G. VOLKOFF The University of British Columbia, Vancouver, B1it:sh Columbia
IT
IS often stated, and quite correctly, that the difference between the liberation of energy by chemical reactions, such as the combustion of coal or the recent disastrous explosion of ammonium nitrate, and by nuclear reactions, such as take place in the sun or in the atomic bomb, is that in the former case we deal merely with an intramolecular rearrangement of atoms, "the smallest building blocks of matter," without changing their identity, while in the latter case the identity of the atoms themselves is profoundly affected, this change of one atomic species into another, e. g., hydrogen into helium, or uranium into krypton and barium, being contrary 40 the principles of conventional chemistry. This point of view, based on the traditional chemical concept of atoms as the 'ismallest indivisible building blocks of matter," tends t o emphasize the difference between chemical and nuclear reactions. However, an alterwtive point of view, based on our present knowledge of the internal structure of the no longer "indivisible" atom, is possible, which tends to emphasize the similarity rather than the difference between chemical and nuclear reactions. This % d lbe the point of view adopted and elaborated in the present discussion of the fundamentals of nuclear energy. The Nuclear Model of the Atom. As chemists you are familiar with the Bohr-Rutherford nuclear model of the atom. You will recall that atoms have diameters of about 10+ cm., and ape composed of pne or more electrons surounding a central, small (about cm. in diameter), positively charged nucleus. The number and arrangement of the electrons in the atom of a given chemical element, and consequently the chemical properties of that element, are uniquely determined by the amount Ze of positive charge carried by the nucleus, where the integer Z is the atomic number of the element in question and e is the magnitude of the electronic charge. The nucleus carries practically all the mass associated with an atom. The existence in nature of several stable isotopes of many of the elements (i.e., atoms with the same value of Z, and therefore identical chemical properties but of different mass), and the possibility of artificial production of additional unstable radioactive isotopes, indicates that the mass which a nucleus of atomic number Z may have is not unique. Altogether over 750 stable and radioactive isotones of 96 different chemi-
cal elements are now known,2 an average of about 8 isotopes per element. The isotopic mass M is defined as the ratio of the exact mass of the neutral atom (iucluding the extra-nuclear electrons as well as the nucleus) of any isotope to one-sixteenth of the mass of the abundant stable isotope of oxygen (O"), whose isotopic mass is taken to be exactly 16.0000 by definition. I n all cases where it has been accurately measured (usually with a mass-spectrograph) the isotopic mass M of both stable and radioactive isotopes is very nearly an integer (cf. examples in Table 1). The integer closest to M is usually denoted by A and is called the isotopic mass number. Thus for our purposes any nucleus may be characterized by the three numbers Z, A , and M. The Proton-Neutron Structure of the Nucleus. As long as experimental techniques for probing the internal structure of nuclei and causing nuclear transmutations were not available, the point of view that atoms represent the immutable fundamental building blocks of matter was justified. However, experimental evidence accumulated during the last thirty years indicates that more than 750 different stable an&-radioactive nuclei now known are themselves complex structures consisting of various combinations of only two fundamental particles-the proton and the neutron, collectively known as nucleons. The proton is the nucleus of the ordinary H atom and is characterized by A = 1, Z = 1, M,= 1.00812. The neutron does n& normally exist in nature in large numbers in the free state, but is found in combination with other nucleons in all nuclei now known except that of ordinary hydrogen. I t is the uncharged counterpart of the proton, having the same small dimensions and a slightly larger mass than the proton. It is characterized by A = 1, Z = 0, M , = 1.00893. According to present views on nuclear structure there are no electrons inside the nucleus. The atomic mass number A of the nucleus simply represents the total number of nucleons in it, of which Z are protons to give the correct charge, and the balance N = A-Z are neutrons. These A nucleons are densely packed together and the volume of a nucleus is experimentally found to be proportional to A , or its radius to A '" . Analogy Between Molecular and Nuc'ear Reactions.
