M. EBERT AND J. W. BOAG 203 THE EFFECT OF THE ENERGY OF THE IONIZING ELECTRON ON THE YIELD IN IRRADIATED AQUEOUS SYSTEMS BY T. J. HARDWICK Chemistry Branch, National Research Council of Canada, Chalk River, Ontario Received 29th January, 1952 A study of the indirect action of X- and y-radiation on aqueous ferrous and ceric sulphates shows that the reaction yield varies with the initial energy of the ionizing electrons. This effect can be explained on the basis of existing theories of the primary action of ionizing radiation in water. The interpretation in terms of the theory advanced by Gray permits the calculation of the reaction probabilities of H + H - t H z HO + OH -+ H202 and as a function of the instantaneous electron energy. It has been established for some time that the chemical effects produced by K-particles on water and aqueous systems differ quantitatively, if not qualitatively, from those produced by y-rays, hard X-rays or fast electrons.This effect has been recognized and partly explained on the basis of a difference in the specific ionization density of a-particles and electrons.1 However, in systems where electrons are the ultimate ionizing particles, e.g. irradiation with X-rays, y-rays or with dissolved beta-emitting nuclides, most comparisons of results have ignored the energy of the ionizing electrons, with consequent unexplainable anomalies in the results. ANOMALIES IN THE IRRADIATION OF CERIC SULPHATE.-AS a case in point, con- sider the investigations on the reduction of ceric sulphate in 0.8 N sulphuric acid solutions by light particle radiation.Clark and Coe 2 irradiated ceric sulphate in air-saturated sulphuric acid solutions with 50 kVp X-rays * from both tungsten * kVp is the kilovoltage peak of the X-ray power supply; keV as applied here to X-rays is the mean energy of the X-rays absorbed by the solution.204 YIELD I N IRRADIATED AQUEOUS SYSTEMS and copper targets. The yield in 0.8 N sulphuric acid, expressed in terms of G (ions reduced per 100 eV absorbed) was 5-5. Boiling the solution previous to irradiation (i.e. removing a large fraction of dissolved oxygen) had no marked effect on the yield. Haissinsky 3 irradiated ceric sulphate in 0-8 N sulphuric acid with 14 keV X-rays * from a molybdenum target. In air-free solution G = 5.2 ; in oxygenated solutions G increased to 6.2; the addition of hydrogen decreased the value of G to 4.5.With radon cc-particles plus active deposit in a substantially air-free system, G was 3.5. The author has investigated the reduction of ceric ion in 0-8 N sulphuric acid solutions by C060 y-rays.4 The yields in air-free and air-saturated solution were the same (G = 3.2); the addition of hydrogen gas to air-free solutions increased G to 6.2. The amount of hydrogen produced from air-free solutions was less than 5 % of the oxygen produced. In preliminary experiments made by the author, in which tritium water was added to the air- saturated ceric ion solution, G = 5.5 & 0.5. Although analysis of the gaseous products was not made in this case, Challenger and Rollefson 5 in a similar experi- ment report the evolution of hydrogen gas.I I I I 1 1 1 1 I I 1 1 1 1 1 1 20- - _ ~ _ _ _ FIG. 1.-The yield in the ferrous and ceric sulphate systems as a function of initial energy of the ionizing electron. The only apparent reason for these anomalies is that the energy of the ionizing electrons was different. The average energy of electrons produced by the ab- sorption of C060 y-rays in water can be estimated; the average P-energy per disintegration of tritium has been measured.6.7 However, with X-ray irradiation, particularly where an unfiltered, full-wave rectified power supply is used, the average energy of electrons resulting from photon absorption in the solution is not easily determined. Most investigators fail to give sufficient experimental details for an estimate of the mean electron energy to be made.This latter point is important. An X-ray tube with a tungsten target operating with an unfiltered full-wave rectified power supply (typical of most commercial models) at a peak voltage of 150 kV has been found to produce electrons in water of 0.5 cm depth with an average energy from 11 to 13 keV. The same machine produces the same average electron energy when operated at 30 kV peak. EFFECT OF INITIAL ELECTRON ENERGY ON THE YIELD IN FERROUS AND CERIC SULPHATE soLuTIoNs.