REACTORS
@@@DVOtSOTOPWS RADIATION
I
W. R. TOMLINSON, Jr. The Johns Hopkins University, Operations Research Office, Bethesda, Md.
The Chemical Industry Part I.
-A
Nuclear Future?
Radioactivity
The change-over of nuclear energy for military use to industrial application has been necessarily slow. Now nuclear technology seems ready to add its awesome potential to the future of the chemical industry. Is the chemical industry ready to accept this challenge? Here is the first of four articles pointing up what nuclear energy can do for the CPI
HUMANITY
stands today at the threshold of the golden nuclear era. Never before in history has the path to the future stood forth in such bold relief, nor been so plainly marked with the signs of great promise. There can be no doubt that the peaceful application of nuclear technologies will be man’s greatest blessing to date. These blessings are not self-generating, however; the applications will not develop themselves. This reaction requires an input of energy, plenty of it. Thought will be needed as a catalyst-bold, imaginative, and resourceful thinking, that will lead to intelligent decisions and forceful action. We are about to take off, let us not try to keep one foot on the ground. To focus the picture a little more clearly, consider the question, “Just where do we stand today?” We have come a long way since, a t the turn of the century, Einstein created his revolution-
ary theory of relativity and pointed out the essential unity of matter and energy. We have learned how to extract energy in enormous quantities from relatively small amounts of matter. The atom bomb, the hydrogen bomb, and prototypes of industrial power plants have been developed. Our exact location, however, depends mainly on economics. Processing costs in the nuclear field are extremely high, although as experience has taught reductions are inevitable as a result of activity in industrial applications. Balancing these high costs are the values of the energy derivable from nuclear materials and of the radioactive isotopes obtainable from them. Paul Genachte, vice president for atomic energy of the Chase Manhattan Bank, last year said that economic nuclear power will be available in America in 5 to 10 years. A technical appraisal task force reported, to the Board of Directors of the Edison Electric Insti-
tute, that “there is a good probability of reducing the cost of nuclear power sufficiently in the next 10 years to make it competitive with power from fossil fuels in some parts of the United States.” Their report was dated February 21, 1958 (6). Willard Libby, past Commissioner of the Atomic Energy Commission, estimated the tangible contributions of radioisotopes to the U. S. national economy from industrial uses a t $500 million for 1957 and that this contribution is growing with extreme rapidity. Last year I/EC presented a closing 50th Anniversary Feature by W. Kenneth Davis which covered nuclear technology in the first 50 years of I/EC; it showed clearly that most of the applications lie in the future. Nuclear industry is very close to its birth datea little bit one way or the other perhaps, depending on the way you want to look at it. One thing is clear-a period of very rapid growth is not far off. VOL. 51,
NO. 10
OCTOBER 1959
1239
The early and rapid growth of the nuclear industry is inevitable. \Ye cannot just sit back and let our economic position dictate completely our course of action. O u r neighbors and particularly our enemies will not let us. Their economic positions are less favorable in fossil fuels, and they are more strongly impelled to develop nuclear polver than we are. They are going ahead--\ve cannot afford to lag behind. Ho\v \vel1 could we compete \vith neighboring societies based on nuclear power, if lve stuck too long to our currently enviable nonnuclear economy? Ere long we would find we tvere driving a model-T economy in a jet age. Let us strain a t the leash to develop the peaceful uses of nuclear power and to cultivate the applications of the priceless radioactive by-products of this power. Let us d o it eagerly with all our resources and reap the consequent ivealth of benefits. Let us work actively in this field and develop the technological key to our nuclear future. \Ve cannot d o this by helping our poor neighbors into the field and then sitting back to see how they make out. There has been considerable complaining in the lirerature of late to the eKect that the AEC should d o more, that industry wants a free ride and, in particular, that the chemical industry is sitting back and doing nothing. This type of approach to the problem seems all wrong psychologically, and certainly it is not a constructive one. People d o not like to be told what to do, they like to make their own decisions. This is particularly true in the chemical industry where preferences for areas may depend heavily (among other things) on interests in types of processing, technological areas, heavy us. light chemicals activities, type of marketing involved, and the like. Assuming that this philosophical note is on key (not sour), we would like to approach the problem in a positive way by discussing nuclear technologies in an interested fashion and developing the tools necessary for evaluation of potential to the chemical industry. T h e proper frame of mind for this undertaking can be expressed in the following quote from the Editor‘s page of I/EC’s December 1958 issue: “The chemical industry does not have forever t o prepare itself for the most satisfying participation in the new nuclear field.” O u r objective is to develop, in a manner as attractive and a form as useful as possible, the information which we as chemists can use to determine what value the developing nuclear industry has to the chemical industry; and, conversely, to understand how chemical activities must develop concurrently. I n particular, the vital quesrion to a given individual or group is: “What role do I wish to play?” This should be borne uppermost in mind. In this connection a few points naturally occur