'CORK, J. M., "Radioactivity and Nuclear Physics," Van Nostrand, New York, 1947, pp. 273-294. sored by the Chemical Institute of Canada and the National Plutonium Project Report, J. Am. Chem. Soc., 68, 2411-2442 Research Council of Canada at McMaster University, Hamilton, (1946). Ontario, May 15-17, 1947. SEABORG, G. T., Rev. M o d e n Phya., 1 6 . 1 3 2 (1944). 538
' Presented before the Conferenoe on Nuclear Chemistry spon-
NOVEMBER, 1947
539
TABLE 1 Sample Data on Isotopes Isotope
Desiyalia n
A Number of nucleons 1
Z Number of protons 0
N =A
-Z
Number of neutrons 1
M Isotopic mass (where known) 1 nnnan
The relation of nuclei to nucleons is similar to the relation of molecules to atoms in a rather simple kind of "molecular chemistry" which deals with only two "atomic speciesv-protons and neutrons which we shall denote by p and n, respect,ively. Just as not all possible combinations of H and C atoms lead to actually observed molecules, so not all possible combinations of nucleons lead to actually observed nuclei. H2, C2. CH, C2H2,CHa, C I H ~C2Hs , are combinations of H and C actually observed in the chemical or spectroscopic laboratory, while other arbitrary combinations of C and H, such as C2H, CH2, CaH, do not occur. In our new "chemistry" ]H2, ,Hs, 2He3,2He4, sLia, 6C'2,etc. (whose nuclei in the notation of L'molecular cheniistry" might be respectively represented by pn, p%, pzn, p2n2,p3na, p m , etc.), are experimentally observed, while the di-neutron, Z H ~~He5, ~ , 3LiS(i.e.) %, pl, pzns,pa%, have not been observed. Just as in ordinary molecular reactions heat may be evolved either by the combination of atoms or simple molecules to form more complex ones, or alternatively by the breakdown of complex molecules into a number of simpler components, so in nuclear reactions both alternatives are also possible. Energy may be liberated by the union of simple components into complex ones, or by the breakdown of complex structures. Neutron capture is an example of the former type of reaction and is analogous to ordinary oxidation. Uranium fission is an example of the latter type and is analogous to the breakdown of ammonium nitrate. We write below the formulas for neutron capture by a proton and by a deuteron, and for one of the many possible modes of uranium fission in the standard notation used in nuclear physics. We then rewrite (in brackets) the same reac-
E Binding energy
E/A
(F)
Binding energy per nucleon
(TI
YoAbundance of stable and aetisily o j unstable isotopes
tions in the form which, although never used in practice, is nevertheless useful for our present purpose of bringing out the analogy with ordinary molecular reactions. We also write down the analogs of these reactions in ordinary chemistry for purposes of comparison. +
---
H9
H2 +
+ +
--
H3 U2a:2
Ba,,,
+
KrsD+ 2n
-+
dpn n pm1" [ p a r r+pssnas p8snbs+ 2n] C '/*On CO CO '/sor C0z NH,N08 2HsO NrO We thus see that if we regard protons and neutrons rather than atoms, as the fundamental entities in nuclear reactions, then the three nuclear reactions used as illustrations ahove represent intra-nuclear rearrangements of nucleons strongly reminiscent of the intramolecular rearrangement of atoms in ordinxy chemical reactions. In both cases the number and nature of t,he fundamental building blocks remain unchanged, for they are merely regrouped. Heat of Reaction. The above equations do not yet tell the full story about the reactions, for no mention has been made of the amount of energy liberated. In ordinary chemistry the energy released in the complete oxidation of a single carbon atom is very small. The reaction as observed in the laboratory involves, even in microanalytic techniques, billions of billions of individual processes symbolized by C 02+COz. The heat of reaction is consequently customarily expressed in kilo-calories per mol (1 mol = 6.02 X 1023 molecules). Thus the thermo-chemist gives the heat of the ahove reaction (heat of combustion of charcoal) as 96.5 kilo-calories per mol of C02 formed. If we, nevertheless, want to obtain an expression for the heat of this reaction per individual molecule of C02formed, we introduce a suitable smell unit of energy, the electron [p 4- n
+
pn]
+
+
JOURNAL OF CHEMICAL EDUCATION
volt (1 e.v. = 1.60 X 10-'2 ergs = 3.82 X 10-Pa molecular rearrangement of atoms. We still have kilo-calories), and obtain 4.2 electron-volts per molecule only a very incomplete phenomenological knowledge of Con. The conversion factor is: of these so-called "specifically nuclear" forces between nucleons. Their most striking characteristics are their 1 e.v./molecule = 23.0'kilo-calories/mol. short range and their large magnitude. In nuclear reactions the energy released in an individThus, although'the picture of nucleons rearranging ual process, although still very small, is nevertheless themselves in nuclear reactions with the evolution of usually about a million times larger than the energy energy is qualitatively very similar to that of atoms rereleased in an individual chemical process, so that it grouping themselves in molecular reactions with the becomes possible to observe an individual nuclear reac- evolution