper proportional 
counting is more critical than for operation in 
the Geiger region and thus proportional counters 
arc essentially laboratory instruments. 
9.08 The Counter Tube Gas. 
Many gases, even though they do not have the 
optimum characteristics, arc suitable for counter 
Figure 9-10.—G-M tube characteristic. 
The associated electronic equipment for record- 
ing the number of pulses will not, in general, 
respond to the small pulses produced in the 
ionization chamber region where there is no gas 
amplification. Consequently the curve will have 
a threshold, A, below which no pulses will be 
132 RADIOLOGICAL SAFETY 
operation. Argon is a very satisfactory gas and 
is used in practically all counters. There are, on 
the other hand, gases which are completely 
unsuitable. These are primarily those gases 
which tend to form negative ions instead of positive 
ions. If negative ions are formed by the addition 
of an electron to the neutral molecule, they will 
move toward the central wire as do the electrons 
but with the lower velocities characteristic of 
heavy ions. Consequently they will arrive at the 
wire long after the first avalanche has been pro- 
duced by the electrons. When they near the 
wire, the extra electron may be removed by the 
intense field, and it will then proceed with a high 
velocity and start a second avalanche. The 
tendency to form negative ions makes oxygen, 
water vapor, and carbon dioxide completely 
unsuitable for use in counter tubes. 
Counter tubes filled with any noble gas, such as 
argon, are said to be nonquenching or slow. In 
such tubes a single discharge will be self-perpetu- 
ating by the photoelectric effect at the cathode, 
even when the voltage is set at the center of the 
Geiger region. To eliminate this the counter 
may be operated with a series resistance, as indi- 
cated in figure 9-11. This is necessary in any 
case since the tube will usually be coupled to a 
voltage-actuated device. If the series resistance 
is made very large, say 109 ohms, there will be a 
substantial voltage drop across it even for a small 
pulse. With a pulse of 0.1 microampere, this volt- 
age drop will be 100 volts. Then during the 
passage of the pulse the tube voltage will be de- 
creased by 100 volts, and the resultant decrease 
in the gas amplification factor will be sufficient 
to prevent the second avalanche that might have 
been formed by the photoelectrons. When the 
discharge terminates, the current drops, the volt- 
age rises to its original value, and the tube is 
ready to respond to a second ionizing event. 
Unfortunately the series resistance must be 
made very large in order to obtain a sufficient 
voltage drop, and this results in a very slow 
counter. If fast operation with non-quenching 
counters is desired, special electronic quenching 
circuits must be used. They will be described 
later. 
It is possible however, to construct counters in 
which the discharge can be stopped with small 
values of series resistance. These are known as 
self-quenching or fast counters. A self-quench- 
ing counter can be produced by adding to the 
usual filling gas a small amount of a polyatomic 
vapor, such as alcohol or xylene. These complex 
molecules strongly absorb ultra-violet light, and 
by this mechanism the photoelectric emission 
at the cathode is prevented. With self-quench- 
ing counters the series resistance may be reduced 
to 106 ohms or even lower. 
Most of the polyatomic molecules introduced to 
make self-quenching counters are vapors at room 
temperature, and these counters are apt to show a 
sensitivity which changes with temperature. A 
further disadvantage lies in the fact that some of 
the quenching gas is broken down (dissociated) 
at each discharge, and so these counters have a 
limited life. Life does not mean deterioration 
with time but with use. A very satisfactory self- 
quenching counter can be made by filling the tube 
with 10 percent alcohol and 90 percent argon to a 
total pressure of 10 centimeters of mercury. In 
such a counter there may be 1020 molecules of 
alcohol. Perhaps 1010 molecules are dissociated 
at each discharge so the alcohol will be completely 
gone after 1010 discharges, and operation will be 
erratic even before this. The self-quenching 
feature usually outweighs this disadvantage, and 
self-quenching counters are widely used. 
The a-particle efficiency of practically any coun- 
ter is 100 percent, for any a-particle which enters 
is almost certain to end its flight within the tube 
and to produce massive ionization along its path. 
With a gas such as argon, which has a high 
specific ionization, it is highly improbable that a 
/3-particle can traverse a counter without producing 
enough ions to initiate the discharge. From this 
standpoint then the /3-particle efficiency of a coun- 
ter is very high and may be well over 99 percent. 
If the efficiency is considered as the ratio of the 
number of counts to the number of particles 
striking the counter tube, the efficiency will be 
somewhat less because some of the alphas and low 
energy betas will not penetrate the wall. This is 
not the usual definition of counter efficiency be- 
cause it gives a figure which depends on the energy 
of the incident particles. 
The efficiency of the ordinary counter for gamma 
radiation is very low, of the order of 1 percent or 
less. A 7-ray is detected only by the electrons 
which it produces in the counter walls or in the 
133 RADIOLOGICAL SAFETY 
gas, and if a 7-ray traverses the counter without 
producing either Compton electrons or photo- 
electrons or possibly electron pairs, it will not be 
detected. The probability of producing any of 
these electrons is low, and consequently a counter 
tube will respond to only a small fraction of the 
impinging 7-rays. The efficiency can be some- 
what increased by making the cathodes of a heavy 
metal with a greater 7-ray absorption, but the 
improvement is not great. 
Some G-M tubes are photosensitive, and this 
is usually an undesirable feature. If the cathode 
surface has a low photoelectric threshold, ultra- 
violet or even visible light may have sufficient 
energy to produce photoelectrons, and these will 
initiate the discharge. All G-M tubes should be 
tested for photosensitivity. This photosensitivity 
can be eliminated by coating the tube with an 
opaque material. 
9.09 Neutron Counters 
With the recent increase in interest in neutrons 
there has been a considerable development in 
counters for neutron detection. Any counter will 
give counts when placed in a neutron field, but 
better results can be obtained with specially 
designed tubes. To detect slow neutrons the 
counter is filled with boron trifluoride, BF3, 
which is a gas at room temperature. A slow neu- 
tron may produce a nuclear reaction with the 
boron. This reaction liberates a considerable 
amount of energy, and the a-p article and the 
recoiling lithium will have sufficient kinetic energy 
to produce heavy ionization which will trip the 
counter. By using the counter in the propor- 
tional range it is possible to obtain a count for 
each disintegration even in the presence of large 
beta and gamma intensities. The capture proba- 
bility decreases with the neutron velocity so the 
reaction is not efficient for fast neutrons. 
Fast neutrons may be detected through the 
recoil atoms which they produce when they collide 
with the gas atoms in the counter. The recoil 
atoms produce intense ionization, and hence if the 
counter is adjusted to the proportional range, the 
counter will discriminate against beta and gamma 
radiation. Fast neutron counters have a rather 
low efficiency because of the low cross section for 
the collision process. Neutron counting is com- 
plicated by the change in behavior with velocity, 
and the present neutron counters are far from 
satisfactory. 
9.10 Geiger Counter Circuits 
Geiger counters are invariably operated with 
the central wire positive and with a resistance in 
series with the tube and the high voltage supply. 
The current pulse produced by an ionizing event 
in the tube will therefore produce a voltage pulse 
across this resistor. This pulse will be negative 
because before the discharge there was no current 
flowing and the wire was at full positive potential. 
Figure 9-11.—G-M tube with a series resistance and a 
coupling condenser. 
With self-quenching tubes condenser coupling, 
as shown in figure 9-11, is the simplest method 
for transmitting the impulse to the counting cir- 
cuits. The pulse from a G-M tube is of short 
duration (perhaps 10“4 seconds) and hence is 
equivalent to a high frequency alternating voltage. 
Because of this the pulses are easily transmitted 
by small condensers of 50-100 micro-microfarads. 
The condenser must be well insulated since it is 
in a high voltage circuit, and any appreciable 
leakage current will disturb the low current 
counter circuit. 
With a non-self-quenching tube an auxiliary 
circuit must be used to stop the discharge with- 
out the use of excessive values of series resistance. 
The Neher-Harper circuit (fig. 9-12) is one method 
for quenching the discharge. A tube with a sharp 
plate current cut-off, such as the 6C6 or 6J7, is 
most suitable for this circuit. The control grid 
is maintained at a point slightly beyond plate cur- 
rent cut-off by battery Bx, and the high voltage 
is applied to both the G-M tube and the quench- 
ing tube plate. With no pulse there is no current 
flow in either the G-M tube or the quenching tube. 
134 When a pulse occurs in the G-M tube, there will 
be a current flow through both Rx and R2, the 
cylinder will become somewhat positive, and a 
positive pulse will be applied to the grid of the 
quenching tube. This tube will then draw a large 
plate current through the resistor R2, and this will 
drop the potential of the central wire and extin- 
guish the discharge. A negative pulse will be 
transmitted by the condenser to the following 
circuits. 
RADIOLOGICAL SAFETY 
vibrator arrangement shown in figure 9-14. 
One tube will be biased nearly to cut-off with 
battery Bx, while the other will have zero bias, as 
shown. Such a circuit will have one stable posi- 
tion with Tx drawing maximum current and 
T2 cut off. When a negative pulse from the 
G-M tube is impressed on the grid of Tx, the plate 
current is reduced, and an amplified positive pulse 
appears in the plate circuit. This is impressed 
on the grid of T2 through C3 and results in a 
current flow in tube T2. The plate drops in 
potential, and this amplified negative pulse is fed 
back to the grid of Tx through C2. This rein- 
forces the original negative pulse, and the process 
continues until T2 is taking maximum plate cur- 
rent and Tx is cut off. As soon as the plate cur- 
rent stops changing (when Tx nears cut-off and 
T2 nears saturation), the condensers C2 and C3 
will begin to discharge, and the circuit will return 
to its original state. When this happens a large 
negative pulse will appear at the grid of TX) and 
when this is transmitted to the G-M tube through 
Cu the discharge will be quenched. Each pulse 
from the counter tube will therefore send the 
circuit through one cycle of operation. 
Because of the regenerative action large voltage 
swings can be attained, and by a proper choice of 
T2 substantial amounts of power are available for 
operating recording instruments. If a tube such 
as a 6V6 or 6L6 is used as T2, a mechanical counter 
can be put directly in the plate circuit to count 
the pulses. With a smaller tube for T2 a direct 
current milliammeter can be put in the plate 
circuit for reading the average number of pulses, 
and a pair of phones may be used for counting 
individual pulses at low radiation intensities. 