-There are only two systems, the reduction of ceric ion in 0.8 N sulphuric acid and the oxidation of ferrous ion in air-saturated 0-8 NT. J . HARDWICK 205 sulphuric acid, where sufficient experimental work has been done to examine the effect of the energy of the ionizing electron on the reaction.The yields G for the two systems have been plotted as a function of the average initial energy of the ionizing electrons in fig. 1. The numbers on the graph refer to the source of the information which is reported in table 1. For no. 5, 6, 13 and 14, all X-ray irradiations, arbitrary values of the average initial electron energy had to be estimated from a consideration of the irradiation technique described. However, much wider limits of error are indicated by the use of areas, rather than points. The discrepancies between point no. 9 and others (no. 1, 2, 3) will be discussed by N. Miller. The data represented by dotted circles were obtained by comparing the rate of reaction for the ferrous and ceric systems under identical conditions of irradi- ation.The source used was an X-ray tube with a tungsten target, using an unfiltered, full-wave rectified power supply operated at various peak voltages. The average initial energy of the electrons produced in the sample was obtained by a crude analysis of the spectrum and a calculation of the stopping effect of filters and the sample. If we assume the interpolation of the ferrous yields in fig. 1 to be reasonable, then the yields obtained with the ceric system are those shown by the dotted circles (no. 16-19). TABLE EF EFFECT OF INITIAL ELECTRON ENERGY ON THE YIELD IN THE FERROUS AND CERIC ION SYSTEMS point 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16-19 average initial yield. source of ionizing e ~ ~ ~ ~ ~ f Ions changed remarks electrons, p~;~,boPb,edv electrons keV.Oxidation of Fez+ in air-saturated 0.8 N sulphuric acid P32 betas 697 21.1 dissolved as P32043- Co60 y -630 20.4 ion chamber comparison Ra Y -450 20.3 ion chamber comparison S35 betas 45.8 20.2 dissolved as S35042- 250 kVp X-rays 25-30 20.3 ion chamber comparison 220 kVp X-rays 20-25 19.5 ion chamber comparison H3 betas 5.69 15.6 dissolved as HTO H3 betas 5.69 15.4 dissolved as HTO Co60 y 630 15.7 calorimetric measurement Reduction of Ce4-' in air-saturated 0.8 N sulphuric acid Co60 y -630 3.2 comparison with Fez+ Ra Y -450 3.2 comparison with Fez+ S35 betas 45.8 3.2 dissolved as S35042- 50 kVp X-ray - 14 5.5 ion chamber comparison 14 kV X-ray 8-1 1 5-2 ion chamber comparison X-rays (see text) comparison with Fez+ H3 betas 5.69 5.5 dissolved as HTO references author 8 author 9 10 author 8 11 12 author 13 14 author 4 author 4 author 8 2 3 author author The data plotted in fig.1 show that as the initial energy of the ionizing electron EO decreases below about 50 keV, the yield in the ferrous system decreases, while that in the ceric system inceases. These results may be explained by the free radical distribution at the end of electron tracks. EXISTING THEORIES OF RADICAL DIsTRIBuTIoN.-Many lines of investigation. both theoretical and experimental, have contributed to an explanation of the events occurring as an ionizing particle is slowed to rest in an absorbing medium, Allen 1 has explained the effects of different types of radiation on water on the basis of the ion (and subsequent free radical) density along the particle tracks. With high energy electrons (regions of low ion density) recombination of unlike radicals to form water, or reaction with solutes, will be the chief fate of the radicals.Regions of high ion density occur only at the end of the tracks (hot spots). In such regions radical-radical reactions occur to form hydrogen gas and hydrogen206 YIELD I N IRRADIATED AQUEOUS SYSTEMS peroxide. The effect on solutes under these conditions will not be as great as for low ion density. The picture of the ionic distribution in ionizing particle tracks has been developed by Lea15 and Gray16 from a consideration of the physics of the slowing down of charged particles