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CHAPTER 3 DISPOSAL OF RADIOACTIVE WASTES IN THE OCEAN: THE FISSION PRODUCT SPECTRUM IN THE SEA AS A FUNCTION OF TIME AND MIXING CHARACTERISTICSl HARMON CRAIG, Scripps Institution of Oceanography, University of California, La Jolla, California I. Introduction: Estimated output of nuclear heat and fission products at "steady state" nuclear power production IN TWO other papers in this report, Wooster and Ketchum discuss mixing rates in the oceans on the basis of oceanographic data, and the present writer reviews the natural isotopic stud- ies which bear on the problem. In this paper we attempt to construct a detailed quantitative picture of the fission product spectrum in the ocean, in steady state with a given fission rate. Such an attempt may well be termed premature, in view of our sketchy knowledge of the in- ternal mixing rate in the sea. Nevertheless, we know a good deal more today than was known five years ago, enough at least to make some simple model calculations which may well yield correct results to an order of magnitude. More- over, the construction of a model and the cal- culation of its characteristics are often highly informative, and, at the very least, provide a basis for the orientation of future studies. The following figures, available in various sources, are pertinent to the estimation of fu- ture consumption rates of nuclear power. Present U. S. electrical energy: 6x 105mwh/yr. Present world electrical energy: 10° mwh/yr. Present world energy consumption (all sources) is about 4.5 x1010 mwh/yr, doubling every 30 years. For the present calculations, we shall assume a stationary world fission rate of U225 equal to 1000 metric tons/yr, supplying all the fission products to be disposed of in the sea. We shall then attempt to construct as reasonable a 1 Contribution from the Scripps Institution of Oceanography, New Series, No. 902a. picture as possible of the fission product ac- tivity in the sea, when this activity reaches steady state with the rate of fission, i.e., when the decay rate of each fission product in the sea is equal to the rate at which it is being dumped into the sea, so that its concentration remains constant. We shall also make some calculations for a linear build up to such a fission rate in 50 years. Since 1 gram of U2,5 is equivalent to 24 mwh, our assumed fission rate of 1000 tons of U255 per year is equivalent to 2.4 x 1010 mwh/ yr of nuclear heat. At 50 per cent efficiency, this is equivalent to a world nuclear power consumption of 1.2x1010 mwh/yr. If this latter figure represents 10 per cent of the total world energy utilization, we are then assuming a world consumption of 1.2x1011 mwh/yr, which seems not unreasonable as an estimate for the year 2000 A. D. Thus a fission rate of 1000 tons of U25B/yr represents a 2.7 fold increase in the present world energy consumption, 10 per cent being derived from nuclear heat with 50 per cent efficiency, which should be reached in about the year 2000 based on the present trend in energy consumption (see above). Our calcu- lations will all be linear with the fission rate, so that data for other fission rates are easily derived from the present calculations. The build up of fission products in a reaactor is given by: dN , where /= fission yield (per cent of fissions yielding an individual fission product, the sum equalling 200 per cent) , R is the rate of fission (atoms U225/yr) here assumed constant and equivalent to 1000 tons of U2"/yr, and N=the