of heat, nevertheless, the quantitative results tion in a cloud chamber or with the aid of a Geiger in the two cases with respect to the amount of energy counter. In fact, until December 2, 1942, the date of liberated differ by many orders of magnitude. the first self-sustaining chain reaction a t Chicago, as a Heat of Formation and Binding Energy. The heat of rule only individual nuclear processes could be readily a chemical reaction may either be measured by a direct observed; and their energy evolution measured. The experiment, or it may be calculated from the extensively most intense sources of both natural and .artificial tabulateda values of heats of formation of the individual radioactive substances available to us before this dawn reactants. The heat of formation is defined as the enof the "Atomic Age" gave rise to nuclear reactions oc- ergy released when the given compound is formed from curring a t rates which, in the most favorable cases, were the individual elements in some specified standard not much in excess of some billions of individual proc- state. The standard states in thermo-chemistry are esses per second. This corresponds to the formation of usually selected with the elements not in their atomic the end products of the nuclear reaction a t the rate of form, hut in some normally occurring and easily reprosome micrograms per year, and to the nuclear energy ducible form, e. g., Hz, N2, 01,diamond crystal, etc. liberation a t the rate of a fraction of a watt. Large However, it is easy to recalculate the heats of formation amounts of the stable isotopes of lead which are the end with respect to the individual atoms considered as the products of the natural radioactive series have been standard state, and this is done in the examples of Table accumulated during the life history of the earth. Mi- 2 to facilitate comparison with the corresponding nunute, yet visible and weighable, microgram amounts of clear quantity-the nuclear hindimg energy-listed in plutonium had been produced by cyclotron bombard- the examples of Table 1. ment in the short space of a few years immediately preThe nuclear binding energy E is completely analogous ceding the operation of the first chain-reactors, in time to the chemical heat of formation as redefined above. to play a vital part in the development of plutonium It is defined as the energy that would be required to extraction processes. Nevertheless the liberation of pull the nucleus apart into A individual nucleons (it has nuclear energy a t the rate of a fraction of a watt by the been suggested that "unb'mding" energy is a more above sources was of no interest from the point of view descriptive term) or, conversely, that would be liberated of generation of power. The participation of gram or if a nucleus were formed from the individual nucleons. mole amounts of the reactants in a nuclear reaction The nuclear binding energies listed in Table 1 are seen within a time interval brief enough to lead to the evolu- to be approximately a million times larger than the tion of macroscopic amounts of poker takes place on chemical heats of formation listed in Table 2. earth only in a pile or an atomic bomb. +It is also reAs in chemical reactions, the energy liberated in a sponsible for the energy evolution in the sun and the nuclear reaction may be calculated if the binding enerstars. gies (i. e., the heats of formation) of the reactants and Because of the earlx experimental emphasis on indi- the end products are known. vidual processes it has become customary to give the Binding Energy and Mass-Energy Equivalence. The nuclear "heat of reaction" (which is usually referred to biding energy of a nucleus is somuch greater than the as the Q of the reaction) per individual disintegration heat of formation of a chemical molecule that an effect or transmutation. Thus the "heat of reaction" of which passes completely unnoticed in chemistry shows uranium fission is roughly 200 Mev/atom (Mev is the up very prominently in nuclear reactions. Is the usual abbreviation for million electron volts). Using weight of C02 formed in the reaction C 02-C01 the conversion factor quoted above this becomes 4.6 equal to the sum of the weights of the C and the O2 billion kilo-calories/mol, or, expressing this in more that went into it? The usual answer is "yes." The convenient large scale units, 220,000 kilowatt-days/- correct answer is "within experimental error, yes, but mol. theoretically, no." For, according to Einstein, energy Why are the heats of nuclear reactions millions of has mass, and if a certain amount of energy is given off times larger than those of ordinary chemical reactions? when C02 is formed then a certain small amount of This is presumably because of the forces holding the mass will be missing also. The familiar E = me2 nucleons together are entirely different in nature and magnitude from the Coulomb forces which, subject to a Brc~qwsn~ F., R., AND F. D. ROSSINI,'The Thermocertain quantum mechanical restrictions, determine chemistry of the Chemical Substmces," Reinhold Publishing molecular structure and the energy released in inti-% Corporation, New York, 1936.