in water. Assuming that the initial distribution of free radicals will correspond to that of the parent ions, probabilities of inter- action between radicals can be calculated for various energies of ionizing particles.This calculation is not very precise, for the diffusion laws for the migration of free radicals contain several arbitrary constants. Interradical reactions interfere with normal migration. The reaction of radicals with solute molecules occurs under a condition where the solute molecules are uniformly distributed, but the radicals are in a large concentration gradient. In practice the agreement between these two approaches has been observed qualitatively. However, no data has heretofore existed which would link these two approaches quantitatively. From the data in fig. 1, it is possible to determine the extent to which the reactions H f H - t H z (1) and HO + OH -+ H202 (2) occur at any particular energy of the ionizing electron.The results have been extended to an explanation of heavy particle irradiation on aqueous systems. In so doing, it is unavoidable that some comparisons and explanations made by other authors be repeated, but as these explanations are now on a quantitative basis such inclusions are made for the sake of completeness. The postulate of significant energy " bursts " in particle tracks, and the subsequent effect on chemical reactions will be discussed. The formation of radicals from ions has been described in detail elsewhere.ll179 18 However, it is important to note that these radicals are formed in an excited state. Degradation to the ground state will take place by reaction, by photon emission, or by deactivating collisions with the water molecules.In regions of high ion density the average kinetic energy of the water molecules in and surrounding the track will be greatly increased, making possible reactions not otherwise occurring at ordinary temperatures. REACTIONS BETWEEN LIKE RADICALS.-The reaction H + H + H 2 (1) will take place on collision, the excess energy being removed by the medium. Hydroxyl radicals may react in two ways : OH + OH + H202 (2) OH + OH -+ H20 + 0 (3) From considerations of dipole attraction, reaction (3) is more probable between radicals in thermal equilibrium with the solvent,lg and there is evidence that this is the case.4 The activation energy of reaction (2) has been estimated at 5.5 kcall mole.1 The formation of hydrogen peroxide can occur in regions of high free radical density for two reasons: (i) as free radicals are formed in the excited state, the probability of collisions between hydroxyl radicals before both have been de- activated will be greater at high concentrations; (ii) in the region of high ion density the kinetic energy of the solvent molecules is increased to the point where the activation energy is supplied by the solvent.A schematic picture of the OH-OH reaction as a function of energy is shown in fig. 2. At low electron energies (region L) collision between hydroxyl radicals will occur before significant outward migration begins. In the region of high ion density (hot spot) the product will be almost completely hydrogen peroxide.AtT. J. HARDWICK 207 slightly higher electron energies (- 5-10 keV) there is migration from the tracks, but collisions between OH radicals will occur within a short interval of time. There is still sufficient energy available from the medium for hydrogen peroxide forma- tion (region M). Beyond a certain distance from the track there will no longer be sufficient energy available for reaction (2) ; the reaction between two hydroxyl radicals will form water and oxygen (3). When a solute capable of reacting with hydroxyl radicals is present in region L, practically no solute-radical reaction occurs. In regions M and N, solute-radical reactions take place, but in the former there is probably a concentration effect of the solute. Region N is the region of concentration independence.Special mention must be made of dissolved hydrogen gas. In region N the hydroxyl radicals will be converted quantitatively to hydrogen atoms (4) H2 + OH -+ H20 + H which are then free to react with themselves or with any solute. In region M any hydrogen atoms produced by reaction (4) will react with OH radicals because of the relatively high concentration of the latter, the net result being the elimination of two hydroxyl radicals from the system. Y rom cenira / where reachon ( B ) becomes more probable Man T / reochon (A) Lmyy of Iemzihy dectron - FIG. 2.