This circuit is therefore well adapted for portable 
instruments. 
The time required for the multivibrator circuit 
to complete one cycle of operation depends on all 
circuit constants, but is strongly dependent on the 
values of C2 and C3. This fact permits a very 
simple method of changing the sensitivity range 
when the circuit is used in a portable instrument 
with a direct current milliammeter in the plate 
circuit of T2. It will be remembered that a direct 
current meter reads average values, and so the 
reading of such a meter placed in the T2 plate 
circuit will depend not only on the number of 
pulses but also on the length of each pulse. This 
Figure 9-12.—Neher-Harper quenching circuit 
In the Neher-Pickering quenching circuit (fig, 
9-13) the quenching tube is in series with the 
G-M tube and the resistance In the absence 
of a pulse there is no negative voltage on the 
quenching tube control grid, and saturation 
current is drawn. When a pulse trips the G-M 
tube, a large negative pulse appears on the grid 
of the quenching tube. This cuts off the plate 
current and removes the voltage from the G-M 
tube. With this quenching circuit the cylinder 
of the G-M tube can be maintained at ground 
potential which is a distinct advantage in many 
biological applications where the outside of the 
counter may be in contact with liquids or body 
tissue. The Neher-Pickering circuit, on the 
other hand, requires a separate voltage source 
for the filament of the quenching tube because 
the cathode is at a high positive potential. The 
quenching tube also puts a large, constant drain on 
the high voltage power supply. It willl be noted 
that a pulse of either polarity can be obtained 
from the Neher-Pickering circuit. 
A third useful quenching circuit is the multi- 
135 RADIOLOGICAL SAFETY 
Figure 9-13.—Neher-Pickering quenching circuit. 
Figure 9—14.—Multivibrator quenching circuit 
is illustrated in figure 9-15 for evenly spaced 
pulses. The same situation will obtain with the 
random spaced pulses produced by a G-M tube 
in a radiation field. 
When the instrument is in a weak radiation 
field and only a few pulses per second are being 
recorded, a large value of C2 can be selected by a 
switch, and the few broad pulses will produce a 
substantial average current which can be read on 
the meter. With high-intensity fields the meter 
will read off-scale, but by changing to a smaller 
value of C2 each pulse can be shortened and a 
lower average current obtained. It is necessary, 
of course, to have a separate calibration for each 
value of C2. It should be pointed out that the 
average current read by the meter depends also 
on the height of the pulses. With constant 
battery voltages this is no problem, as the tubes 
swing from cut-off to saturation, but the height 
will decrease with battery voltage and result in 
a reading that is too low. It is evident that with 
a mechanical recorder the above circuit will record 
the total number of counts from the G-M tube. 
With an averaging meter in the circuit the instru- 
136 RADIOLOGICAL SAFETY 
When a negative pulse comes in from the G-M 
tube or quenching circuit, it will have no effect on 
the tube that is already cut off, but it will reduce 
the plate current of the other tube of the pair and 
produce an amplified positive pulse in the plate 
circuit. This amplified positive pulse is applied 
to the grid of the cut-off tube through the cross- 
coupling condenser, and current will flow in this 
tube. The net result of a single pulse then is to 
reverse the roles of the two tubes. The tubes 
will remain in the reversed position until the 
arrival of a second pulse which will restore the 
circuit to its original state. 
The amplifier tube Ta, is biased to cut-off so 
that negative pulses on its grid will have no effect 
on the plate current. A positive pulse will 
produce a plate current pulse, and a negative 
signal will be transmitted through (74. 
It is evident then that this circuit will transmit 
every second pulse, and by constructing a series 
of such circuits the incoming pulses can be reduced 
by a factor of 2, 4, 8, 16, 32, 64, etc. The most 
common scaling circuits are usually scales of 32 
or 64. It is customary to insert neon indicator 
lamps in one side of each stage. This serves two 
purposes. By observing them it is possible to 
determine whether the instrument is scaling 
properly. They are also used as interpolation 
indicators to record counts less than the total 
number required to record once on the mechanical 
counter. As a simple example assume the circuit 
of figure 9-16 used as a scale-of-two with the 
mechanical counter in the output of Ta. The 
counter will record one for every two pulses but 
will take no account of the odd pulses. At each 
odd pulse the neon lamp will be lighted so this 
can be used to keep track of the odd pulses. In 
an extended scaling circuit the lamps are given 
values of 1, 2, 4, 8, 16, etc. The sum of the 
values of all the lamps that are lighted when the 
counter is stopped is the total number of pulses 
not counted by the mechanical recorder. 
The mechanical counters are invariably mag- 
netically actuated with a ratchet and pawl 
mechanism for transferring the pulses to a suitable 
scale indicator. The moving parts are made as 
light as possible to obtain a high response speed 
and to avoid excessive driving power require- 
ments. 
Figure 9-15.—Pulse shapes. 
ment becomes a rate meter which will measure 
the intensity of radiation. 
9.11 Scaling circuits 
If a mechanical counter is connected directly 
in the multivibrator circuit, the possibilities for 
fast counting inherent in the G-M tube cannot be 
realized. A G-M tube can produce a pulse, be 
quenched, and be ready to receive a second pulse 
in perhaps 2X10-4 seconds and hence should re- 
spond to 5,000 equally spaced counts per second. 
The associated electronic circuits can be made 
equally fast so in a simple direct counting circuit 
the limit on speed is set by the mechanical register. 
These can be made to count perhaps 100 times 
per second, but this is an upper limit, and it is 
more satisfactory if they do not receive over 50 
impulses per second. To fully utilize the capa- 
bilities of the G-M tube it is desirable to scale 
down the number of pulses so the mechanical 
counter will have to respond to only a known 
fraction of the total. The electronic arrange- 
ments for doing this are known as scaling circuits. 
Scaling circuits are based on a two-tube basic 
circuit which divides the number of pulses by 
two and is known as a scale of two. There are 
many circuits capable of doing this, and it is not 
possible to discuss them in detail here. A typical 
scale-of-two circuit is shown in figure 9-16. This 
circuit is somewhat similar to that of the multi- 
vibrator but is completely symmetrical and has 
two stable positions instead of one. Because of 
the cross-coupling condensers C2 the circuit will 
be in equilibrium when either tube is cut off and 
the other is at maximum plate current. 
137 RADIOLOGICAL SAFETY 
Figure 9-16.—G-M counter scaling circuit. 
9.12 Calibrations and Standards 
The instruments that have been described can 
be used to measure accurately ionization currents 
or the amount of ionizing radiation that enters a 
G-M tube, but it should be pointed out that none 
of these devices give an absolute measure of 
radiation intensities. It is therefore necessary to 
calibrate them in terms of known standards. 
This is not difficult if a 7-ray calibration is re- 
quired in terms of roentgens. It has been estab- 
lished by careful measurements that 1 milligram of 
radium, in equilibrium with its products and 
enclosed in 0.5 millimeters of platinum or its 
equivalent, will produce an intensity of 8.4 
roentgens per hour at a distance of 1 centimeter. 
If the radium is in a small container, the inverse 
square law can be used to calculate the intensities 
at other distances. The radium must be in 
equilibrium with its products to insure a constant 
amount of radon and all of the lower members of 
the disintegration series. The filter of 0.5 mm. of 
platinum is sufficient to stop all alpha and prac- 
tically all beta particles and thus leave a pure 
gamma radiation. Standard 7-ray sources, prop- 
erly aged and carefully calibrated, are available 
from the National Bureau of Standards. 
If X-ray measurements are desired, it is pref- 
erable to calibrate at the energies which are to be 
measured. Even though thimble chambers are 
carefully designed they may show variations in 
response with changes in energy. G-M tubes are 
worse because the efficiency of the photoelectric 
and Compton effect changes considerably with 
energy. Calibration of X-ray measuring instru- 
ments should be carried out against primary 
standard ionization chambers or carefully cali- 
brated secondary standards by a well-equipped 
laboratory such as National Bureau of Standards 
or by a reliable instrument manufacturer. 
In making a- and 0- particle measurements quite 
different considerations enter Practically all a- 
particles are emitted with a few discrete energies, 
and all particles which enter an ionization chamber 
or G-M tube will produce a response. The 
problem then is to get a window thin enough to 
admit all of the particles or to introduce the active 
material directly into the chamber. Even when 
this is done the problem of chamber geometry 
138 RADIOLOGICAL SAFETY 
must be faced. Radioactive materials emit par- 
ticles in all directions with equal probability and in 
general a chamber or G-M tube will intercept only 
a fraction of the total emission. For example, if 
the active material is spread in a thin layer on the 
bottom of the chamber, only one-half of the 
ejected particles will reach the gas and produce 
ionization. The remainder will strike the con- 
tainer and be lost. In general the geometrical 
arrangement is such that it is not possible to cal- 
culate the fraction of the particles intercepted by 
the sensitive volume of the chamber. It is then 
necessary to calibrate the chamber in terms of a 
known radioactive material. Various members 
of the naturally radioactive series are useful for 
this purpose. The disintegration constants for 
nearly all members of this series are well known, 
and it is possible to calculate the number of dis- 
integrations per second expected from a known 
weight of the material. 
In calibrating an instrument for /3-particles the 
same general procedure is followed, but the energy 
range of the particles introduces a complicating 
factor. Most /3-particles are detected by allowing 
them to pass through the thin wall of a G-M tube 
or ion chamber. Since the /3-particles have all 
energies from zero to a maximum value, some of 
the low energy particles are bound to be lost in the 
window, and the fraction lost will depend on the 
maximum energy. In making jS-particle calibra- 
tions, therefore, it is desirable to choose as a 
standard source an element which has about the 
same /3-particle energies as the unknown. This is 
not always possible and so it is sometimes neces- 
sary to make corrections for differences in energy. 
Methods for /3-particle calibration are not entirely 
satisfactory at present, and better sources are 
sorely needed. 
Mention should be made of the behavior of thin 
wall G-M counters used as survey meters in ex- 
tensive areas contaminated with /3- and y-emitters. 
These instruments have been calibrated in terms 
of the roentgen, which is a unit applicable only to 
electromagnetic radiation. If the tube is directly 
exposed to beta radiation, as by opening a pro- 
tective window, the instrument will respond to 
/3-particles, and in general this reading will be 
several times the y-ray reading obtained when the 
window is closed. It must be kept in mind that 
the /3-Particle reading bears no relation to roent- 
gens and cannot be converted into these units. 