1240
which merit a comment. I:/EC provides excellent coverage of the chemical processing aspects of the study of nuclear industry and we will not attempt a duplication. Although reactor physics and design are not of primary interest to the chemist, some knowledge is essential to proper appreciation of the implications of many of the possible chemical plans likely to arise. Further, Ivhile power production is not a primary interest of the chemical industry, its development requires participation by the latter, and, indeed, some large chemical complexes may even find nuclear power production attractive-at least in participation u i t h another group. Certainly, the chemical industry has strong interest in the potential of nuclear process power. It is pertinent therefore to cover reactor physics, design, and operation. Perhaps one of the most interesting aspects of the subject is that o f radioactivity, especially the production and use of radioactive materials. The tremendous potential of radioisotopes for future industrial applications could \vel1 be a n important factor in determining just when economic nuclear power tvill be achieired. As such it deserves a special place in our attentions and we will start off in this part of the nuclear field. An important part of the information to be developed is most useful in equation form; for purposes of evaluation thr equations are essential. T h e material covered, hoivever, will be presented in such a way that those lvho abhor mathematical symbols and hieroglyphics
may cover them without detractiiig from the picture presented. Rcfercnccs M-ill take care of interests more advanccd than the text. Radioactivity
T h e Nucleus. As you may or may not remember from your freshman general chemistry, the atomic nucleus consists of essentially hvo building units--the proton and the neutron. \Vhile other entities are also involved, we can safely ignore them for our purpose. The hydrogen atom stripped of its classical planetary electron is the proton. The proton deprived of its positive charge is the nrutron; the lattrr characteristically and spontaneously decays in thc. frer state to provide a proton, an electron (a neutrino----neutral particle of negligible mass) and a goodly amount o f energy---0.78 1n.e.v. per event or about 18 million kcal. per mole of events. (.i convenient unit of energy. One million electron volts, 1 m.e.v., per rvrnt is about 23,000,000 kcal. per mole of cvents.) I n this event, the neutron Xvould be the simplest radioactive spccics, and its half life has been c,alculated iis roughly 20 minutes. Essentially, the atomic nuclei of thr elements consist of variwus nunibers of neutrons and protons. T h e nuntber of protons, Z> determines the charqcon the nucleus and is called the atomic number. The nuclear charge is positive and equal in magnitude to Z times thr electronic charge, P; electrons and
N=Z
/.
\
/ /
/ / /
zFigure 1. Atomic nuclei of the elements consist of various numbers of neutrons, N, and protons, Z, which achieve a state of equilibrium-depending on the numbers of units involved
INDUSTRIAL AND ENGINEERING CHEMISTRY
NUCLEAR FUTURE protons carry charges of the same size, but opposite in sign. If N stands for the number of neutrons in the nucleus, Z plus N is the total number of building units (nucleons) in the core or the mass number, A . Neutrons and protons are in a certain sense approximate equivalents. Thus, in the lower atomic weight nuclei, the two types of building unit are roughly equi-numerous. With increasing atomic weight, some seem to become more equal than others, and the protons, when too numerous, become noticeably repulsive to themselves as a consequence of their unit positive “electronic charges.” A sort of state of equilibrium is achieved, depending on the numbers of units involved, and this is depicted in Figure 1 where N is plotted against Z. In this plot, a t low Z, N and Z are approximately equal, but as Z increases, N increases somewhat more rapidly so that there are considerably more neutrons than protons in very heavy nuclei. The shaded area contains all the stable nuclei. Unstable nuclei occur in a region lining the border of the stability region for a depth of several neutron numbers above and below the stability region. I n addition, however, unstable nuclei occur scattered through the stability region; to understand this requires a close look at the energy which binds the nucleons together in the nuclear core. These energies and the forces which are responsible for them are not too well understood (4, 8), but