+
NOVEMBER, 1947
541
S a m p l e Data o n Chemical C o m p o u n d s Substance and state
0 (P&~~PUS) N H C
0 2
"
" (W;OUS)
N2
H2 " C (diamond) C (chsrcoal)
co ( COz
~ ~ 0 ~ s )
NH,NOa (solid) NnO (gaseous) H10
Heat of formation as usually defined in theno-chemistry (kilo-calories/mol) -59.10 -85.1 -51.90 -170.0 0.000 0.000 0.000 0.000 -2.0 26.84 94.45
Heat of formation redef ned with respect to free a t o m (kilo-calmies/mol) (e.v./molecule) 0.000 0.000 0.000 0.000
Sample heats of reaetia
0 0 0 0
118.2 170.2 103.8 170.0
5.139 7.400 4.513 7.391
168.0 255.9 382.6
7.304 11.13 16.64
C
-
+ On
Con (combustion of charcoal)
+
382.6 - (168.0 118.2) = 96.4 kg.-oal./ mol = 4 . 2 e.v./molecule
87.13 57.801 -19.65
equation of Einstein stated numerically says that the quantity of energy whose mass is one gram is 9 X 10" ergs = 2.15 X 10'0 kilo-calories = 10%kilowatt-days, or that 1 atomic massnnit = 931 Mev of energy. Thus the total rest-mass of a C02 molecule is equivalent to 44 X 931 Mev = 4.1 X 10'0 e.v. so that a loss of mass corresponding to the heat of formation of only 4.2 e.v. passes by completely unnoticed in ordinary chemistry. This loss of rest-mass amounts to only one part in 10'0, i. e., 0.0001 microgram per gram of C02 as compared with the original C and 0 2 . However, in nuclear reactions the usual binding energy of several million electron volts per nucleus forms an appreciable fraction (of the order of several parts in a thousand) of the total rest-mass of a nucleus, and the amount of energy theoretically available for any particular nuclear reaction may be calculated with the aid of Einstein's equation from th$ difference between the accurately known isotopic masses (e. g., as determined by a mass-spectrograph) of the reactants and the end products. In many cases the "heat of reaction" energy & released in a nuclear reaction may itself be directly measured, and thus a direct experimental verification of Emstein's equation in the form & = (Am)c2may be obtained, where Am is the net loss in rest-mass in the reaction. The fission of I gram of uranium results in approximately 989 mg. of fission products and 10 mg. of neutrons. About one milligram of mass disappears and is transformed into about 1000 kilowatt-days of kinetic energy of fission products, which is immediately converted into heat. There is a subsequent further small loss of mass (about an eighth of a milligram) corresponding to the gradual liberation of over a hundred kilowatt-days of energy in the form of fl and y radiation of the decaying fission products and of the radioactive isotopes formed by neutron capture. We note that although the equation E = me2tells us how much energy will be released in any particular
nuclear reaction for which the loss of mass is known, it tells us nothing a t all about how this energy was stored in the nucleus, nor about the mechanism of its release. This equation offersno explanation as to why the mass of a uranium atom should be bigger than the mass of the fission products and neutrons produced in fission by about one part in a thousand rather than by some other fraction. However, once the loss of mass has been determined experimentally this equation enables us to calculate the amount of energy released without knowing any details of the mechanism of release. The equation is simply a bookkeeper's statement of the fact that energy, whatever its form, has a definite amount of mass associated G t h it, and the loss of energy can be detected by a loss of mass and vice versa. Beta and Gamma Activity. The decay of radioactive isotopes with the emission of 9, pai-ticles (fast moving negative or positive electrons) referred to above is a form of nuclear reaction that does not have an analog in molecular chemistry. Here, even when we consider protons and neutrons as the fundamental entities, we are concerned not merely with a regrouping of these elementary building blocks but-with a transmutation of one of the fundamental entities into the other. Thus the spontaneous radioactive disintegration of the A P nucleus: ,rAl" ---r ,8P