It is permissible to refer to the reading as roentgens 
equivalent, as is sometimes done, although even 
this is misleading, for the reading is a roentgen 
equivalent only as far as the meter is concerned. 
Such readings are useful for comparison purposes, 
but must be interpreted with caution. 
9.13 Correction of Measurements 
(a) Statistical deviations.■—When radiation meas- 
urements are made, it is soon observed that all 
readings show fluctuations. This is not always 
due to the instability of the measuring instrument 
but is inherent in the radiation source. Nuclear 
disintegrations are completely random and inde- 
pendent processes. Thus whether or not a given 
nucleus disintegrates at a particular time does not 
depend on the state of any other nuclei. Such a 
process will obey the laws of statistics, and these 
laws predict that even though there is a definite 
average rate of disintegration, the number of dis- 
integrations actually counted in a given time will 
show deviations from this average. 
If a total of N particles are counted in any time 
interval it can be shown that the expected devia- 
tion D from the true value is given by 
D=4N (3) 
The probable error P. E. is defined as 0.67D, so 
P. (4) 
If a total count of 10,000 is made, the most prob- 
able deviation will be: D= and the 
probable error will be 67 counts. It is usually 
more instructive to calculate the relative deviation 
or relative probable error, which is merely the 
deviation or error expressed as a fraction of N. 
Thus: 
D t/N 1 
relative deviation = -j—~ (5) 
and 
relative probable error (6 ) 
In the above example the relative deviation will be 
. - —0.01 or 1 percent, and the relative prob- 
Vio,ooo 
able error will be 0.67 percent. With these ex- 
pressions it is possible to calculate the total num- 
139 RADIOLOGICAL SAFETY 
her of counts that must be made to obtain a 
desired accuracy. 
If counts are made on weak samples, the above 
considerations have to be modified because of the 
background count. It is found that all instru- 
ments show a small reading even when no radio- 
active material is brought near. This residual 
count or background, is due to cosmic rays, to 
radioactive materials in the earth, and to a slight 
radioactive contamination in the materials of 
which the instruments are made. The back- 
ground is somewhat variable with geographical 
location but is fairly constant at a given place. 
The background also depends, of course, on the 
size of the chamber or counter tube. As a rough 
approximation a G-M counter in an uncontam- 
inated area will have a background count of about 
1 per minute per square centimeter of cathode 
area. 
For an accurate count on a radioactive sample 
it is necessary to determine the background and 
subtract this from the count obtained when the 
sample is in position. The accuracy of the final 
result depends then on the accuracy of the two 
counts which are subtracted. Statistical theory 
shows that the deviation in the final result will be 
or 
= j2,=:0.01 
Therefore 
iV2=30,000 and 
Thus because of the presence of the background, 
nine times as many counts must be made to 
achieve the same accuracy and this will require 
six times the original counting time. 
In general any sample whose activity is less 
than background is scarcely worth counting. (In 
this case the count with the sample in position 
will be less than twice that with the sample re- 
moved.) This shows the necessity for keeping 
the background as low as possible by avoiding 
all possible contamination of laboratory or in- 
struments. Particular care must be taken when 
measuring liquids, either with immersion or jack- 
eted counters. A background count should be 
taken before each count to be sure that no residual 
activity is left from previous samples. The exact 
methods for removing contamination depend on 
the nature of the contaminant and the structure 
of the measuring equipment. 
(b) Counter dead time.—Another factor which 
affects the results of G-M tube measurements is 
the counter dead time. It has been pointed out 
that a G-M tube requires a definite time to neu- 
tralize the positive ions from one pulse and be 
ready for the next. This time is of the order 
2X10~4 seconds, and so the tube should respond 
accurately to 2-—z-4=5,000 evenly spaced 
counts per second. But if a radioactive material 
is ejecting an average of 5,000 particles per second 
into the tube, many counts will be missed because 
many of the particles will be less than 2X10-4 
seconds apart. This is another effect of the 
random nature of nuclear disintegrations. Even 
though the average rate is well below the limit of 
the counter, a few pulses will be too closely spaced 
and will be missed. It can be shown that if Tv, 
the dead time of the counter, is small compared 
to the average time between pulses, T, then the 
relative error due to counter dead time will be 
D= VA2+A2 (7) 
where Dx is the deviation of the count of back- 
ground plus radiation, and D2 is the deviation of 
the background count. Since from Eq. 
(3) then: 
D—-^Ni-\-N2 (8) 
As an example of the use of these relations 
assume a measurement made with zero background 
to have a relative standard deviation of 1 percent. 
Then Z>=0.01 =—L= whence N—10,000 counts. 
-JN 
Now suppose the same accuracy is desired when 
the background is equal to the activity. Then 
the count of background plus sample Ni will be 
twice the background alone N2, or Ni—2N2. 
Then: 
relative deviation — ~ -J?1 =0.01 
A^i—iY2 Nt—N2 
/ 
or 
_V3iV2=o.01 
n2 
T 
relative error (9) 
140 As an example consider a counter with a dead 
time of 2 X 10~4 seconds counting 1,000 times a 
second. Then T= 1/1000= 10~3 seconds and the 
2x 10-4 
relative error =—^q_3—— 0.2, or 20 percent. At 
this average rate therefore the counter will be 
missing 20 percent of the counts because of dead 
time. It will be noted that the error increases with 
counting rate, and hence high speed counting 
should be avoided if a high accuracy is desired. 
It will be evident that this particular error does 
not enter into ionization chamber measurements 
because an ion chamber will respond to simul- 
taneous ionizing events. 
RADIOLOGICAL SAFETY 
per milligram axis will give the value that would 
have been obtained with no self-absorption. 
This curve can then be used to correct all weighed 
samples to zero thickness if the materials being 
measured have comparable densities. 
9.14 Decay Curve Measurements 
In all of the previous discussions it has been 
assumed that a single measurement would be 
made on a given radioactive sample. In most 
cases this gives sufficient information, but occa- 
sionally it is desirable to make a series of measure- 
ments to determine the decay curve of the active 
components. This is a useful method of analysis 
since it is usually possible to identify a radioactive 
material if its half-life is known. 
In determining decay curves care must be taken 
to locate the sample in the same geometrical posi- 
tion at each measurement. If possible the sample 
should be left in position between measurements. 
If a series of counts are taken and the logarithm 
of each count is plotted against the time at which 
it was taken, a straight line of slope X will be 
obtained. 
If there are two radioactive substances in the 
sample, each will have a characteristic value of X, 
and a simple linear relation will no longer be ob- 
tained. Figure 9-18 shows the results with two 
Figure 9-17.—Self-absorption curve with extrapolated 
value for zero absorption. 
(c) Self-absorption.— In measuring the beta ac- 
tivity of solid and liquid samples it is usually neces- 
sary to correct for the self-absorption of the 
particles by the sample itself. This is particularly 
true if the maximum beta particle energies are low, 
as for C14 with 0.14 Mev particles or S35 with 0.11 
Mev particles. In any case, ejected j8- particles 
will have energies ranging from zero to a definite 
maximum value and the low energy particles will 
be stopped by relatively thin layers of material and 
will not reach the sensitive volume of the counter. 
To correct for this a series of counts is made 
with a series of weighed samples. From these 
data a plot can be made of counts per milligram 
of material against the milligrams in the sample 
(fig. 9-17). The curve can be extrapolated back 
to zero milligrams, and the intercept on the counts 
Figure 9-18.—Semilogarithmic plot of the decay of a 
short and long lived isotope. 
Note.—The separation of two half-lives from a composite 
decay curve. (N is the number of counts per minute with 
the sample in constant orientation.) 
141 RADIOLOGICAL SAFETY 
il alf-lives present. If the plot is continued long 
enough the short-lived element will decay to a 
point where it no longer makes an appreciable 
contribution, and the curve will become linear. 
The straight portion of the curve can be extra- 
polated back to zero time, and this line will rep- 
resent the activity due to the long-lived com- 
ponent. If a series of values along this curve are 
subtracted from the corresponding values on the 
experimental curve, the remainders will be the 
activity due to the short-lived component. If 
these values are plotted logarithmically, a straight 
line will be obtained having a slope equal to the 
short-lived decay constant. 
9.15 Photographic Dosimetry 
Photographic materials are also important tools 
for the measurement of radiation since high speed 
particles and high energy photons produce de- 
velopable images. It was, in fact, the effects 
of penetrating radiations on photographic plates 
that led Becquerel and the Curies into the research 
that has developed into the present field of nuclear 
physics. 
Although photographic films and papers lack 
the accuracy attainable in the laboratory by elec- 
trical methods, they still play an important role in 
radiation measurements. A film is one of the 
simplest detectors of radiation, is small and light, 
can be obtained with a wide range of sensitivity, 
provides a permanent record of exposure, and has 
no complicated electronic circuits to get out of 
adjustment. For many applications these facts 
more than outweigh the disadvantages of film 
processing, the time required to obtain a measure- 
ment, and the variations inherent in photographic 
materials. 
A photographic emulsion consists of a thin 
ayer of a silver halide and gelatin spread on a 
base of glass, cellulose, or paper. When visible 
light strikes such an emulsion, some of the silver 
halide is rendered developable by suitable chem- 
icals into a deposit of metallic silver. The inter- 
action of light with the silver halide is not well 
understood, but some sort of ionization process is 
undoubtedly involved. After an emulsion has 
been exposed to radiation, there is no visible sign 
of any change, but a latent image exists which can 
be made visible by development. In the develop- 
ing solution the latent image is converted into a 
black deposit of metallic silver. The amount of 
blackening is a function of the amount of exposure 
and the conditions of development. 
The blackness of the processed film or plate 
is usually measured with some sort of a densitom- 
eter, figure 9-19. A strong light source is fo- 
Figure 9-19.—Schematic arrangement of densitometer 
with photocell. 
cussed to a small image and allowed to fall on a 
photocell which is connected to a meter. When 
the light falls directly on the ceil, a meter reading 
will be obtained which is proportional to the 
light intensity 70. When the film is put in the 
light path, some of the light will be absorbed by 
the developed silver, and a lower reading corre- 
sponding to an intensity I will result. The ratio 
of these intensities is called the opacity, 0. 
Opacity=y 
(10) 
The inverse ratio is the transmission, T. 