remembering that mass and energy are related a simple approach is possible. Mass and energy are associated by Einstein’s equation, mass equals energy divided by the square of the velocity of light, c, or alternatively, energy equals mass times c squared. For a given mass number, as the number of protons and neutrons in the nucleus are varied, the actual atomic weight of the nucleus varies a small amount. If the masses of the nucleons are added together and from this sum the actual atomic weight of the nucleus is subtracted, the remainder is equivalent to the binding energy. This binding energy varies somewhat from nucleus to nucleus, and is, of course, proportional to the mass difference noted. As protons and neutrons have very nearly the same masses, the nuclei apparently have the same masses if the binding energies are ignored. As binding energies are subtracted to get the actual atomic weights, the lighter of the nuclei of constant mass number are clearly the more tightly bound and thus the more stable. If then a third axis is added to the figure, perpendicular to the plane of the paper and increasing in the direction of the reader, and the actual atomic weight (nuclear mass)
be plotted here, the shaded area is a valley-deeper toward the center of the shading and rising toward the bounding lines of this stability region. Now, when the positions of unstable nuclei, within the stability region, are examined, the unstable nuclei lie above the floor of this valley (or canyon) as determined by the stable nuclei. This three dimensional diagram provides a pretty good picture of nuclear stability. However, if we remember this picture and its consequences, it is simpler to talk about isotopes in terms of the two dimensional one with a stability curve, defined by the valley bottom, running along the approximate center of gravity of the shaded area of the figure. This will be adequate for our purposes. Thus nuclear instability and tendency to be radioactive are related to the numbers of the two types of particles, or to the distance from the stability curve, and the degree of instability is roughly proportional to the departurefrom equilibrium. Is there any good reason for this? That is a good question, but let us just consider that this is a good general rule and go on to cover some others. Radioactive elements may be conveniently divided into two groups: those with 2 values (proton numbers) over 82 (lead), which are naturally occurring radionuclides (although a few lighter elements fall in this group), and those of any atomic number whose proton to neutron ratio departs too far from the stability curve. (The term radionuclide refers to radioactivity in elements generally; for those different active varieties of a single element the term radioisotope applies.) This division is convenient because it distinguishes between what God bestowed on us and what he intended we should make for ourselves. Radionuclides in these categories, finding that their internal structures are unbalanced by an insupportable deviation from equilibrium, are doing something about it. They are, for instance, returning their proton-neutron ratios in the direction of the stability curve and in the process liberating rather intriguing quanitites of energy, normally gaged in million electron volts per event (billions of calories per mole of events). As chemical reactions release energies of the order of 10 electron volts per event, nuclear reactions are attractive indeed. The emission of energy in such enormous amounts intuitively explains why changes in conditions do not affect nuclear processes and is the reason for display of considerable interest in certain applications. Further interest attaches to other features of radioactive decayemission of gamma radiation, alpha
particles (helium nuclei), and positive or negative beta particles (positrons or electrons). Let us take a little closer look at this process, radioactive decay. Why d o alpha and beta (plus or minus) particles or gamma rays appear? Suppose the unstable nucleus contains too high a proportion of protons. Emission of a positive beta particle is equivalent to exchanging a proton for a neutron, a change in the right direction. If our nucleus contains too many neutrons, emission of a negative beta particle (electron) is equivalent to a move toward equilibrium-Le., trading a neutron for a proton. Now how about gamma’s? Groups of neutrons and protons are bound together by forces; different groupings, of course, are associated with different binding energies. Removal of any particle from a group, or sufficient treatment of the group by radiation, impact, or the like, changes the energy content of the group, which by other laws must be related to the type group and the characteristic binding energy of the group. The nucleus, being naturally lazy, takes the easy way out and lets off steam (the gamma’s) and settles back into the ground state. Emission of alpha particles is a similar situation. While gamma and beta emission is commonly found throughout the range of the periodic table, alpha emission is possible only among the heavier elements. Alphas are tightly bound groups of two neutrons and two protons. Remembering the old maxim associating equilibrium positions with potential energy minima, it is not surprising that emission of alpha particles accomplishes a reduction in this important type of energy. Radioactive Decay. Recalling the earlier statement on the lack of environmental effects on nuclear processes, the type we have been primarily considering called radioactive decay follows a well defined, invariant law. The law is very simple, the number, N ( N will not be referred to again as a neutron number), of radioactive nuclei present after a decay time, t, is exponentially related to the number, No, orginally present at the start of the decay time: N =