which may also be written as: ptanlr dpan14
+ e-
+ e-
consists of one of the neutrons in the Al" nucleus spontaneously transforming itself into a proton by creating and ejecting from the nucleus a negative electron. The experimentally observed liberation of energy in this process is an indication that the "speci6cally nuclear'' forces between nucleons must be such that a fourteenth proton is capable of entering into a more intimate union with thirteen protons and fourteen neutrons than a fifteenth neutron.
JOURNAL OF CHEMICAL EDUCATION
The emission of y-rays by a nucleus is analogous to the familiar emission of quanta of electromagnetic radiation in the visible or infrared frequency range by molecules going from an excited to the ground state. Both cases are concerned with a rearrangement of the elementary constituents from a less stable to a more stable configuration without a change in the number or in the nature of the constituents. The energy released in such B and 7 transformations may be directly measured and also may be calculated from the net change in mass if the isotopic masses are known. Usually this energy amounts to a few Mev or less per nucleus, or to some hundred kilowatt-days per gram of fission products. The Stable Isotopes and Deviations from Stability. If the approximately 270 stable isotopes existing in nature are plotted (cj. Figure 1) as points on a plane on which the number of protons Z and the number of neutrons N = A - Z (or, alternatively, the total number of nucleons A = N Z and the number of L'excess"neutrons I = N - Z = A - 22) are chosen as rectangular coordinates, they are found to lie in a narrow band vhich starts out dong the line N = Z (i. e., I = 0) near the origin, and curves away from this line in the direct,ion of an excess number of neutrons for heavier nuclei. I t is believed that if only the "purely nuclear" short range forces acted between nucleons their effect would be to make N = Z hold for stable nuclei of all values of A. The progressive deviation from this condition for increasing A is due to the progressively increasing effect of the long range Coulomb electrostatic mutual repulsion of the protons in the nucleus. Compared to the effect of the "purely nuclear" forces this repulsion is small for small Z but increases with Z2 and eventually plays an important role in determining the stability of nuclei. Some four hundred and fifty additional radioactive isotopes with values of N and Z lying on either side of this narrow band have been produced Qther by bombardment of stable isotopes with various nuclear projectiles or by fission of uranium. Any nucleus which lies outside the band of stability is found to undergo a series of B transformations during which A = N Z remains constant, while both N and Z change, until the nucleus reaches the region of stability. For a nucleus with odd A this stable combination of protons and neutrons is almost always unique (with only three exceptions). For a nucleus with even A there are frequently two, and occasionally three, consecutive stable isobars of even Z and even N (i.e . , nuclei with the same A , but diffekent Z) separated by unstable isobars of odd Z and odd N with higher energy than either of their two even-even neighbors. Only four stable nuclei of odd Z-odd N are known. Since in the naturally occurring isotopes of heavy elements, such as uranium, the neutron-proton ratio is higher than in the stable isotopes of elements of medium atomic weight, the fragments of the uranium nucleus formed in fission will usually have too many neutrons compared with the stable isobars of the same A , and
will consequently undergo a series of P disintegrations by emitting negative electrons, thus giving rise to a chain of radioactive fission products. Dependewe of Binding Energy on A. The binding energy E of stable nuclei lying in the narrow region of stability along the curve of Figure 1may be calculated
+
+
J Fiw..