T=J 
-*0 
(11) 
A more useful measure of film blackening is 
optical density, D, defined by: 
U—logic Opacity—logic j 
(12) 
When density measurements are made, the values 
obtained depend to some extent on the type of 
optical system used in the densitometer. The 
silver deposit scatters light as well as absorbs it, 
and hence the reading depends upon how much 
of this scattered light reaches the photocell. In 
some of the simpler densitometers there is no 
142 focused beam, all measurements being made with 
diffused light. It is preferable to use instruments 
with sharply focused light beams. In any case 
a particular set of density measurements should 
be made on the same type of densitometer to 
avoid variations due to changes in scattering. 
If the density is plotted against log10 (exposure), 
the characteristic curve of the emulsion is ob- 
tained (fig. 9-20). The characteristic curve con- 
RADIOLOGICAL SAFETY 
Figure 9-21.—Characteristic curves for Types K and 
A emulsions. 
Table I 
Emulsion: 
Useful sensitivity 
range (roentgens) 
Type K__ __ 
0. 05-2. 0 
Type A __ 
1. 0-10 
Cine positive 5301 
5-80 
Cine positive fine grain 5302 
40-400 
Kodalith 6567 
70-700 
Kodabrornide G-3 _ 
400-8, 000 
548-0, double coat . 
2, 000-10, 000 
548-0, single coat . _ 
5, 000-20, 000 
Figure 9-20.—Characteristic curve of a photographic 
emulsion. 
It can be seen from table I that a single emulsion 
will cover an exposure range of about 1-10. One 
emulsion on paper is included because it is the 
only product having that particular sensitivity 
range. Density measurements on paper are made 
by reflected light and in general are more difficult 
and less satisfactory than density measurements 
made by transmission. Fortunately there is little 
use for emulsions in the high ranges, and the low 
exposures are adequately covered by transparent 
materials. 
Photographic film meters are usually made into 
packets of dental film size (1 % X 1% inches) and 
covered with an opaque wrapping to protect the 
sists typically of three portions; the toe AB, the 
linear portion BC, and the shoulder CD. Obvi- 
ously one emulsion can respond to only a limited 
range of exposures. For greatest accuracy only 
the linear portion should be used because there 
is the greatest change of density with exposure 
in this region. If a different exposure range is 
desired, a different emulsion can be used. Figure 
9-21 shows the characteristic curves of two emul- 
sions which have proved useful in monitoring 
radiation hazards. Table I lists a series of emul- 
sions that have proved useful for measuring beta 
and gamma radiation. 
143 RADIOLOGICAL SAFETY 
Whatever procedure is used, it is most important 
to control time and temperature as accurately as 
possible. The developer should be in a tank 
surrounded by a constant temperature hath, and 
the films agitated throughout development. Fix- 
ing and washing baths need not be temperature 
controlled, but temperatures above 75° F. should 
be avoided to prevent frilling of the emulsion from 
the base. The importance of time and temperature 
control, scrupulous darkroom technique, and the 
use of fresh chemicals cannot be overemphasized 
9.16 Film Calibration 
Films are not absolute measures of radiation 
and must be calibrated with sources of known 
strength. For a 7-ray calibration, radium gives a 
convenient source whose 7-ray field is well known 
in terms of the milligrams of radium. For /3- 
particle calibration, uranium metal is frequently 
used. This has a weak 7-ray component, and the 
a-particles cannot penetrate the film wrapping so 
any blackening will be due entirely to /3-particles. 
Photographic materials are not exactly repro- 
ducible in spite of great care in manufacture so it 
is necessary to calibrate at least one film from each 
batch. Actually films in a single batch may show 
some variation, but there is no way of calibrating 
each film, and variations of perhaps 20 percent in 
sensitivity may be expected with the best possible 
processing and calibration procedures. Processing 
techniques for calibration should be identical with 
those used to measure unknown radiation. 
It must be remembered that films are always 
sensitive to radiation, and hence great care must 
be taken to prevent exposure before issue. This 
may be difficult when operating in a large con- 
taminated area. Whenever it is suspected that 
unissued films have been exposed, a blank film 
should be processed and a new calibration run. 
9.17 Alpha Particle Emulsions 
Special emulsions are now commercially avail- 
able which are almost insensitive to visible light, 
beta and gamma radiations, but which will respond 
to heavy particles such as protons, deuterons, or 
alpha particles. These particles have such a low 
penetrating power that the emitting substance 
must be placed in direct contact with the emul- 
sion. These emulsions are not used for person- 
nel monitoring but rather to detect a-particle 
film from visible light. Any combination of suit- 
able emulsions can be put into a single packet. A 
cross of thin sheet lead about 1 mm thick is cus- 
tomarily attached to the packet. This absorber is 
sufficient to stop all /3-particles so any darkening 
under the cross will he due to 7-rays. The cross 
also serves to enhance the darkening due to 7-rays 
because of the larger number of electrons ejected 
from the lead. The regular wrapping is sufficiently 
thin to permit the penetration of all but low energy 
/3-particles. Thus the film can be used to measure 
both beta and gamma exposures. 
In determining the characteristic curve of emul- 
sions the assumption was made that all processing 
procedures were uniform. This is a very important 
restriction because the film density depends on 
processing methods, particularly on the develop- 
ment time and temperature. The slope of the 
characteristic curve is known as the gamma (this 
has no relation to 7-rays) of the emulsion. Figure 
9-22 shows the effect of development time on 
Figure 9-22.—Effects of developing time on gamma and 
density. 
density and gamma. Since the speed of develop- 
ment increases with temperature, similar effects 
will be observed if the developer temperature is 
changed. Furthermore, there is always some 
blackening due to the direct action of the chemicals 
on the emulsion, and this chemical fog must also 
be controlled. 
In general, film processing is carried out in 
accordance with the manufacturers’ recommenda- 
tions, but variations may be used satisfactorily. 
144 contamination. These emulsions will detect 
a-particles in the presence of strong beta and 
gamma radiation, and under conditions that make 
the operation of electrical a-particles detectors 
uncertain if not impossible. 
With weak exposures the plate will not be 
uniformly darkened and individual a-particle 
tracks can be seen in a microscope. Since a- 
particles are emitted with an energy characteristic 
of the emitting nucleus, the track lengths may 
frequently be used to identify the alpha emitter. 
Figure 9-23 shows typical a-particle tracks from 
polonium. 
RADIOLOGICAL SAFETY 
Figure 9-24.—-Radio-autograph of a surgeon fish caught 
on the reef between Bikini and Amen Islands. 
mining the precise position is limited, and it is 
scarcely possible to determine the location of 
radioactivity to less than 1/100 mm. 
To obtain such radio-autographs the sample is 
placed in direct contact with the film in a dark- 
ened room or container. The time of exposure 
may vary from a few seconds to several days or 
weeks. The radioactive material may be detected 
by the darkening of the negative or by light areas 
in the positive. By suitable selection of exposure 
time it is possible to investigate a wide range of 
intensities and detect extremely small amounts of 
radioactivity. By observing the film with a 
microscope and noting the different types of tracks 
it is frequently possible to determine the nature 
of the radioactive material in the sample. 
9.19 Conclusion 
While the authors have attempted to present 
both a comprehensive and a consistent picture of 
nuclear physics as related to this manual, it should 
be pointed out that the discussion has been of an 
elementary and semiquantitative nature. Certain 
fundamental properties of elementary particles, 
namely their statistics, spins, and magnetic mo- 
ments, have not even been mentioned. Further- 
more no attempt has been made to introduce wave 
mechanics other than as a crude explanation 
for alpha-emission. Many of the topics which 
have been treated here in a sentence or two are 
found well developed in the science of physics. 
Furthermore, many topics have been greatly sim- 
plified in this manual either by omission of detail 
or by modification of this detail. 
Figure 9-23.—Alpha particle tracks on a photographic 
emulsion. 
If the a-particle contamination is low, exposures 
of several days may be required to obtain sufficient 
tracks for counting. In some cases this delay in 
obtaining information may be serious. It must 
be remembered, however, that the alpha emitters 
commonly encountered in radiological safety op- 
erations have long half lives and in some cases a 
delay in measuring the alpha activity may not 
be important. 
9.18 Radio-autographs 
The various film emulsions can be used to make 
radio-autographs of specimens containing radio- 
active materials. In figure 9-24 is shown the 
radio-autograph of a fish caught on the Bikini 
reef following the underwater detonation. Such 
a photograph reveals the distribution of radio- 
active material within the sample. By exposing 
sections of the specimen it is possible to deter- 
mine the cross-sectional distribution as well. 
However it must be emphasized that the resolv- 
ing power of photographic emulsions for deter- 
145 RADIOLOGICAL SAFETY 
BIBLIOGRAPHY 
Part II 
1. Atomic Physics—Bora—Blackie & Sons—1945. 
2. The “Particles of Modern Physics’’—Stranathan—Blackiston—1946. 
3. Radiations from Radioactive Substances—Rutherford, Chadwick, and 
Ellis —MacMillan —1930. 
4. Introduction to Atomic Physics—Semat—Farrar and Rinehart—1939. 
5. X-Rays in Theory and Experiment—Compton & Allison—Van Nos- 
trand—1935. 
6. A Manual of Radioactivity—Henesy and Paneth—Oxford Press—1938. 
7. Procedures in Experimental Physics—Strong—Prentice-Hall—1939. 
8. Electron and Nuclear Counters—Korff—Van Nostrand—1946. 
9. Electron and Nuclear Physics—Hoag—Van Nostrand—1938. 
10. Applied Nuclear Physics—Pollard and Davidson—John Wiley and 
Sons—1945. 
146 RADIOLOGICAL SAFETY 
Appendix I 
Nucleus 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
z 
.A 
Particles 
Gamma radiations 
30 
Zn « 
49h 
P~, y 
1.5X10-5 
0.3(~95%), ~1.6(~5%) 
y 
Zn 7» 
<2m 
P~ 
31 
Ga 7i 
stable 
. 