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Chapter 3 35 Effects of Time and Mixing Characteristics number of atoms of an individual fission prod- uct present in the reactor at any time.2 Integration with appropriate limits gives the number of atoms of a given fission product in the reactor as a function of time: N=f(1-,-) (1) where the build up factor (1 — e~^) varies from 0 to 1 as / varies from 0 to infinity, and gives the fraction of the equilibrium amount attained at any time. At secular equilibrium in the reactor, dN/dt = 0, and \N = fR; we then have: N , -1— (t\ JV««!6 — ^~ \*l from which one sees that at any time in the reactor, N=N,aII)(1-*-*'). The assumed fission rate of 1000 tons U22S/yr is equivalent to 2.2x10" megacuries of fission (1 curie=3.7x1010 disintegrations/sec), and since the sum of the fission yields is 200 per cent, at equilibrium the total activity of all fission products present in the world, in mega- curies, could be roughly estimated by multi- plying 4.4 x 10" by the average number of radioactive members per fission chain. The amount of an individual fission product would be fR/\, using the appropriate decay constant, and its activity would simply be fR, using the appropriate fission yield. The lengths of the fission chains are diffi- cult to estimate because of the extremely short half-lives of the first members. However, Dr. E. C. Anderson (personal communication) has 2 The above equation actually applies only to the first member of a fission chain; for the build up of the second member (y) of a chain with initial mem- ber (x), the correct expression is: where /. and /, are the individual direct fission yields, and so forth for the succeeding members of each mass number chain. However the decay constants are very large for the first members of a chain, and thus one can neglect the exponential terms and assume a fission yield which is the total yield of the isotope under consideration plus all preceding members of the chain, for all irradiation times with which we shall be concerned. The experimental fission yield figures gen- erally refer to the total chain yield, but because of the very low production of the later members of a chain by direct fission, there is no error involved in apply- ing them to the first significantly long-lived chain member. studied the experimental data on the activity of fission product mixtures directly after fission, and concludes that for times beyond one day after cessation of fission, on the average only £ of the chains are still active (i.e. from this time on there are left only about 0.3 radioactive members per pair of fission chains initiated). Thus he points out that assuming a fission rate of 1000 tons U225/yr as used above, and taking one day as an assumed minimum delay between accumulation and disposal, the steady activity in the sea for continuous stripping and disposal after one day would be roughly 7 x 105 mega- curies. This is about the same total activity as that found below for an average irradiation time of one year with a 100-day cooling period before disposal, namely 7.7x105 megacuries (see calculations in Section IV and Table 1). The rough agreement of these numbers merely emphasizes the great predominance of the few long-lived isotopes of high fission yield in the fission product activity after very short times. II. Rate of introduction of fission products into the sea A more realistic picture is obtained by con- sidering the irradiation time, or reactor holding time for uranium slugs, which is limited by structural weakening from irradiation, poison- ing by fission products, etc., and the cooling period necessary for safe handling and for the growing in of plutonium in breeder piles. We assume the fission products of the world are distributed between (1) reactors, (2) cooling pits, and (3) the oceans (or any gross disposal site for that matter). The distribution among these reservoirs and the fission product spec- trum in each depends on the irradiation and cooling times. We shall assume an irradiation time of tr years, equivalent to any of the following physi- cal interpretations: 1. The reactors of the world are operated, on the average, /r years, then stripped down and rebuilt. 2. The reactor slugs are continuously pushed through the reactors, each spending, on the average, tr years in the reactor. 3. Continuous stripping into a holding tank which is opened every tr years for removal of fission products.