Noe-ht
(11
This exponential decrease means that the rate of disappearance of the radionuclide is large initially and decreases with time (Figure 2). I t has an even more useful characteristic-for equal time periods, the ratio of material before and after the periods are equal. Thus, the important and useful concept of half life develops. This is the time interval during which half of the material VOL. 51, NO. 10
OCTOBER 1959
1241
disappears every second there will be little left to detect in 10 or 15 seconds. I n Equation 1, which states the exponential decay relation, if we differentiate with respect to time, we find that the rate at which nuclei decay is minus X times the original expression: d:V/dt
t+
Figure 2. Rate of disappearance of the radionuclide i s large initially and decreases with time
originally present (at any time) decays. In Equation 1, the constant X is called the decay (or transformation) constant. Substituting .Y/’.VO = l / 2 and the halflife value t l i z for t , ire find that the half life is given by :
What does this mean? IVhy is a half life useful? Radioactive materials emit alpha, beta, and gamma particles, and all three are detectable as a result of the things they do (interaction with matter). A gamma ray is referred to as a particle because it often acts as though it were one. I n this connection, Rutherford when asked “What is an electron?,” replied “An electron is what an electron does.” These particles are all detectable with an ease related specifically to the particle and its energy content, the detector used, and so on. They all carry that interesting commodity energy; they share the energy liberated in the decay process with the decayed nucleus itself. As alpha and beta particles are easy to stop, little shielding is involved and the energ>is easily collected. Gammas are difficult to stop, considerable shielding is called for, and thus energy collection is generally more difficult. \\’e can make use of the radionuclide in two principle ways: first, collection of the decay energy and utilization in suitable form; second, by labeling atoms, materials, etc., so that they can be easily observed and followed in the course of their maneuvering in chemical or physical processes. In each case, two things are important; the energy of decay and the rate at which decay processes occur. From an energetics point of view, rate of decay times energy liberated per decay leads to power available (theoretically, at least) for the quantity of nuclide considered. Both decay rate and decay energy figure importantly in the matter of detectability, and the time over which detection is feasible. For instance, if half the activity-i .e., half the radionuclide-
1242
= - LYoe --X1
=
- A.V
(3)
This is the rate at Lvhich radionuclei disappear; changing the sign of the expression gives the rate at Trhich the decay process occurs : A.V”l --h(
=
A,t-
(5,
To compare decay rates: a unit must be used for the disintegration rate. Two in use are the curie = 3.7 X loL0 disintegrations per second and the rutherford = 106 disintegrations per second. In discussing radioactive decay, a life span other than the half life is often used; this is the average life expectancy of a radioactive species and is designated as T . T is greater than the half lift. by a factor of 1.633 and is actually thr time required to decay to 1 eth of t h e original value: in terms of activity or numbers of radionuclei present. It is interesting to inquire as to the relation betlreen decay energy and half life. For alpha emitters there is a fairly good inverse rclation-i.e., the radioactive materials of higher decay energy have shorter half lives. For beta emitters there are many such relations, as these radionuclides seem to dispose themselves amongst several different families from this standpoint. Thus in the beta case the relation is not of much help in predicting the half life. Further: the half lives of beta emitters cover a smaller range in powers of 10 than the alpha emitters which span a range of about 10”’. Also, gammas and alphas are emitted with discrete values of decay energies, while the beta decay energy values cover the continuous range from z r r o to a definite maximum value. Having reached this point, we should realize clearly that short half life means a rapid decay rate; long life, a slow decay rate. Further, the number of processes occurring in a given sample is the product of the specific decay rate and the amount of material in the sample-i.e., so many disintegrations per second. T h e number of alpha or beta particles (according to which is emitted) is the number of processes, unless branching occurs, in \vhich case I
INDUSTRIAL AND ENGINEERING CHEMISTRY
.‘\l)UIl-
.Itoinic Mas:,
Eletiieiit No.
K Rb Sm
Lu Re
19 37 62 71 75
No.