Ga 72 
14.25h 
14.Ih 
P~, y 
0.8(~65%), ~3.1(~36%) 
1.71 
0.64(-10%), 0.84 
(-45%), 2.25(—45%) 
1.17, 2.65, 2.1 
Ga 73 
5h 
P~ 
i.oxio-5 
1.4 
no y 
32 
Ge 72 
Ge 7* 
Ge 7< 
stable 
stable 
stable 
Ge 75 
89m 
P~, y 
1.2, 1.1 
y 
Ge 
stable 
Ge 77 
12h 
11 h 
P~, y 
0.0037 
2.0 
1.9 
y 
Ge ”8) 
2.1h 
P~, y 
0.020 
-0.9 
y 
33 
AS 75 
stable 
AS 77 
As 78 
40h 
80m 
0.0091 
0.7 
1.4 
P~, y 
0.27 
65m 
AS (78) 
90m 
p- 
0.020 
1.4 (70%), 4.1 (30%) 
— 
As 81 
Se 77 
Se 78 
<10m 
stable 
stable 
P~ 
34 
Se 7» 
< 10m or >7X 
10«y 
B~ 
Se so 
stable 
Se 8i* 
59m 
57m 
I.T., 
y, e~ 0.008 
e~: 0.0868 (80%), 
0.0964 (20%) 
e~: 0.085 
0.099 
0.098 
Se 8i 
17m 
19m 
P~ 
0.125 
1.5 
no y 
Se 82 
stable 
Se 83 
25m 
30m 
P~, y 
0.21 
1.5 
0.17, 0.37, 1.1 
At* 84 
35 
Br 7* 
Br 8i 
stable 
stable 
P 
Br 82 
34h 
P~, y 
2.8X10-5 
0.465 
0.547, 0.787, 1.35 1.0 
Br 83 
2.4h 
2.45h 
2.33h 
p- 
0.40 
0.30 
0.9 
1.0 
1.3 
no y 
Br 85 
30m 
33m 
P~, y 
0.65 
5.3 
4.5 
y 
x3r°° 
3.0m 
P 
r>r5# 
ous 
p 
»w.uS 
56s 
P w 
* Reprinted from the Journal of the American Chemical Society, 68, 2411 (1946) 
Table I.—Table of fission products: characteristics 
147 
774689 O 4: RADIOLOGICAL SAFETY 
Table I.—Table of fission products: characteristics—Continued 
Nucleus 
Z A 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
Particles Gamma radiations 
00 
O 
*00 
stable 
low 
• 
J£p83 
113m 
I.T..C- 
r:0.032, 0.045, 0.028 
e~: 0.035 
X-ray 
Kr83 
stable 
Kr84 
stable 
Kr86 
4.5h 
0~>y 
0.94 
0.17, 0.37 
4.6h 
4.Oh 
0.85 
Kr85 
~10y 
P~ 
~0.24 
0.74 
no 7 
Kr86 
stable 
Kr87 
75m 
0- 
~4 
74m 
Kr(87) 
instantaneous 
n 
0.026% of fission 
neutrons 
n;0.30, 0.25 
Kr88 
3h 
0- 
2.5 
2.8h 
Kr88 
2.6m 
pr 
2.5-3m 
2-5m 
Kr80 
P~ 
P~ 
Kr81 
9.8s 
5.7s 
KrW) 
Pr 
P~ 
P- 
0- 
Kr(M) 
2.0s 
Kr(84) 
1.4s 
Kr87 
short 
37 Rb85 
stable 
Rb86 
19.5d 
0~, 7 
~1.6X10~4 
1.60 
1.56 
y 
Rb87 
6.3 X 10*°y 
0~, y, r 
0.132, 0.13, 0.25 
0.034, 0.053, 0.082, 0.102, 
0.129 
Rb88 
17.8m 
0~ 
4.6 
18m 
17.5m 
5.1 
Rb88 
15.4m 
0~ 
3.8 
15.5m 
Rb80 
short 
0~ 
0~ 
0~ 
Rb81 
short 
Rb(92) 
short 
RbW) 
short 
0~ 
Rb(94) 
short 
0~ 
0~ 
0- 
Rb97 
short 
Rb 
80s 
38 Sr86 
stable 
low 
Sr87 
stable 
Sr88 
stable 
Sr89 
53d 
54d 
55d 
0~ 
4. 6 
1. 50 
1 52 
1. 5 
no 7 
Sr80 
25y 
0~ 
0. 6 
no 7 
Sr9* 
9. 7h 
lOh 
8. 5h 
0~, y 
5. 0 
1. 3 (40%), 3. 2 (60%) 
~1. 3 
148 RADIOLOGICAL SAFETY 
N udeus 
Z A 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
Particles Gamma radiations 
Sr(92) 
2. 7h 
0- 
5. 1 
Sr(fl3) 
7 m 
0~ 
Sr(94) 
~2m 
0- 
Sr97 
short 
0~ 
39 Y89 
stable 
« 
Y»o 
65h 
0~ 
2. 2 
no 7 
62h 
2. 45 
60h 
2. 55, 2. 6 
Y»i* 
51m 
l.T.,y,e~ 
e~: ~0. 5 
0. 61 
50m 
(~10% converted) 
Y»i 
57d 
0~ 
5. 9 
1. 53, 1.6, 1. 7 
no 7 
Y«) 
3. 5h 
0~, y 
3. 4, 3. 6 
p 
a 
p 
Y(»3) 
lOh 
0~, 7 
3. 1 
0. 7 
11. 5h 
Y (M) 
20m 
0~, 7 
'"■'5 __ _ 
7 
Y»5 
<3h 
0~ 
Y»7 
short 
0~ 
40 Zr90 
stable 
Zr91 
stable 
Zr92 
stable 
Zr93 
2. 5m 
0- (?) 
Zr94 
stable 
Zr95 
65d 
0~, 7 
~6.4 
0.394 (98%), 1.0 (2%) 
0.73, 0.92 (?) 
65.5d 
63d 
~0.35 (98%). 1.0 (2%) 
0.80 
0.88 
r: 0.71, 0.90 (?) 
Zr96 
stable 
Zr97 
17.Oh 
0~, 7 
2.1 
~0.8 
41 Cb93 
stable 
Cb95* 
90h 
I. T., e-, 
e~: 0.22, 0.23 
7 highly conv. (?) 
80h 
X-ray 
0.22 
X-ray: ~0.016 
Cb95 
35d 
0~, 7 
0.15 
0.75 
36.5d 
0.15 
0.77 
conv. 
e-: 0.75, 0.77 
0.79 
0.75 
-0.7 
Cb97 
75m 
0~, 7 
1.4 
0.78 
42 Mo95 
stable 
Mo97 
stable 
Mo98 
stable 
Mo99 
67h 
0~, 7 
6.2 
1.2, 1.4 
0.24, 0.75, 0.4 
Mo100 
stable 
Mo101 
14.6m 
0~, 7 
1.0, 2.2 
0.3, 0.9 
14m 
1.9, 18 
n (102) 
12m 
0- 
Mo105 
short 
0- 
Table I.—Table of fission products: characteristics—Continued 
149 
774689 O - 48 - 12 RADIOLOGICAL SAFETY 
Nucleus 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
Z A 
Particles 
Gamma radiations 
43 43"* 
5.9h 
I.T., 7, 
X-ray 
. e~: 0.116 
0.136 
6.6h 
0.12 
0.129, ~0.18, X-ray 
43" 
4X108y 
~108y 
~3X105y 
>3000y 
>40y 
0.3 
43101 
14.0m 
P~, y 
P~ 
p- 
1.3, 1.2 1 1 
0.30 
43U02) 
< Irn 
43105 
short 
43(107) 
<1.5m 
P~ 
44 Ru" 
stable 
Ru101 
stable 
Ru102 
stable 
Ru103 
42d 
P~, y 
3.7 
0.2 (95%), 0.80 (5%) 
0.56 
45d 
V 
0.2 (97%), 0.8 (3%) 
0.54 
Ru104 
stable 
Ru105 
4.5h 
4h 
P~, y 
~0.9 
1.35 
1.5 
0.76 
Ru108 
l.Oy 
P~ 
0.48, 0.53 
~0.03(?) 
no y 
RU007) 
4m 
p- 
~4 
45 Rh103* 
56m 
I. T., e- 
X-ray 
e~: ~0.03 
X-ray: 0.020 
48m 
45m 
Rh103 
stable 
Rh105 
36.5h 
P~, y 
0.60 
0.33 
34h 
r: ~0.3 
Rh108 
30s 
P~, y 
~2.8 (20%), 3.9 (80%) 
~4.5 
0.3, 0.8 (low intensity) 
Rhd07) 
24m 
P~, y (?) 
1.2 
7(?) 
26m 
Rh109 
< Ih 
P~ 
P~, y 
Rh 
9h 
~1.3 
0.8 
46 Pd105 
stable 
Pd108 
stable 
Pd107 
very short or 
>3X 108y 
>8.6X 107y 
P~ 
Pd108 
stable 
Pd109 
13.4h 
13.2h 
13h 
P~ 
0.028(t) 
t.l 
1.03 
no y 
Pd'io 
stable 
Pdiu 
26m 
P~ 
P~ 
. 3.5 
pdH2 
21h 
0.011 
0.2 
no y 
Table I.—Table of fission products: characteristics—Continued 
150 RADIOLOGICAL SAFETY 
Table I.— Table of fission 'products: characteristics—Continued 
Nucleus 
Z A 
Half-life 
Decay 
Fission yield, % 
Energjrof radiations in Mev 
Particles Gamma radiations 
47 Agi« 
stable 
Agl09* 
40.4s 
1. T., e~, 
7. 
Xray 
er: 0.0664, 0.0896 
0.0915 
0.0426 
0.092 
0.09 
40s 
Agl09 
stable 
Agm 
7.6d 
7.5d 
B~, 7<?1 
0.018(t) 
~0.24(?), 1.0 
~0.8 
no y(?) 
7 (low intensity) 
Ag112 
3.2h 
B~, 7 
3.6, 2 2 
0.86 
48 Cd111 
stable 
Cd112 
stable 
Cd113 
stable 
Cd114 
stable 
Cd115 
2.33d 
2.5d 
B~, 7 
0.011 
~0.6, 1.13 
1.11 
0.56 (60%), 1.20 (40%) 
0.65 
0.55 
Cd115 
44d 
43d 
40d 
B~, 7(?) 
0.0008 
1.7 
1.8 
1.5 
~0.5(?) 