1.
The Neutron-Proton Dirrtrib9tiii a-Asti.. Nuclsi +
in Stable and
with the aid of Einstein's equation from their measured isotopic masses. If E is divided by A and the resultant values, E / A , of the average binding energy per nucleon are plotted for stable nuclei as a function of A , a curve represent.ed schematically in Figure 2 is obtained. The radioactive nuclei lying on either side of the band of stability of Figure 1 have less binding energy per nucleon than a stable nucleus of the same value of A , and by undergoing @ transformations they tend t o achieve that particular combination of protons and neutrons in which the value of E / A is a maximum. The curve in Figure 2 represents these maximum values of E / A plotted as a function of A. The phenomena responsible for the more prominent features of this curve are now understood at least qualitatively, but for the sake of brevity we shall treat this curve merely as an experimental result and shall not attempt to give any theoretical interpretation of its various features beyond saying: that the drov from 8.6 t o 7.5 Mev uer nucleon in tlhe case of heavv nuclei is due to the mutual Coulomb repulsion of the pi-otons in the nucleus.
NOVEMBER, 1947
543
"drop" is greater than the decrease in the Coulomb repulsion energy,due to the increase in the average distance between the protons, with the result that a potential harrier has t o be overcome before the nucleus will undergo fission. A measure of the height of this fission barrier, and therefore of the "activation energy" required to overcome it, may be obtained by comparing the decrease in the Coulomb energy which is proportional t o Z2e2/R, i. e., to Z2/A1'3, where the nuclear radius R is assumed propbrtional to with the increment in the "surface tension" energy which is proportional to R2,i. e., to A2'3, as the nucleus is slightly deformed from the spherical state. The ratio of these two Lenergies, and therefore the parameter Z2/A, may be taken as the measure of the ease with which a nucleus 50 1W 150 200 250 Numb.= of Nucleon. A may be made to undergo fission. The activation energy Fig".. a. Dependence of Binding Energy per Nuc1o.n on 1sotopi. needed to cause the fission of a uranium nucleus turns Mms. Number out to he only a f e v Mev, and may be communicated to the uranium nucleus either in the form of a y-ray quanPossibilities for Energy Release by Regrouping the tum (photo-fission), or in the form of the kinetic and Nucleons in a Nucleus. Examination of the curve in binding energy supplied by a neutron captured by the Figure 2 shows that the binding energy per nucleon mill uranium nucleus. increase and energy will be released, i. e., the reaction Fission by charged particles has also been observed, will be exoergic, either if lightest nuclei combine into but of course in this case there is the additional Coulomb heavier ones (e. g., four protons into an or-particle, or a harrier to he overcome. The height of the fission barneutron or a proton with most light or medium nuclei) rier, and therefore the value of the activation energy reor if the heaviest ones (e. g., U, Bi, Pb) break dovvn into quired for fission, is a rapidly varying function of Z2/A, nuclei of medium weight. so that although from the binding energy of a lead or Why then do we not see such strongly exoergic 'eac- even a still lighter nucleus, me can definitely calculate tions taking place in nature spontaneously? For one that fission is energetically possible, nevertheless no of the same two reasons that many exothermic chemical fission of lead has been observed4even when bombarded reactions are not observed in nature: either because with 100 Mev y-ray quanta from the General Electric they can take place so readily that there are no reactants betatron. Thecharacteristic'difference of the UZS8 and existing in nature in the free state, or else because a UZa5 isotopes with respect to fission by thermal ncufairly high energy of activation is required to take the trons is associated not with a difference in the height of system over a potential barrier separating the initial the fission barrier but with a characteristic difference in from the final state. the binding energy of the incoming neutron in an even As an example of the former, pure phosphorus oxi- 2-even N, as compared with an e+en Z-odd N type of dizes very readily and catches on fire vgry easily. Yet nucleus. , the discovery of fire by man was not aneasy matter, for Thus, in order to observe any of the theoretically because of its great chemical activity phosphorus does possible exoergic nuclear reactions me must have on not exist in nature in the free state. Likewise neutrons hand one of three conditions: combine with most nuclei very readily, and just for that (a) free neutrons with which to irradiate nuclei. reason do not exist in nature in the free state. (b) high voltage devices, etellar temperatures, or