-Schematic representation of the OH-OH reaction at various energies of the ionizing electron. EFFECTS CAUSED BY THE SLOWING OF FAST ELEcTRoNs.-(i) At energies greater than 15 keV.-When the instantaneous energy Ex of the ionizing electron is greater than 15 keV successive radical pairs are formed relatively far apart H20 -+ H + OH.(R) These radicals diffuse out of the tracks and are all available for reaction with solute molecules. In the absence of a solute, recombination of unlike radicals to form water occurs. A portion of the electron energy is released in '' bursts " of several hundred electron volts,l giving a region of high specific energy release. This results in the formation of H2 and H202 directly, either through immediate radical com- bination, or by excitation rearrangement 1 3 ~ 2 0 2H20 -+ H2 + H202. (F) The magnitude of this effect has been measured by Hart, by Hochanadel and by Johnson on a variety of systems.The results are recorded in table 2. Thus, in the tracks of high energy electrons, 20-25 % of the water molecules which de- compose form H2 and H202 directly, the remaining 75-80 % forming free radicals which are free to migrate.208 YIELD IN IRRADIATED AQUEOUS SYSTEMS (ii) At energies less than 15 keV.-As the energy of the ionizing electron is decreased below 15 keV, both the number of energy bursts and the amount of energy released per burst becomes smaller. Any contribution from this source to the overall reaction will not be significant; in the following discussion on the effect of low energy electrons any products from bursts are ignored. As Ex decreases below 15 keV, the initial distribution of the radicals becomes such that the probability of like radicals reacting within the track increases. This will occur first between hydroxyl radicals, because of their higher local con- centrations.For reasons outlined previously the product will be hydrogen peroxide. The reaction of hydrogen atoms to form hydrogen gas within the track becomes significant at Ex < 4 keV. TABLE 2.-EXTENT OF IMMEDIATE HYDROGEN AND HYDROGEN PEROXIDE FORMATION IN FAST ELECTRON TRACKS relative number of water molecules product source of decomposed by ref. measured irradiation reaction system irradiated R F HCOOH in 02-saturated solution H2 COG0 y 0.79 0-21 20 dilute Orfree KBr solution H202 7, 0.75 0.25 14 ferrous ion in air-saturated 0.8 N &So4 H2 ?, 0-78 0.22 14 H202 in KBr and KI in water H2 2 MeV electrons 0.80 0.20 21 This picture of the behaviour of free radicals explains the decrease in yield in the ferrous system at low Eo.The formation of hydrogen peroxide from two hydroxyl radicals will not affect the yield, as in each case reaction with ferrous ion gives the same products. The decrease in yield must be ascribed to the in- creased formation of hydrogen at the end of the tracks. The increase in yield in the ceric system may be explained by the increased formation of hydrogen peroxide at Ex < 15 keV. As neither ceric nor cerous ions react appreciably with hydroxyl radicals, the increase in yield will be due to the increase of hydrogen peroxide formed within the tracks plus that formed near the tracks after outward diffusion has begun (region L and M, fig. 2). At Ex < 4 keV increased hydrogen gas formation will cause a decrease in yield.A maximum in the yield would therefore be expected at low values of Eo. PROBABILITY OF LIKE RADICAL REACTIONS AS A FUNCTION OF &.-In practice one cannot measure the results of an instantaneous radical distribution at a particular Ex, but must measure the sum of all the effects which occur as an electron of initial energy Eo is slowed to rest. This complicates the problem and renders any interpretation of the results less certain. However, from a knowledge of the mechanism and yield of the ferrous oxidation and ceric reduction one can create a picture of the reactions occurring in the radical tracks. The magnitude of the interradical reactions can be calculated from the change in yield measured at different values of Eo.From the data on the ferrous system (curve A, fig. 1) the extent of hydrogen gas formation can be found ; from data on the ceric system (curve B, fig. 1) the hydrogen peroxide production may be calculated. (i) The reaction H + H --f Hz.