Cd118 
stable 
Cd117 
2.83h 
2.72h 
B~ 
0.01 
1.3-1.7 
Cd* 
48.7m 
I. T., «- 
. e-: 0.17 
50m 
49 In115* 
4.53h 
I. T.. 7, e- 
e~: 0.308, 0.332 
0.48 
0.338 
4.5h 
4.1h 
<'>■'0,4 
In118 
stable 
• 
In117 
1.95h 
B~ 
. 1.73 
no 7 
1.9h 
1.90 
50 Sn117 
stable 
Sn"8 
stable 
Sn119 
stable 
Sn120 
stable 
Sn<121> 
62h 
60h 
~80h 
b~ 
0.014 
0.76 
no 7 
gn (121,123) 
130d 
B- 
0.0012 
1.44-1.53 
no 7 
Sn122 
stable 
Sn(123) 
lOd 
lid 
B~, 7 
0.0044 
2.6 
7 
Sn124 
stable 
B~ 
Qn 
R- 
Sn(126) 
r, t(?) 
0.1 
(70m Sn"28>+~60m 
(70m Sn(126) + ~60m 
Sb(126)): 0.7 (60%), 
2.7 (40%) 
Sb(126)): 1.2 
151 RADIOLOGICAL SAFETY 
Nucleus 
Z A 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
Particles Gamma radiations 
51 Sb12i 
-stable 
Sb123 
stable 
Sb125 
~2.7y 
B~,y,X-ray 0.023 
0.3(~65%), 0.7 
0.6 
0.018 
(-35%) 
0.56 
~0.6 
X-ray: 0.027 
Sb(126) 
~60m 
B~, 
see 70m Sn(ll6) 
see 70m Sn(126) 
Sb127 
93h 
B~, y 
1.15 
0.72 
80h 
Sb129 
4.2h 
P~ 
Sb(132> 
~5m 
P~ 
Sb133 
< 10m 
P~ 
Sb(134) 
< 10m 
B~ 
52 Te125 
stable 
Te126 
stable 
Te127* 
90d 
I. T., e~, 
0.033 
0.055, 0.082, 0.085 
X-ray: 0.028 
X-ray 
Te127 
9.3h 
B~ 
0.70 
no y 
Te128 
stable 
32d 
I. T., e- 
0.19 
e-: 0.070, 0.10 
X-ray 
Te129 
70m 
B~, y, X- 
1.8 
0.3, 0.8 
ray. 
72 m 
1.75 
F. 
0.3, 0.7 
1.7 
1.6 
X-ray: ~0.030 
Te13u 
stable 
Te131* 
30h 
I. T., er 
~0.5 
e~: 0.147, 0.175 
29h 
Te131 
25m 
P~ 
30m 
Te (132; 
77h 
B~, 7, e~, 
3.6 
0.28 
0.22 
66h 
X-rav 
~0.3, e- 
X-ray 
Te133 
60rn 
B~ 
To 034! 
43m 
B~ 
Te135 
>2m 
p- 
To 
~lm 
B~ 
53 I127 
stable 
1129 
very long 
B~ 
1131 
8.0d 
B~< 7, 
2.8(t) 
0.595 
0.367 
7.9d 
0.60 
0.080, 0.36, 0.4 
|(132) 
2.4h 
B~, 7 
1.0 (~50%), 2.1 
0.6 (-50%), 1.4 
2.3h 
(-50%), 1.3 
(~50 %), 0.85 
1133 
22h 
B~, 7 
~4.5 
1.3 
0.55 
I8.5h 
1.1 
| (134) 
54m 
B-. 7 
~5.7 
. >1 
1135 
6.7h 
, y 
5.6 
1.35 
1.6 
6.6h 
1.5 
1.3 
[(136) 
1.8m 
8- 
1137 
30s 
B~ 
I(137) 
22.0s 
P~, (n) 
23s 
Table I.— Table of fission products: characteristics—Continued 
152 RADIOLOGICAL SAFETY 
Table I.— Table of fission products: characteristics—Continued 
Nucleus 
Z A 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
Particles Gamma radiations 
54 Xe129 
Xe131 
stable 
stable 
Xe132 
stable 
Xe133 
5.3d 
0~, y. e~, 
X-ray 
0.35 
0.085, 0.083 
Xe134 
5.4d 
stable 
0.33, 0.32, 0.26 
e-:0.049 
X-ray: 0.031, 0.040 
Xe135* 
13m 
I. T.,y,e~ 
0~, y 
e~: 0.50 
0.54 
Xe133 
Xe13* 
15.6m 
10m 
9.2h 
9.4h 
9.5h 
stable 
5.9 
Al; 0.6 
0.94 
0.96 
0.92 
0.90-1.0 
~0.5, 0.6 
0.25 
0.26 
Xe137 
3.4m 
0~ 
n 
0~ 
0~ 
0~ 
0~ 
0- 
0~ 
0- 
I. T. (?) 
0- 
0~> y 
0~, y 
0~, y 
0~ 
R- 
~4 
Xet,37) 
Xe138 
Xe139 
Xe140 
Xe141 
Xe143 
Xe144 
Xe(145) 
Xe 
55 Cs133 
Cs135 
Cs(136) 
Cs137 
Cs138 
Cs'38 
3.8m 
instantaneous 
17m 
0.17% of fiss. 
neutrons 
n: 0.67 
0.56 
16-18m 
41s 
~30s 
16s 
9.8s 
3s 
1.7s 
Is 
short 
0.8s 
68m 
stable 
> 2.5 X 104y 
> 2X 103y 
13d 
33y 
32m 
33m 
7m 
10m 
0.008, 0.011 
~0.28 
0.5 (50%), 0.8 (50%) 
~0.4 (50%), 0.8 (50%) 
2.6 
1.2 
0.75 
0.7 
1.2 
R- 
Q~ 
~l-2m 
R ~ 
ft- 
short 
ft~ 
ft~ 
56 Ba135 
Ba13fl 
Ba137 
Ba138 
stable 
stable 
stable 
stable 
low 
153 RADIOLOGICAL SAFETY 
Table I.—Table of fission products: characteristics—Continued 
Nucleus 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
Z 
A 
Particles 
Gamma radiations 
Ba139 
85m 
86m 
87m 
8~, y 
6.3 
2.2 
0.6 
Bal4u 
12.8d 
P~, y, 
6.1 
1.05 
0.542 
~12.5d 
5.8 
~0.4 (25%). 1.0 (75%) 
I 0 
e~: 0.50 
0.529, 0 5 
Ba141 
18m 
P~, y 
P~ 
P~ 
p- 
4.6 
y 
Ba<>42> 
6m 
Ba143 
>0.5m 
Ba144 
short 
Ba(145) 
short 
P~ 
57 
La139 
stable 
La140 
40.Oh 
40.2h 
P~, y 
0.90 (20%), 1.4 (70%), 
2.12 (10%) 
1.45, ~2.2 (low intensity) 
1.41 
1.6 
1.75 
0.335 (1%), 0.49 (7%), 
0.83 (14%), 1.63 (74%), 
2.3(4%) 
0.335 (2%), 0.49(5%), 0.87 
(10%), 1.65 (77%), 2.3 
(6%) 
0.333, 0.505, 0.832, 1.61, 
2.52. 
1.69 (>97%), 2.5 «3%) 
2.0 
2.1 
La141 
3.7h 
Pr, y(?) 
P~, y 
2.8 
y (?) 
La'142) 
74m 
7 
77m 
La143 
19m 
P~ 
>4.3 
20m 
~ 15m 
La144 
short 
P~ 
P~ 
La(145) 
short 
58 
Ce,4° 
stable 
Ce141 
28d 
P~, y 
5.7 
0.55 
0.21 
30d 
0.65 
0.22, 0.2, 
Ce142 
stable 
Ce143 
33h 
32h 
36h 
P~, y 
5.4 
1.35 
0.5 
Ce144 
275d 
300d 
8- 
5.3 
0.348 
~0.3 
no y 
Ce”43' 
1.8h 
p~ 
Ce(,46> 
14.6m 
8- 
~15m 
59 
Pr141 
stable 
Pr143 
13.8d 
8- 
1.0 
no y 
14d 
14.2d 
0.95 
13.5d 
PrH4 
17.5m 
P~, y, e~ 
3.07 
0.135, 0.145(?) 
18m 
3.0 
154 RADIOLOGICAL SAFETY 
Table I.— Table of fission products: characteristics—Continued 
Nucleus 
Half-life 
Decay 
Fission yield, % 
Enerey of radiations in Mev 
Z A 
Particles 
Gamma radiations 
17m 
3.1 
0.22, 1.25 (low intensity) 
Pr744 
3.2 
2.8 
e~\ 0.091, 0.128, 0.103(?) 
Pr (145) 
4.5h 
B~ 
3.1 
no 7 
4.7h 
pr (146) 
24.6m 
B~, 7 
~3 
1.4 
25m 
60 Nd743 
stable 
Nd144 
stable 
Nd145 
stable 
Nd146 
stable 
Nd147 
11. Od 
B~, 7, e~, 
X-ray 
2.6 
~0.4 (40%), 0.90 
(60%) 
0.03 
0.58 
X-ray: —0.040 
Nd148 
stable 
Nd(149) 
l.?h 
B~, 7 or 
X-ray 
1.5 
7 or X-ray 
2.Oh 
Nd150 
stable 
Nd(757) 
short 
B~ 
61 61147 
3.7y 
4y 
2.2y 
B' 
0.20 
no 7 
61149 
47h 
B~, 7, 
X-ray (?) 
1.4 
1.1 
0.25 (low intensity) X- 
ray(?) 
61(151) 
12m 
B~ 
61158 
<5m 
< 5m 
stable 
B~ 
B~ 
61156 
62 Sm147 
Sm148 
stable 
Sm<151) 
8m732 
long 
stable 
8m153 
47h 
B~, 7 
I. T. (?) 
0.15(t) 
0.73 
0.7 
0.10. 0.57 
0.11, —0.6 X-ray (?) 
Sm154 
stable 
Sm155 
25m 
21m 
B~, 7 
0.031 
1.9 
1.8 
-0.3 
Sm156 
— lOh 
B~ 
~0.016 
~0.8 
63 Eu,£I 
stable 
Eu153 
stable 
Eu155 
2y 
B~, 7 
~0.03 
~0.23 
0.0844 
Eu159 
15.4d 
B~, 7 
0.013 
-0.5 (60%), 2.4 
(40%) 
2.0 
Eu’57 
15.4h 
B~< 7 
0.0074 
-1.0 (75%), —1.7 (25%) 
0.2, 0.6 
Eu(158) 
60m 
B~ 
0.002 
-2.6 
64 Gd759 
stable 
Gd159 
stable 
Gd757 
stable 
Gd758 
stable 
155 RADIOLOGICAL SAFETY 
Table I.— Table of fission -products: characteristics—Continued 
Nucleus 
Z A 
Half-life 
Decay 
Fission yield, % 
Energy of radiations in Mev 
Particles Gamma radiations 
Unidentified 
fission product 
nuclei with 
daughters emitting neutrons 
instantane- 
ously 
% of fission 
neutrons 
(I) 
4.51s 
4.5s 
3s 
0~ (n) 
0.21 
n: 0.430 . 