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Atomic Radiation and Oceanography and Fisheries From these sources, the fission products are assumed to enter the cooling pits, from which they are dumped into the sea. At the end of the irradiation time /„ the amount of a fission product is given by (1) as: Assuming for the moment no cooling time, the fission products are stripped out every tr years and dumped into the sea. Thus the introduc- tion rate into the sea of a given fission product is equal to its activity A, in the sea at steady state, and is given by Ntr/tr or: where tc denotes the cooling time, here assumed to be 0. The activity of the fission products in the world reactors at any time, Ar, may be evaluated in the following way. The fission products are stripped out every tr years, and Nr, the amount in the reactors, varies from 0 to Nir in cycles, as / varies from 0 to tr. For many reactors operating independently (the sum of the fission rates being R) with random distribution on the tr cycle, we take the average of Nr consistent with R by integrating equation (1) from 0 to tr and dividing by tr; i.e., the steady state value of Nr is: Performing the integration, and setting Ar = \Nr, we have for the steady state activity of a fission product in the reactors of the world: and from equations (4) and (5) we see that N, + Nr=fR/*.=N,vlt, the total amount of the fission product in the world, as of course it must. Still neglecting cooling time, the fraction of the world total of a fission product which is in the sea is given by N,/N,Qit = A,/A,0lt =F,, and: (6) A/r Neglecting cooling time, the effect of irradia- tion time may be demonstrated by considering the long and short-lived radioisotopes of stron- tium, calculating the fraction of the world totals, for the assumed fission rate, which is in the sea, as a function of tr, as given below. (%). tr (years) Sr90 (28y) 5r* (54<*) 0.1 99.9 79.8 0.5 99.4 38.6 1 98.8 21.2 2 97.5 10.7 10 88.5 2.1 Equation (6) shows the following character- istics: For long half -lives (\}r small): F,= 1-^ . . .(approaching 1). For short half-lives (A/r>5): F,= — A/r For tr= 1 year, and for any isotope with a half- life of less than 60 days: F, = 0.4/1/2 (where tltl is here in days, /„= 0). Thus, as shown above, increasing the irradia- tion time from 0.1 to 1 year cuts the fraction in the sea of a 60 day isotope by $', neglecting cooling time effects, but does not affect the long-lived isotopes. We next interpose the cooling time between the reactor stripping and the disposal in the sea. The amount of an isotope left after the cooling period is: and from (4), the steady state activity of a given fission product in the sea, equal to its introduction rate, now becomes: and Ft is reduced to: A/r (7) (8) III. Fission product concentration in the sea as a function of linearly increasing fission rate We can get some idea of the transient char- acteristics of the fission product spectrum in the sea by examining the build-up of fission products with an increasing rate of fission. We

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Chapter 3 37 Effects of Time and Mixing Characteristics shall take R, the world rate of fission, as 0 at the present time (/ = 0) and increasing linearly from the present time until it reaches the 1000 ton rate in 50 years. We shall further assume continuous stripping of fission products into the sea, and examine the transient character- istics of long-lived and a short-lived fission product. The rate of increase of a fission product in the sea is given by: f =/(?>-' where (R/t) is a constant by virtue of the assumed linear increase from R = 0. N is now the amount of a fission product in the sea at any time /. We thus have: JN+ [AN— (fR/t) f]dt — 0 Multiplication by e** makes the equation exact, and the solution is: (A/-1) Activity (megacuries) in the sea -AN A2 Evaluating the constant from N = 0 at / = 0, we have the general solution: NI = ,§}&-(! -«-*)] (9) where N( is the amount in the sea at the time /. Multiplication by A to give the activity is seen to give an equation of the same form as (5) for the steady state amount in reactors, except that in (9) both R and / are variables, with R/t being constant. We take R=0 at the present time, increas- ing linearly to 1000 tons U225/year in 50 years. As noted previously, this rate is equivalent to 2.2x10° megacuries of fission, and thus R/t= 4.4 x 