-The fraction of the hydrogen atoms combining to form hydrogen gas (FH) will increase as the instantaneous energy of the ionizing electron El decreases, (FH = j { E I ) ] . The area under this curve, f(Er)dEr, will be proportional to the decrease in yield found in the air-saturated ferrous oxida- tion at low values of Eo. If, in general, two ferrous ions are oxidized for each J",T . J . HARDWICK 209 H atom formed,* the value of [: f(E)dEI can be calculated (see appendix). J Co Furthermore, from estimates of the initial H distribution in the track, one would not expect hydrogen formation within the track at energies greater than 4 keV ; below this energy FH would increase gradually.Applying these limitations to the value of 1 f(Er)dEr (= 0.70) one obtains curve A in fig. 3. (ii) The reaction HO + OH -+ H202.-The extent of formation of hydrogen peroxide from hydroxyl radicals at low values of EI may be calculated from in- crease in yield in the ceric ion system as EO decreases. The equation FOH = fQ3) will express the fraction interacting as a function of instantaneous electron energy. The area under this curve f(Er)dEI may be calculated from the variation in yield 0 EO 0 s Eo FIG. 3.-Probability of like radical reactions as a function of the instantaneous energy of the ionizing electron.with EO (curve B, fig. 1). Applying the limiting conditions described below, curve B (fig. 3) is obtained. s( f(EI)dEI = 6.0). ) 0 EO There are three limiting conditions to the equation FOH =f(EI). (i) At low Er the formation of hydrogen gas within the tracks causes a de- (ii) The radicals are assumed to have a high probability of interreaction in (iii) Both the hydrogen peroxide formed within the tracks and after the onset This latter process will predominate at higher crease in yield as fewer H atoms will be available for reaction with ceric ion. this region, hence FOH will approach unity. of migration will be measured. * The quantity 2 is the average yield for the two sets of reactions H + 0 2 + HO2 H + 0 2 ++ HO2 H02 + H -+ H202 H+ + HO2 + Fez+ + H202 + Fe3+ j' H202 + 2Fe2+ +- 2Fe3+ + 20H- '(H02 + H02 +- H202 t 0 2 Fe3+ formed ratio -_____ : 3 H used H202 + 2Fe2i.--f 2Fe3-k + 20H- Fe3 formed ratio = 1. H used The use of any other quantity between these limits does not greatly affect the value of210 YIELD I N IRRADIATED AQUEOUS SYSTEMS E,, but as it involves a diffusion mechanism before reaction, the increase in the amount of hydrogen peroxide formed will vary only gradually with EI. The shape of curve B at high El is therefore somewhat uncertain. Although the curves in Fig. 3 follow the restrictions imposed, the loci are somewhat speculative. However, values of G at various EO calculated from the area under the curve (or portion thereof) agree with those obtained from the curves in fig.1. From the shape of curves A and B in fig. 3, one would expect hydrogen gas and hydrogen peroxide to be the products in regions of much higher ion density, for example, in a-particle tracks. When pure water is irradiated with a-particles, hydrogen peroxide and hydrogen gas are formed initialIy in high yield (GH2 = 0.9-2-5).22-25 The formation of oxygen does not occur until a consider- able concentration of hydrogen peroxide has been built up. APPLICATION To OTHER SYSTEMS.-(I) Irradiation of water.-The reactions of water under various types of radiation have been successfully explained by application of Allen’s “ hot-spot ” theory.l.26 When the above results are applied to the irradiation of pure water qualitative agreement is found in all cases. Sufficient experimental data on the reaction of low energy X-rays on pure water are not available for quantitative comparison.(ii) Irradiation of the ceric and ferrous systems with a-particles.