(2) 
1.52s 
1.8s 
0~ (nl 
0.24 
n: 0.620 
(3i 
0.43s 
0.4s 
0~ (n) 
0.084 
n: 0.420 
(41 
0.05s 
0- (n'» 
~0.029 
Symbols; 
P~—Negative electrons emitted from the nucleus. 
7—Gamma rays. 
e~—Internal conversion electrons. 
n—Neutrons. 
I.T.—Isomeric transitions. 
*—Nucleus in a metastable excited state, decaying by isomeric transition. 
Where several values of the half-life or energy of radiation are given, they are those obtained by different investigators 
or by different experimental methods. 
156  
Table II 
— Table of fission products 
chains and yields 
PART 1. LIGHT GROUP 
Mass. 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 40 
41 
42 
43 
44 
45 
46 
47 
48 
49 
50 
No. 
Zn 
Ga 
Ge 
As 
Se 
Br 
KV 
Rb 
Sr 
Y Zr 
Cb 
Mo 
Ru 
Rh 
Pd 
Ag 
Cd 
In 
Sn 
yield, % 
71 
• 
stable 
• 
• 
• 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
72 
49h— 
—>14.3h— 
> stable 
# 
• 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
1.5X10-8 
73 
<2m— 
—»5h 
►stable 
• 
• 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
1.0X10-8 
74 
• 
• 
stable 
• 
• 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
75 
• 
• 
(89m)— 
►stable 
• 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
76 
• 
• 
stable 
• 
• 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
77 
• 
• 
12h- - 
->40h 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.0091 
78 
• 
• 
• 
(80m)— 
-►stable 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
(78) 
• 
• 
• 
• 
• • 
• 
• 
0.02 
79 
• 
• 
• 
. j 
<10m or 
instable 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
1 
>7X10*y 
80 
• 
• 
• 
• 
• 
• 
• 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• • 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.008 
8! j 
-- 
' i 
1 
• 
• 
• 
<10m >17m 
-►stable 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.125 
82 
• 
e 
• 
• 
stable 
34th 
-►stable 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
2.8X10-8" 
1 
• 
• 
• • 
• 
• 
o 
• 
0.40 
83 < 
• 
• 
• 
• 
• 
• 
i 
stable 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
84 
• 
• 
• 
• 
~2m— 
—►30m—^stable 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.65 
• 
• 
• 
• 
• 
3.0m >4.5h—►stable 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
85 - 
S 
• 
• 
• 
• 
• 
• 
~10y 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
~0.24 
86 
• 
• 
• 
• 
• 
• 
stable 
t 
nstant.d 
19.5d—►stable 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
2X10-88 
• 
• 
• 
• 
• 
55.6s-►! 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.026c 
(87) ■ 
. 
• 
• 
• 
• 
• 
• 
• 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
87 
• 
• 
• 
• 
• 
50s »75m->6.3 X 1010y->stable 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
88 
• 
• 
• 
• 
• 
3h— 
-►17.8m— 
stable 
• • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
89 
• 
• 
• 
• 
• 
• 
2.6m— 
-►15.4m >53(1— 
-►stable • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
4.6 
90 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
_ 51m (~40%) 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
9.8s— 
-►short 
►9.7h— 
i 
►57d - -►stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
5.9 
(92) 
• 
• 
• 
• 
• 
• 
3s 
-►short 
>2.7h— 
-»3.5h—>stable 
• • 
• 
• 
• 
• 
• 
* 
• 
• 
• 
• 
• 
• 
• 
• 
• 
5.1 
(93) 
v nV» 
(94) 
• 
• 
• 
• 
• 
• 
• 
95 
* 
• 
• 
• 
• 
• 
• 
• 
• 
• • ,90h (~ 
X i 
'2%) 
• 
• 
• 
• 
• 
• 
• 
• 
• 
►stable 
• 
% 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
97 
■►stable 
98 
• 
f * 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• • 
• • 
• 
• 
stable 
• 
• 
5.9h 
• 
(-10%) 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
99 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• • 
• 
67h 
i 
4X105y- 
—►stable 
• 
• 
• 
• 
• 
• 
6.2 
100 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• • 
• 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
101 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• • 
• 
14.6m—►14.0m- 
—►stable 
• 
• 
• 
• 
• 
• 
(102) 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• • 
• 
12m— 
<lm— 
—►stable 
• 
• 
• 
• 
• 
• 
157 Mass. 
No. 
30 
Zn 
31 32 33 34 35 36 37 38 
Oa Oe As Se Br Kr Rb Sr 
39 
Y 
40 
Zr 
41 42 
Cb Mo 
,o 44 45 46 
M Ru Rh Pd 
47 
Ag 
48 
Cd 
49 
In 
50 
Sn 
Fission 
yield, % 
• 
• •• • • • • • 
• 
• 
• • 
• 
• 56m (2=97%) • 
• 
• 
• 
• 
103 
• 
• •• * •••• 
• 
• 
• • 
• 42d >stable • 
• 
• 
• 
• 
3.7 
104 
• 
• •• • •••• 
• 
• 
• • 
• stable • • 
• 
• 
• 
• 
105 
• 
• •• • • • • • 
• 
• 
• short—‘short >4.5h >36.5h ‘stable 
• 
• 
• 
• 
~0. 9 
106 
• 
• •• • •••• 
• 
• 
• • 
• l.Oy >30s ‘stable 
• 
• 
• 
• 
0.5 
107 
• 
• •• • • • • • 
• 
• 
• • 
<1.5m > 
.. v. short or 
m->24m- -M „ 
->stable 
• 
• 
• 
[ >3X108y 
108 
• 
• •• • • • • • 
• 
• 
• • 
• 
• stable 
• 
• 
• 
• 
• 
• •• • •••• 
• 
• 
• • 
• 
• • 
(40.4s) 
• 
• 
• 
109 
• 
• •• • • • • • 
• 
• 
• • 
• 
<lh ‘13.4h— 
->stable 
• 
• 
• 
0.028 
110 
• 
• •• • •••• 
• 
• 
• • 
• 
• stable 
• 
• 
• 
• 
111 
• 
• •• • • • • • 
• 
• 
• • 
• 
• 26m— 
—>7.6d— 
->stable 
• 
• 
0.018 
112 
• 
• •• • •••• 
• 
• 
• • 
• 
• 21h 
—>3.2h— 
->stable 
• 
• 
0.011 
113 
• 
• •• • •••• 
• 
• 
• • 
• 
• • 
• 
stable 
• 
• 
114 
• 
• •• • • • • • 
• 
• 
• • 
• 
• • 
• 
stable 
• 
• 
• 
• •• • • • • • 
• 
• 
• • 
• 
• • 
• 
2.33d ‘4.53b 
• 
0.011 
115 
• 
i 
• 
• •• • •••• 
• 
• 
• • 
• 
• • 
• 
44d— 
—>stable 
• 
0.0008 
116 
• 
• •• • •••• 
• 
• 
• • 
• 
• • 
• 
stable 
• 
• 
117 
• 
• •• • •••• 
• 
• 
• • 
• 
• • 
• 
2.83h- 
—>1.95h— 
->stable 
0.01 
* 
• •• • ••• • 
• 
• 
• • 
• 
• • 
• 
48.7m 
1 
• 
• 
• 
• •• • •••• 
• 
• 
• • 
• 
• • • 
• 
stable 
• 
• 
Zn 
Qa Oe As Se Br Kr Rb Sr 
Y 
Zr 
Cb Mo 
43 Ru Rh Pd 
Ag 
Cd 
In 
Sn 
“Yield of 34h Br** formed directly in fission; not representative of total chain yield. 
‘Yield of 19.5d Rb" formed directly in fission; not representative of total chain yield. 
'Delayed neutron yield based 
on fission neutrons rather than on fissions. <* Instantaneous, via delayed neutrons. 
Mass 
No. 
50 
Sn 
51 
Sb 
52 
Te 
53 
I 
54 
Xe 
55 
Cs 
56 
Ba 
57 
La 
58 
Ce 
59 
Pr 
60 
Nd 
61 
62 
Sm 
63 
Eu 
64 
Od 
Fission 
yield, % 
118 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
119 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
120 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
(121) 
62h 
—^stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.014 
(121,123) 
130d 
—^stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.0012 
122 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
(123) 
lOd 
—^stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.0044 
124 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
125 
(9m) 
->~2.7y— 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.023 
(125) 
~20m 
>7 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
(126) 
70m 
—>60m 
>stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.1 
( 
• 
• 
jr90d 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0. 033 
127 { 
i 
I 
• 
93h 
>9.3h 
—^stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
128 
• 
• 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
Table II.—Table of fission products: chains and yields—Continued 
PART 1. LIGHT GROUP 
PART 2. HEAVY GROUP 
158 129 { . 
• *32d 
.' ' i 
• 
• 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0. 19 
I 
130 • 
131 | . 
• 
• 
stable 
30h 
i 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
~0. 5 
1 
(132) • 
133 • 
(134) • 
• 
• 
2.8 
stable 
• 
• 
3.6 
• 
• 
~4. 5 
• 
• 
~S-7 
135 { . 
• 
• 
• 
• 
(~10%) • 
i 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
1 
(136) • 
(137) I * 
• 
• 
13d 
• 
->stable 
• 
• 
5.9 
• 
• 
22.0s— 
T 
—> instant." 
• 
• 
• 
• 
• 
• 
• 
• 
• 
0.01" 
o. m 
1 
137 • 
138 • 
139 • 
140 • 
141 • 
(142) • 
143 • 
144 • 
(145) • 
• 
(146) • 
147 • 
148 • 
149 • 
150 • 
(151) • 
152 • 
153 • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
6.3 
• 
• 
• 
• 
• 
• 
• 
40s 
—»? 