On the other hand, before a proton mill get close natural radioactive sources to provide protons, deuenough to a nucleus to feel the attractive effect of the terons, or a particles of energy sufficient t o overcome short range "purely nuclear" forces it has t o overcome the Coulomb barrier of the lighter nuclei. quite a high potential barrier due to the Coulomb repul( e ) a supply of free neutrons, energetic +-rays or sion of the positive charge on the nucleus. This energy charged particles to provide the necessary activation may be supplied to a proton either by accelerating it in energy for the fission of heavy nuclei. the laboratory with a high voltage device such as a Van Before the discovery of fission the only may in which de Graaff generator or a cyclotron, or by subjecting we could obtain free neutrons was to knock them out of hydrogen to a temperature of several million degrees, a.s stable nuclei by energetic charged particles, so that a happens in the interior of the sun. supply of free neutrons was dependent on a supply of Similarly, a heavy nucleus, assumed to he of spherical charged particles. Although with modern devices shape, has to pass through a series of ellipsoidal and energetic charged particles are fairly easy t o produce, dumhell-like shapes before breaking up into two smaller added after submission of menuscript. The author has spheres, in analogy with the splitting of a small liquid beenNote kindly informed by the Editor that the August 15, 1947, drop. For small deformations from the spherkd shape issue of the Ph?,siczl Reoieq will carry a n article announcing the the increase in the "surface tension" energy of such a fission of bismuth, lead, thallium, tantalum, and platinum.
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544
the vast majority of these particles fritter away their energy in ionization of the outer electronic structure of the atoms of the target material and only a very small proportion of them leads to nuclear disintegrations or transmutations. Although these rare events are of great scientific interest they are of no interest from the point of view of releasing energy for power purposes, since much more energy is wasted in accelerating those many projectiles which miss their nuclear targets than is regained from those few tliat make successful hits. If we had to depend on artificially accelerated charged particles t o provide the neutrons with which to cause fission, fission processes would also have remained of scientific interest only and would be observed only on the same small scale on which previously known exoergic nuclear reactions were observed. The fact that macroscopic release of energy from fission is possible depends entirely on the fact that uranium nuclei undergoing fission provide their own neutrons with which further fissions can be triggered off. Rhpuirements for a Chain Reaction. The requirement for a self-maintaining or a divergent chain reaction is very simple: the average number of neutrons produced per fission must be sufficiently large so that after all losses of neutrons by escape from the chain reacting system and by capture of neutrons in the various structural and other nonfissile materials introduced into-the chain reacting system have been taken care of, there is still on the average at least one neutron left to produce
JOURNAL OF CHEMICAL EDUCATION
the next fission. Since the average number of neutrons produced per fission lies somewhere between one and three it is clear that the margin is not great, and that care must he taken not to introduce into the chain reacting system large amounts of material which captures neutrons readily. It is also clear that control of the chain reaction by the addition of strongly neutronabsorbing materials is possible. Possibility of Energy Release by the Complete Annihdation of Matter. The exoergic nuclear reactions we have so far discussed consist of a regrouping of the nucleons in a nucleus with an energy release of at most ahout 8 Mev/nucleon, which corresponds to a loss of mass of only slightly under one per cent. Is it not possible that some day a method for converting the entire mass of an atom into energy will he discovered, leading to reactions of the type H -+,Fe -+, or U +, where there is nothing on the right hand side of the arrow except energy? It is certainly pdssihle in principle, but a t the moment we have no clues-just as before 1939 we had no clues to uranium fission. Or perhaps the clues are there and we are m u f i g them, just as clues to uranium fission were muffed during the years 193P39. I t may be that au intensive study of the various phenomena of cosmic rays, or of the reactions yet t o he discovered with the new powerful cyclotrons, betatrons, and synchrotrons, will provide those clues .which will lead to discoveries that will even further complicate our present day international problems.