40 87 152 176 187
Note thc long half live,, still around.
Half Life. lo8 Years
danre,
1.6 60 200 24 4000
0.01 27 27 2.5 63
rio
%
wontier tllcy :Ire
(4)
hlost experiments measure tlie rate of disintegration rather than the number of atoms prrsent at any given time. As d.1- dt is - A,\-, and at the initial dt), is - A.VO, it is clear that the decay rates, kno\rn as the activities of the samples, folloir the same laup Equation 1 : d.V ‘dt = (d.V,fdt I(,? -XI
Table I. Lighter Natural Radionuclides Which Exist in Nature
tlie several branches must be taken into account on a proportionate basis. (;ammas, of course, can be handled in the same way based on the details of the decay scheme. Energy output is the number of particles times the associated decay energy, and pobver is rnergy output per unit time or energy times decay rate. Poirer, like the nurnher of radioactive nuclei, and the activity of a sample will decline hy a factor of two with the passage of each half life. Properties of Radionuclides S a t u rally, whether we are considering energy release or detectable particles, we wonder Lrhat ranges of decay rates, particle types and distribution, and decay energies are available, as the obvious relation between these and application has been t-xposed. Further, it is important to know of the nuclides concerned, Lrhich occur naturally, how the others are made, and what the availability picture is like. The naturally occurring radioactive materials have been around for quite some time now, and are quite well known. We can pass over them briefly by stating that a t present over 40 radioelements of high atomic weight are known to exist in nature along with a fe\r related to the lighter elements, which are shown in Table 1 . Artificially produced radioactive materials are made by several different processes, including bombardment with various particles, such as protons or alpha particles, the fissioning of certain nuclei, such as UZ3j,Pu239,and by neutron activation (exposure in a neutron flux). M’e shall concern ourselves solely with neutron irradiation and fission and, a t present, with fission primarily. Rather complete information on all types of isotopes both stable and radioactive, including decay information, may be found in the literature (77, 78). Considerable information is also available on fission yields for U233, U235, P ~ 2 3 ~and , on decay chains for U236 (76). For our purposes, however, a couple of examples will suffice. Table I1 shows the characteristics of certain fission products selected on the basis that they will produce useful energy (hrat) at an initial rate of say 5 hp.
NUCLEAR FUTURE ~~
Table II.
Radioisotope Power Units
Decay Radio- Energy, isotope M.e.v. Zreb-Nb@s 1.63 Sra' YO1 Irls*
0.57 0.60 1.09 RulO'-Rh'O6 1.61 Ce144-Pr144 1.38 cot0 2.59 CP' 1.86 Tm17o 0.34 Po210 5.30 Pula8 25 P0210,
Half Life, Days
Theoretical Power," Watt/G.
65 54 58 74 365 285 1926 854 129 138 (24,300 yr.)
133 92 88 60 32 26 17 13 12 141 0.002
86 hp. per pound.
per pound or more, with a useful life of a month or more; this useful life is one or more half lives. Table 11 shows clearly the relation between rate-as reflected by half life-of decay and decay energy on the one hand and power output on the other. Polonium and plutonium are not fission products, but are shown for comparison. (The Pu decay is an alpha decay and has no relation to the fission of Pu.) The table also shows quite a range of half lives for power over 10 watts per gram; the range on all variables but decay energy is large and much wider ranges are available. The decay energy range can also be extended, but not by so many factors of 10. For instance, for the naturally occurring radionuclides half life varies from 4.5 x 108 years for Ug" to 3 X lov7 seconds for Poa12; alpha particle energies vary from about 4 to 8 m.e.v., beta particle energies vary from about 0.02 to 3 m.e.v., and gamma ray energies vary from about 0.2 to 2 m.e.v.. In Table 11, in some cases where two radioisotopes are shown, the second has so short a half life that its energy is liberated immediately and can be added to that liberated by the first radioisotope (which has been done). Thus, in the case of Ru106 - Rh1O8 the half lives are 365 days, 30 seconds. There are some things pertinent to a given use in this area which are not shown. No mention is made of radiation type and how much of each. Most of the fission products emit gammas and these require shielding. The nonfission product Po2l0,however, is an alpha emitter; alphas are easily shielded, so that the problem of application is considerably facilitated. Two thoughts immediately arise from this. First Po210 is certainly an attraktive material for certain uses. Second, how do we get it? Po21o is obtained from Bimgby the addition of a neutron. [Nuclei (and particles) are written zX*, where X is the atomic nucleus con-