• 
• 
• 
• 
• 
• 
• 
• 
6. 1 
• 
• 
• 
5.7 
• 
• 
• 
) "'oTm 
)10m 
5.4 
• 
• 
• 
jlo. 0(1 
• 
• 
• 
—^stable 
5.3 
• 
• 
• 
• 
• 
• 
(68m) 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
2.6 
1.4 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
stable 
(1.7h) - 
stable 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
stable 
• 
• 
0.15 
~0.03 
0.013 
0. 0074 
0.002 
154 • 
155 • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
stable 
25m 
• 
• 
156 • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
) stable 
157 • 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
058) • 
Sn 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
• 
Sb 
Te 
I 
Xe 
Cs 
Ba 
La 
Ce 
Pr 
Nd 
61 
Sm 
Eu 
Gd 
"Yield of 13d Cs »3« formed directly in fission; not representative of total chain yield. 6 Delayed neutron yield based on fission neutrons rather than on fissions. 
( )—Parentheses around mass number indicate the mass assignment is uncertain. 
— Broken arrow indicates the genetic relationship has not been definitely established. 
" Instantaneous, via delayed neutrons. 
159 SUBJECT INDEX 
Absorption curve 52, 81, 84. 
Acceleration 9, p, 
Accelerators 89, 92-95. 
Alpha particles 64,65. 
Alpha particles, absorption 64, 79-81. 
Alpha particles, bombardment 89-92, 95. 
Alpha particles, emission theory 78, 80, 85, 86. 
Alpha particles, ionization 81, 129. 
Alpha particles, measurement 126, 129. 
Alpha particles, measurement with films. 144, 145 
Alpha particles, range-energy relation- 
ship 79-81. 
Alpha particles, spectra 80, 85. 
Americium 120. 
Annihilation radiation 54, 97. 
Artificial radioactivity 91, 92. 
Atomic mass unit 75, 76, 92, 99. 
Atomic weight 16, 56, 58, 61. 
Avogadro’s number 16, 26. 
Background radiation 140. 
Balmer series 44—46. 
Beta particles 63, 65, 66. 
Beta particles, absorption 64, 83-85. 
Beta particles, emission 81-83, 112. 
Beta particles, measurement 126, 129, 139. 
Beta particles, range 84, 85. 
Betatron 49,93,94. 
Binding energy 75, 76, 86, 106- 
108. 
Biot & Savart law 22, 23. 
Black body radiation 38, 39. 
Bohr atom 45-48. 
Bomb (atomic), mechanism 115. 
Boron 95, 100, 101, 134. 
Bremsstrahlung 83. 
99, 100, 117, 118. 
Capacitance 20,21,125. 
Capture 95, 99, 116, 117. 
{See also Cross 
section.) 
Chain reaction 105. 
Chain reaction, fast 112, 114. 
Chain reaction, slow 116, 117. 
Characteristic curve, photography 143, 144. 
Charge, unit 22. 
Cloud chamber 52, 54, 79, 80, 86, 
121, 122. 
Collisions, elastic 14, 83, 101, 102, 
116, 117, 123. 
Compton effect 53, 66. 
Condenser r meter 126-128. 
Condensers 20, 21. 
Cosmic radiation 35, 36, 102, 103, 
140. 
Coulomb force 76, 77, 108, 109. 
Coulomb’s law 19. 
Counter dead time 140, 141. 
Counter gas 133. 
Counters, Geiger-Mueller (GM) 129-140. 
Counters, neutron 134. 
Counters, proportional 131. 
Counters, self-quenching 133. 
Cross section 90, 91, 92,- 97- 
101, 111.’ 
Curie, the 68, 73, 74. 
Curium 120. 
Cyclotron 93, 94. 
Dead time, counter 140, 141. 
De Broglie equation 55. 
Decay constant 66-68, 79, 82, 83, 
141. 
Densitometer 142. 
Deuterium 42, 58, 95, 98. 
Deuteron 95, 96, 98, 116. 
Diffraction 33. 
Diode 27. 
Discharge, continuous 131. 
Dosimeter 124. 
DuLong & Petit law 17. 
Efficiency, bomb 115. 
Electrometers 123-125. 
Electron 22. 
Electron charge 22. 
Electron mass 22, 65, 94, 
Electron volt 25. 
Electroscopes 123-125. 
Energy 12, 37. (See also 
Fission energy 
and binding 
energy.) 
Enriched uranium 111. 
Fermi theory, beta decay 82. 
Film sensitivity 143. 
Fission Chapter 8. 
Fission energy 105, 106, 107, 
109, 110, 115. 
Fission products 105, 109-11 1, 
147-159. 
Fission, spontaneous 110. 
Fission yield 112, 113. 
Force 10, 11. 
Gamma (Photographic measurements) _ 144. 
Gamma rays 35, 36, 64, 65. 
Gamma rays, absorption 64, 66, 86. 
Gamma rays, measurement Chapter 9. 
Gamma rays, theory of emission 85, 95-97. 
Geiger-Mueller (GM) counters 129-140. 
Geiger-Nuttal relation 78, 79. 
Geiger region 131, 132. 
Gram atom 16. 
Graphite 117. 
Gravity 12. 
161 INDEX 
Half-life 66-68, 72, 73, 92. 
Half-life, transuranium elements 120. 
Half-life, uranium series 69-72. 
Heavy water 42. 
Hiroshima 1. 
Hydrogen, heavy See deuterium. 
Induced radioactivity 99-102. {See 
also Artificial 
radioactivity.) 
Inertia 10. 
Insulators 21, 125. 
Insulator soak-in 125. 
Interference (waves) 33. 
Ion pair. 121. 
Ionization, avalanche 123, 129-133. 
Ionization chamber 126-129. 
Ionization potential 48. 
Isobar 60. 
Isomer 85, 96. 
Isotope 56-61, 92, 99, 
100, 108, 120. 
Isotopes, uranium 105, 111, 120. 
Joule’s law 25. 
K-electron capture 96, 97. 
Lauritsen electroscope 124. 
Magnetic field 22-24, 94. 
Mass defect 60, 75, 76. 
Mass-Energy law 7, 74. 
Mass number 42. 
Mass, rest 11, 12, 65. 
Mass spectra 56-60. 
Mass spectra, uranium 111. 
Mass units, atomic 75, 76, 92, 99. 
Mean free path 17, 123. 
Mesotrons (Mesons) 103. 
Millikan’s oil drop experiment 21. 
Moderator 116. 
Momentum 14. 
Moseley’s law 50. 
Multivibrator circuit 135, 136. 
n unit 128. 
Neher-Harper circuit 134, 135. 
Neher-Pickering circuit 135. 
Neptunium 116, 120. 
Neutrino 82, 103. 
Neutron Ch. 8, also 42, 60, 
61, 76, 82, 91, 
122. 
Neutron capture 97-102, 116. 
Neutron energy 99, 101, 111. 
Neutron measurement 128, 134. 
Neutron sources 91, 96, 98. 
Neutrons, delayed 110, 112, App. I 
Neutrons, fast 91, 99. 
Neutrons, fission 110, 112, 114, 
115. 
Neutrons, prompt 110. 
Neutrons, thermal 99, 110, 116, 118. 
Newton’s laws 10, 11. 
Nuclear forces 75-78,106-110. 
Nuclear reactions 95-102. 
Nucleon 42. 
Nucleus, structure 75-77, 82. 
Ohrr’T law 24. 
Opacity 142. 
Optical density 142, 143. 
Packing fraction 60. 
Pair production 53, 54, 66, 97. 
Periodic table 43, 44, 59. 
Photoelectric effect 37, 52, 66, 133. 
Photoelectric production of neutrons98. 
Photoelectrons 52. 
Photofission m. 
Photon 37, 53. 
Pile 117-120. 
Planck’s constant 37. 
Plutonium 116-120. 
Polonium 69, 70, 72, 145. 
Positron 53, 92. 
Positron emission 96, 97. 
Potential barrier 77, 78,89, 90, 101, 
109. 
Power 12. 
Power pile 118-120. 
Proportional counter 131. 
Protactinium 69, 72, 106. 
Proton 41, 42, 55, 56, 
111. 
Proton emission , 82, 89, 90, 100, 
101, 103. 
Proton number 60, 61. 
Proton reactions 92, 98, 102. 
Quantum 37-39. 
Quenching counters 133-136. 
Radioactive decay 66-68, 72-74. 
Radioactivity, artificial 91, 92. 
Radioactivity, natural Chapter 6. 
Radio-autographs 145. 
Radioisotopes 70-72, 92, 147- 
159. 
Radium 63, 68-72. 
Radon 68-72. 
Range See beta particles 
and alpha par- 
ticles. 
Reactor 116. 
Refraction 33. 
Relativity, theory 11, 12, 65. 
Resonance capture 97, 116. 
Rest mass 11, 12, 65. 
Ritz combination law 45. 
Roentgen, the 55, 74. 
Roentgen equivalent, man 74. 
Roentgen equivalent, physical 74. 
Rydberg constant 44, 48. 
Sargent diagram 83. 
Saturation current 123. 
Scaling circuits 137, 138. 
162 INDEX 
Self-absorption 141. 
Specific heat 16. 
Specific ionization 80, 81. 
Specific resistivity 24. 
Spectrum 35, 36. 
Spectrum, alpha 80. 
Spectrum, atomic 44, 45. 
Spectrum, beta 81, 82, 85. 
Spectrum, gamma 85, 86. 
Spectrum, mass 56-58, 111. 
Spectrum, X-ray 49-51. 
Tamper 115. 
Thimble chambers 126. 
Thorium 69, 70, 72, 87, 
106, 120. 
Threshold energy 96, 109. 
Transmutation. 90. 
Transuranium elements 105, 120. 
Triode 27,28. 
Uranium, enriched 111. 
Uranium, fission 105, 106, 110- 
115. 
Uranium, isotopes 105, 111, 120. 
Uranium, neutron absorption (capture). 98, 110-117. 
Uranium, series 68-72. 
Vacuum tubes 27-29, 128, 129, 
135-138. 
Van de Graaff generator 93. 
Velocity 9. 
Wave length 31. 
Wiedemann-Franz law 17. 
Wien’s law 38. 
Wilson cloud chamber 52, 54, 79, 80, 86 
121, 122. 
Work 12. 
X-rays 35. 
X-rays, absorption 51-54. 
X-rays, production 36, 48^51. 
163 
U. S. GOVERNMENT PRINTING OFFICE : 0—1948