-The reactions of solutes in solutions irradiated with a-particles will be mainly those of hydrogen peroxide and hydrogen. The yield in the ceric system has been found to be about the same as with y-rays, although reduction occurs through hydrogen peroxide (GP = 3*2,4 G, = 3.5 3). The irradiation of gas-free ferrous solutions with a-particles should give a similar yield ; experimentally G = 3.05.28 (iii) Irradiation of Iiydrogen-saturated cerric ion solutions.-The discrepancy which occurs on irradiation air-free ceric ion solutions containing dissolved hydrogen (first section) is explained by the various reactions occurring at different electron energies (fig.3). With high energy electrons the reaction H2 + OH -+ H2O + H (4) provides a new reducing atom which results in an increase in yield. With low energy electrons hydrogen reacts with those OH radicals which diffuse a short way from the track, but which would ultimately form hydrogen peroxide. The presence of one hydrogen molecule in this region results in two hydroxyl radicals reacting with it to form water, with consequently fewer ceric ions reduced. The yields in the system, (i) ferrous ion in air-saturated 0.8 N sulphuric acid and (ii) ceric ion in air-saturated 0.8 N sulphuric acid under light particle irradi- ation have been examined as a function of the initial energy of the ionizing electron.From the change in yield occurring at known initial electron energies, the fraction of like radicals reacting has been determined as a function of the instantaneous electron energy. When the predictions inherent in this picture have been com- pared with experimental results obtained on a variety of systems, including those irradiated by a-particles, satisfactory agreement has been found. CoNcLusIoNs.---The results place Allen’s “ hot-spot ” theory of reactions in particle tracks on a quantitative basis. They confirm that the initial ionic dis- tribution proposed by Gray may be used to predict the probability of solute- radical and radical-radical reactions in an irradiated aqueous system.T. J . HARDWICK 21 1 A P P E N D I X 0 Calculation of S, f(Er)dEl.Reaction H + H --f Hz. From curve A, fig. 1 : EO > 100 keV EO = 10 keV G = 17.6 hG = 2.8 2.8 Fractional change in G __ = 0.14. 20.4 Fraction of H atoms combining to form H2 = 0.07 G = 20.4 ferrous ions oxidized per 100 eV. Y Y Y, 9 , Y Y Y, 2, 9 , Y Y Each H atom removed by H2 formation results in two less ferrous ions oxidized. f(EJdE1 = 0.7. Reaction HO + OH* -+ H202. From curve B, fig. 1 : EO = 10 keV G = 4.8 ceric ions reduced per 100 eV. EO > 100 keV G = 3.2 Y Y Y, 9 , Y Y AG = 1.6 Y, Y, 9 , ,, 1.6 3.2 Fractional change in G - = 0-50. Each OH radical forming H202 causes the reduction of one ceric ion. The formation of H2 at the end of the electron tracks decreases the number of ceric ions reduced. A correction (0.07(v.s.)) must therefore be added to the fractional change in G. Fraction of OH radicals combining to form H202 = 0.50 + 0.07 = 0.57 :o f (Er)dEI = 5.7. Similarly, at Eo = 20 keV, G = 3.95 ceric ions reduced per 100 eV l:,f(EJdEl = 6.0. 1 Allen, J. Physic. Chem., 1948, 52, 479. 2 Clark and Coe, J. Chem. Physia, 1937, 5, 97. 3 Haissinsky, Lefort and Le Bail, J. Chirn. Phys., 1951, 48, 208. 4 Hardwick, Can. J. Chem., 1952, 30, 23. 5 Challenger and Rollefson, AECU-1187. 6 Jenks, Sweeton and Ghormley, ORNL-333. 7 Hanna and Pontecorvo, Physic. Rev., 1949, 75, 983. 8 Hardwick, Can. J. Chem., 1952,30, 39. 9 Hardwick, Can. J . Chem., 1952,30, 17. 10 Miller, J. Chem. Physics, 1950, 18, 79. 11 Todd and Whitcher, AECU-458. 12 Weiss, private communication. 1 3 Gordon, Hart and Walsh, AECU-1534. 14 Hochanadel, paper presented at Amer. Chem. SOC. meeting (Cleveland, April, 1951). 15 Lea, Action of Radiations on Living Cells (Cambridge University Press, 1946), chap. 1 . 16 Gray, J. Chim. Phys., 1951, 48, 172. 17 Weiss, Nature, 1944, 153, 748. 18 Dainton, J. Physic. Chem., 1948, 52, 490. 19 Weiss, Trans. Faraday SOC., 1940, 36, 856. 21 Johnson, J. Chem. Physics, 1951, 19, 1204. 22Duane and Scheuer, Radium, 1913, 10,33. 23 Nurnberger, J. Physic. Chem., 1934, 38, 47. 25 Lanning and Lind, J . Physic. Chem., 1938, 42, 1229. 26 Lefort, J. Chim. Phys., 1950, 47, 624. 27 Allen, Hochanadel, Ghormley and Davis, AECU-1413. 28 Hart, private communication. 20 Hart, ANLJ4636.