104 megacuries/year. Thus the activity of a fission product in the sea at any time / is given by: /4, = 4.4x104— [A/— (1 — *~*')] (10) where At is in megacuries, A=yrs~1, / is in years, and / is the fission yield. We tabulate below the increasing activity in the sea for a long-lived and a short-lived isotope with con- tinuous stripping into the sea. Sr9° JlSl >i/2 = 28;y t1/2 = 84 / (years) /=0.05 f = 0.028 1 26.4 1200 10 2640 12,300 50 4.8x104 6.2 x 104 100 1.4x105 1.2 x105 200 3.5 x105 2.4x105 1000 2.1x10" 1.2 x 10" At 50 years, when the fission rate of 1000 tons/year is reached, the Sr90 activity is half the amount which would be in steady state with this fission rate with an irradiation time of 1 year (see below and Table 1). If R continues to increase at the same rate, the steady state Sr90 activity for constant R is reached in about 100 years, and thereafter the activity increases lin- early at a rate given by: At= 2200(1 — 40), the mean life of Sr90 being 40 years. The factor (1— e-*f) grows in to 95 per cent at 3 mean lives or 4 half-lives. With a constant fission rate of 1000 tons U225/year, irradiation time one year, and no cooling time, the I121 steady state activity in the sea would be 2000 megacuries (calculated as in Table 1, but with no cooling time). With the linear increase of fission rate and continu- ous stripping as shown above, this level is sur- passed in two years. These data illustrate rather strikingly how rapidly the short half-life iso- topes build up to secular equilibrium with an increasing fission rate. Sr90 does not equal the I121 activity until after 100 years of dumping into the sea, under the above conditions. For all species which have grown into secular equi- librium with the increasing fission rate, the ac- tivity ratios in the sea are simply given by the fission yield ratios. IV. Steady state fission product spectrum in a homogeneous, rapidly mixed sea The first three columns of Table 1 list all the fission products of any significance, together with their half-lives and fission yields. Col- umns 4 and 5 show the total amounts of each isotope in the sea, in metric tons and mega- curies of activity respectively, in secular equi- librium with a fission rate of 1000 tons U22B

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38 Atomic Radiation and Oceanography and Fisheries per year (2.2x10° megacuries of fission), as- suming an irradiation time ( /, ) of one year, and a cooling time (tc) of 100 days (0.274 years). With such conditions, the expression for the activity of each fission product in the sea, as given by equation (7), becomes: x 2.2 x 10' megacuries (11) where A is in years-1. For half-lives greater than 1 year there is essentially no reduction in the oceanic activity by the cooling time. For all isotopes with half- lives greater than 5 years, more than 90 per cent of the isotope will be in the sea at steady state. Of the 30 isotopes shown, 22 are independ- ent and 8 are short-lived daughters which come quickly into secular equilibrium with their par- ents, decaying thereafter with the activity of the parent. Cs127 has a branching decay with 8 per cent going directly to the ground state of Bat9T; thus the secular activity of Ba127m is only 92 per cent of the parent activity. The activities listed are beta activities only, for all isotopes except Ba127m, TeI29m, and Cd11Bnl, which decay from their excited states by gamma emission. The Sm and Eu activities depend on the actual rate of burn-up in the reactors, and may vary considerably with different reactor conditions. In the calculations, the first long-lived mem- ber of each fission chain was taken, and the fission yield for the entire chain was used for this isotope. The direct fission yield for the 11-day Nd which lies above the 2.5-year Pm in the 147 fission chain is not known, and thus this isotope has been neglected; the Nd comes quickly into secular equilibrium in the reactor, so that the total chain fission yield can be used for the Pm calculation. The fission products are listed in order of decreasing total activity in the sea, with radio- active daughters paired with their