cerned and Z and A are the atomic and mass numbers; ,d is a neutron and an electron.] saBi*os
+ on1
s3BiB10-P
S~PO*~O 4-
Bim has a natural abundance of 100% and reactors are excellent sources of neutrons. This makes Po2l0 even more attractive. We will return to consideration of polonium a t a later time. The second thought generated by Table 11 is that it is quite specific to the particular abstract use we had in mind. This is certainly so and tabulations generated for other uses, for instance, medical would be quite different. The construction of such tables are excellent exercises and we leave them to the student. The general method of approach is simple and direct. First, formulate the use problem clearly and qoncisely. Derive from it the time, e n e r h , type radiation, etc., requirements. Study the need for shielding to afford protection. Take into account any special conditions or requirements. Using this derived information, the problem of constructing a specific tabulation is simple. Much useful information will be found in the literature (7-79) and the journals in the field. For instance, Nucleonics in June of 1955 contains a classification of beta emitters arranged by energy and half life and in February 1958 a table of radionuclides arranged by gamma-ray energy. Applications of Radioisotopes. First let us take a look at types of uses. The field of chemistry is replete with excellent examples, both in basic and applied areas. Labeling techniques and their utiiiation for the unraveling of complex reaction mechanisms and the study of rates and analytical applications are well known and have been used for some time. Their increased application is a foregone conclusion to be catalyzed primarily by increased availability and reduced price. Many of the things that can be accomplished by use of radioisotopes, the elucidation of photosynthesis as an example, both in and out of the chemical field, would be prohibitively difficult or time consuming by other methods. Willard Libby's estimate of industrial savings is cited as an indication of the opportunity which exists here. The value of the field of radioisotope uses to the chemical industry can scarcely be overemphasized ; remember the uses, even here, are mainly in the future. In spite of what has already been done, we have hardly scratched the surface. I t isn't difficult to find an application where radioisotopes fit beautifully. Quite the reverse, it is almost difficult to find one where they will not. Many of the applications are very well known-
tracers in processing and flow problems, static elimination, wear in frictional and flow studies, liquid level indicators, and thickness gages. But how about things like counterfeiting, identification, and surveying. Libby suggests spotting bills with an innocuous quantity of radioisotope; this would make counterfeiting difficult. O n the other hand bills could be made from paper derived from coal, a good source of nonradioactive carbon; normal paper would be immediately detectable. Survey stakes containing a small amount of Cow would be detectable through a foot or two of soil for years. Plants and animals can be made radioactive by growing them in the proper environment. Deterioration of paper could be studied very nicely using paper made from plants grown in an atmosphere containing radiocarbon, C14, as carbon dioxide. Insects like cockroaches can be labeled with P32 by injection and for some insects radioactive adults obtained by adding the isotope to the larval environment (water). Mosquitoes studied in this way traveled mainly where air currents take them. A great deal has been learned about the nature of the stratosphere and the troposphere and the motion of air masses on the basis of isotopes generated by cosmic rays; think what we could learn by use of isotopes made for the job and placed to yield the information desired! As Libby was moved to say, certainly ''. seldom in history has such a wealth of opportunity existed for technological development to improve human welfare." Radioisotopes also have many possible uses involving substantial amounts of energy or power or activity. For instance, units have been described to power satelites or harbor bouys (73) and units to provide space heat, propulsive power or for conversion of heat to electricity are readily visualizable. In 1353, Lenihan (74) cited a Stanford Research Institute study which suggests the following industrial uses for radioisotopes:
.