parents. The total amount of all fission products in the sea is found to be about 3200 metric tons, cor- responding to almost one million megacuries of activity. This represents almost twice the pres- ent activity in the sea, which is mainly due to the radioactivity of potassium 40. The figures for K40 and Rb57 are shown for comparison, the activity of the other radioactive elements in the sea being negligible relative to these isotopes. We shall now discuss the effects of the mix- ing barrier at the thermocline in the sea on the distribution of the fission products between the deep sea and the upper mixed layer of the sea. V. Distribution of fission products between the deep sea and the mixed layer We shall assume a simple model, convenient for calculation, in which we divide the ocean into two geophysical reservoirs: a mixed layer above the thermocline, and the bulk of the ocean, termed the "deep sea," below the ther- mocline. The exchange of fission products be- tween these two reservoirs is assumed to be a first order process, the rate of removal of a fission product from a reservoir being simply proportional to the amount of the isotope in the reservoir. The thermocline is assumed to represent the boundary across which the hold-up in mixing takes place. Thus, for example, the rate of transfer of water from the mixed layer to the deep sea is assumed to be kmNm, where Nm is the mass of water in the mixed layer and km is the exchange rate constant for transfer of material from the mixed layer to the deep sea. In general, we write kt as the fraction of material in reservoir / removed per year. The residence time of a molecule in a reser- voir, r, is defined as the average number of years a molecule spends in the reservoir before being removed by the physical mixing process. The meaning of T may be shown by the follow- ing derivation which gives a rigorous definition. Assume a reservoir with a steady-state fixed content of N molecules of a substance, and a continuous flux into and out of the reservoir of molecules/year. At a particular time, /=0, we have N0 particular molecules in the reser- voir, and at some later time /, we have N' of these original N0 molecules still present. Then we define the average life of a molecule in the reservoir in the usual way, as /=oo,N'=0 r 2< nt *** N0 J ' where «< is the number of molecules of the original N0 which remain in the reservoir for each time /<, and dN' is the number of mole-

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Chapter 3 39 Effects of Time and Mixing Characteristics cules removed in the interval / and t+dt, i.e., the number of molecules with a reservoir life- time equal to /. The number of molecules of the original particular set of N0 which are removed in any interval dt is simply given by the concentration of such molecules in the reservoir, multiplied by the total flux from the reservoir, i.e.: which yields on integration N =N0 exp Substituting for dN' and then for N' in the integral expression for r, and integrating be- tween / = 0 and infinity, we obtain: N m = average depth of mixed layer of the sea (taken as 100 meters). D = average depth of the ocean (taken as 3800 meters). We assume that the fission products are intro- duced into the deep sea after the 100 day cool- ing period, the disposal rate or flux of a given fission product isotope, termed <£, being equal to the steady-state total activity in the sea A, as given by equation (11). is thus in "mega- curies of flux," = atoms/sec divided by 3.7x 1010. We wish to ask what steady-state activity per unit volume of water will be in the mixed layer, as a function of the rate of cross-thermo- cline exchange of sea water and fission products. The water balance between the reservoirs is given by: and from the expression for N' one sees that T, the average life, is also the time required for the original number of N0 particular mole- cules to be reduced to l/e times the initial number, r is thus formally equivalent to a radioactive mean life. In our particular model we are assuming the rate of removal to be dependent only on the total amount of substance, N, in the reservoir, so that the outgoing flux is given by OCR for page 34
40 Atomic Radiation and Oceanography and Fisheries particular model in the paper by Craig. From these discussions, we choose for the present calculations a value T(J = 300 years as perhaps the best guess. As discussed by the writer in a separate chapter of this report, radio carbon data indicate a residence time for water of about 1000 years, as a world-wide average. Mixing in the Atlantic is probably a good deal faster than in the Pacific, and 300 years is probably a safe lower limit estimate for the Atlantic, con- sidering the material to be deposited on the bottom. Thus the mixed-layer activities we cal- culate should be upper limits, which would be approached more closely in the Atlantic than in the Pacific. The average world-wide depth of the mixed layer, m, is taken as 100 meters, and the average depth of the sea is taken as 3800 meters. The volume of the sea is 1.4x1021 liters; thus the volume of the mixed layer is taken as 1/38 of this or 3.7 x1019 liters. Putting these nu- merical values into (16), and noting that — A,, we have for the activity of any fission prod- uct per unit volume of sea water in the mixed layer: in disintegrations per second per liter, where A, is in megacuries, as tabulated in column 5 of Table 1, and X is in years-1. From this equation the values tabulated in column 8 of Table 1 were calculated, and were converted to microcuries per liter for column 9. From the relation ad/am= (AJ/m/A^A) = (Ad/Am) (m/D-m) we obtain: a* — \ _i_t -- ATm+1 am where Tm the residence time of a water mole- cule in the mixed layer, is given by (12) as 1/37 of 7,1 = 8.1 years. We thus write: = 8.1A+1=a (18) from which, given the values of am computed above, the values of ad tabulated in column 7 of Table 1 were computed. We call a the "oceanographic partition factor." It is a func- tion of the mixing rate of the sea and the decay constant of the individual isotope, and is a measure of the effectiveness of the cross-thermo- cline exchange rate in buffering the mixed layer from the fission products introduced into the deep sea. Values of a are tabulated in column 6 of the table, and range from about 1 for the longest lived isotopes to about 250 for an isotope with a half-life of 8 days. For stable isotopes A is 0, a is 1, and (18) reduces to simple statistical partitioning. From (17) we see that as A, the decay con- stant of an isotope, increases, the activity in the mixed layer decreases; i.e., if more of the isotope can be removed from the deep sea by decay, less needs to be transferred to the mixed layer to preserve the steady state. If the half- life were so long that the radioactivity did not affect the distribution between the mixed layer and the deep sea, we would have simply a sta- tistical partitioning of the isotope between these reservoirs, such that the activity per unit volume in each reservoir would be the same. From the above equations we can derive the ratio of the activity in the mixed layer for an isotope to the activity per unit volume which would be ob- served if the partitioning were statistical: am . Tj + Tm 1 —., j <=*— am(stat) art+rm a and we see that a~1 is approximately the frac- tion of the statistical activity per unit volume attained by a fission product in the mixed layer. Equation (19) can be written exactly as: »m '!/» (20) where /1/2 is the half-life of the isotope in years. The ratio am/am(stat) is plotted in Figure 1 as a function of the half-life, and one reads, for example, that an isotope with a 5 year half- life attains about 48 per cent of the activity per unit volume in the mixed layer which it would have if its half-life were so long, relative to the mixing rate in the sea, that its radio- activity had no effect on its distribution. The values of a^, && and a are tabulated in Table 1, in which the isotopes are arranged in order of their activity in the deep sea. For comparison, the activities of potassium 40 and rubidium 87, which provide essentially all the radioactivity in the sea, are also listed. In the deep sea, the predicted fission product activity is 19.3 disintegrations per second per liter, as compared with the natural activity of 12.2 dps/ liter; thus the fission products in steady state with the 1000 ton fission rate would almost triple the deep-sea activity.