I
Phosphor activators for luminous paints. Wide spread use in road signs would require tens of thousands of curies per year. Static elimination-potential market in the thousands of curies per year. Starters for fluorescent lamps and other discharge devices-a few hundred curies per year. Industrial radiography-100,000 curies per year. Sterilization of food-I00 curies per pound of material processed per day. The curie which was based on the estimated activity of a gram of radium-now defined as the quantity of any radioactive species decaying at the rate of VOL. SI, NO. 10
OCTOBER 1959
1243
3.7 x 10‘O disintegrations per secondis a small unit from a weight standpoint. (The mass of an isotope is related to the rate of disintegration by the folloirinq equation : Mass per curie = ___l,13‘4;?lo,3
gram)
Thus, the five significant uses just cited do not involve very large amounts of material and do not represent an availability problem. Material availability would, however, seriously limit possibilities in the po\rer field of application. I t is important, therefore, to knoiv something about prospects for supply of radioactive materials. Today the most irnportant source of radionuclides are the fission products from nuclear reactors. An excellent approach to availability is through the nuclear power program. Availability of Radioactive Materials. T h e fission products which are obtained by the operation of power reactors? if not processed and used, must be stored in underground storage facilities, an expense, or must be disposed of, creating a nasty disposal problem. I t might be well if the AEC were to conduct a vigorous campaign to acquaint industry with the isotopes available and the methods for their processing to produce useful materials, and then to give them away or sell them “dirt cheap.” Such a
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procedure, considering the potential value of the materials in question, would help immensely in solving the problem of introducing radioactive materials to industry, in approaching cost reduction, and in developing a healthy activity in the field of radionuclide applications. Based on recent projections of U. S. and free world nuclear electrical installed power ( 7 , 2, 75), the ball park figures depicted (at left) are indicative of the installed electrical power trend. If we assume 2570 efficiency in the generation of the electrical pow’er, and use the ratio between reactor heat power and fission product power applying for 100 days of reactor operation and 60 days elapsed from rcmoval of the fission products to their application as polver sources, fission product power may be obtained in horsepower by multiplying the figures in megaivatts by 4 (25% efficiency) times 5 x 10Y4 (77), or 2 X times 1500 (rough) to convert million electron volts to horsepower-total factor 3. ‘These are pretty respectable figures for power, but it is clear that isotopes, even in the time period covered, will not represent a source of poLver for general large scale uses like the heating of houses or the propulsion of automobiles. They do represent excellent power sources for special applications, ho\rever, because of their desirable characteristics-especially if the more attractive ones are selected. Furthermore, they offer a tremendous range of specific powers and endurances. They may for some uses prove so attractive that it \vi11 be desirable to consider ways in which more can be made availableby speeding up our plans for installation of nuclear poxer on the one hand, or by planned manufacture of various isotopes on the other. Radioisotope power units may be attractive as processing poirer units, and certainly they have very interesting features for long term use in special circumstariceswhere it is desired to pay little attention to the power unit, in remote, inaccessible locations. Again polonium Lvith its easily shielded and utilized alphas and practically no gammas to worry about from the protection standpoint, springs immediately to mind. Materials like this will certainly warrant a careful study; their manufacture may \vel1 be tvorrh the head- and heartaches associated with the problems that must be solved. Formulas for Radioactive Decay. I n rewriting Equations 1 and 5, the latter with activity d.V/dt replaced by the symbol -4, we have
For mixtures of independently decaying activities, the observed total activity is
INDUSTRIAL AND ENGINEERING CHEMISTRY
the sum of the two separate activities, d = AI :12, similarly for n species. T o follow the growth of a radioactive daughter (subscript 2) formed in the decay of its parent (subscript 1 ) the
+
following equation applies:
Another variation which is met in the general decay scheme is rhe branching decay Ivhere the parent decays in t\vo (or more) w a y to produce two daughters (subscripts 1 and 2). IJI this case: the t\vo partial decay constants XI and A:, must be considered. Here substance 1 is formed at the ratr A,.Yp ( p refers to the parent) but the parent is exhausted at the rate ( A I A?).\-,,. I n computing the half life of the parcnt, remember that the rate of exhaustion of the parent is in the definition, so that t 1 1 r = 0.633, ( X I X2). The parent has of course only one half life.
+
+
literature Cited (1 ) Atomic Industrial Forum. ‘..I Growth Survey of the Atomic Industry:,“February 1958. . .. ( 2 ) .ltomic Industrial Forum .\leino 5 S o . 10: 9 (1958). ( 3 ) Bethe, H. A , . hforrison, P., ..Elemen~
tary Nuclear Theory,” 2nd ed., \Viley, New l-ork, 1956. (4) . . Blatt, J. hl.. LVrisskopf, V. F.. ”’I‘hcoretical ‘ Nuclear Physics,” \Vilcy, Kcwr 1
.
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