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Chapter 3 41 Effects of Time and Mixing Characteristics TABLE 1 FISSION PRODUCT SPECTRUM IN THE OCEAN AT STEADY STATE DISPOSAL INTO DEEP SEA. CALCU- LATED FOR FISSION RATE OF 1000 TONS U*M/YR (2.4 X 101 0 MWH/YR OF NUCLEAR HEAT), IRRADIATION TIME OF 1 YR AND COOLING TIME OF 100 DAYS. AVERAGE LIFE OF A WATER MOLECULE IN THE DEEP SEA TAKEN AS 300 YEARS; AVERAGE DEPTH OF THE MIXED LAYER TAKEN AS 100 METERS. Total amount in ocean Activity (dps/liter) Isotope Half- life 33 y Fission Metric yield % tons 6.3 1750 Activity megacuries 1.4 X 10* 1.3 X 10* a = 1.17 Deep sea 3.64 3.35 tm Mixed layer Microcuries per liter 8.4 X 10'* 7.7 X 10-* MBa1*™ 2.6m 3.12 2.87 •Sr*0 28 v 5.0 780 — 0.20 1.1 X 10* 1.1 X 10* 1.20 8.32 2.90 2.90 2.42 2.42 6.5 X 10-* 6.5 X 10-* •Y" . 64h •Ce1" . . . 280 d 5.3 19 6.0 X 10* 6.0 X 10* 1.62 1.62 0.19 0.19 5.2 X 10-* 5.2 X 10-* .JV" . 17.5 m 2.5v 2.6 48 0.7 630 4.6 X 10* 1.5 X 10* 3.24 1.06 32.5 1.23 0.40 0.38 0.38 1.0 X 10-* 1.0 X 10'* 1.0 X 10'* «Smm . 100 y tiZ]St 65 d 6.4 0.58 — 0.32 1.2 X 10* 1.2 X 10* 0.33 0.33 2.7 X 10-' 2.7 X 10-' uNbK . 36 d i.o x 10-* »Y" 60 d 5.9 0.39 0.5 2.0 9.4 X 10* 35.1 6.61 0.25 7.2 X 10-1 1.9 X 10-* «Ru100 1 v 6.6 X 10* 6.6 X 10* 0.18 0.18 2.7 X 10J 2.7 X 10-* 7.2 X 10-' 7.2 X 10'7 . 35s «Sr* 54 d 4.6 0.22 3.7 7.2 X 10-* 6.0 X 10* 38.9 52.0 0.16 4.1 X 10-* 1.1 X 10-' uRuM. . 40 d 2.3 X 10* 6.1 X 10-* 6.1 X 10'1 1.2 X 10-* 1.2 X 10-* 3.2 X 10-* 3.2 X 10-* . 55 m 2.3 X 10* /"—Ml 32 d 5.7 6.3 X 10-* 0.03 0.44 0.3 3.4 X 10-* 1.8 X 10* 5.1 X 10* 65.0 3.8 4.9 X 10-* 1.4 X 10J 7.6 X 10-4 3.6 X 10-* 2.0 X 10-* 9.7 X 10-* caEu™ 2 v 33d 1.0 X 10* 1.0 X 10" 63.4 2.8 X 10-* 2.8 X 10J 4.4 X 10-* 4.4 X 10-* 1.2 X ID-* 1.2 X 10-* saTe1** 70m ..Pr1" 13 7d 5.4 — 6.1 40 151 161 1.1 X 10-* 7.2 X 10-* 2.0 X 10-" wBa1" . 12.8 d 30 30 8.0 X 10-* 8.0 X 10-* 5.0 X 10-* 5.0 X 10J 1.3 X 10-" 1.3 x 10-" 1 7d soSn1" 130 d 1.2 X 10-* — 8 X 10-* — 2.8 — 0.01 — 0.01 — 0.02 — 0.018 — 6.8 0.64 0.35 0.15 7.5 X 10-* 1.7 X 10-* 1.4 X 10-* 16.8 47.4 256 134 151 206 268 1.8 X 10-* 1.7 X 10-* 9.5 X 10-* 4.0 X 10-* 2.0 X 10-* 4.7 X 10'T 3.9 X 10-* 19-3 1.1 X 10-* 3.6 X 10-' 3.7 X 10J 3.0 X 10J 1.3 X 10-* 2.3 X 10J 1.4 X 10-10 12.1 3.0 X 10-" 9.8 X 10-" 1.0 X 10-u 8.0 X 10'1* 3.6 X 10-" 6.2 X 10-" 3-9 X 10-" 3.2 X 10-* aCd1"- .... . 44d 8d BEu"" . 15.4 d •.Cs"" . 13.7 d wSn1" 10 d nAg"1 7.6 d Totals: Natural K" Rb" potassium 3230 and rubidium in the 6.3 X 10" 1.2 X 10" 7.7 X 10* sea: 4.6 X 10* 1 1 12 0.22 12 3.2 X 10-* 5.9 X 10^ 8.4 X 10* 0.22 All activity values are Beta activities only, except where isomeric transitions are indicated. Conversion: 1 disintegration per second = 2.7 X 10-° microcuries. 1 curie = 3.7 X 1010 disintegrations per second.

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42 Atomic Radiation and Oceanography and Fisheries 100 90 80 ro 60 50 40 SO 20 10 .2 .3 .4 .5 2345 10 HALF-LIFE (YEARS) FIGURE 1 20 30 40 50 100 However, the effect of the internal mixing rate of the sea in the model adopted, is to cut the activity in the mixed layer down to 12.1 dps/liter which is, by coincidence, just equal to the natural activity and which would thus just double the activity in the mixed layer. It should be noted that the figures given in the table for the predicted activities in the mixed layer refer only to cross-thermocline mix- ing by physical processes, exclusive of biological transfer through the thermocline. However, the figures listed provide a basis for speculation on the hazardous effects of the mixed layer activity, in that comparison may be made with biological concentration factors, discussed else- where in this report, to predict the activity levels in marine organisms. In this way, rough predictions may be made of the hazard to man, not only by direct exposure to the waters of the mixed layer of the sea, but by the activity con- centrated in marine organisms used for food.