38 



Atomic Radiation and Oceanography and Fisheries 



per year (2.2 xlO*' megacuries of fission), as- 

 suming an irradiation time (Z^) of one year, and 

 a cooling time (/g) 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: 



A,= ~{l-e-^){e'<^-^-''-^) 



X 2.2 X 10*^ megacuries (11) 



where A is in years- ^. 



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. Cs^^^ has a branching decay with 

 8 per cent going directly to the ground state of 

 Ba^^^; thus the secular activity of Ba^^"'" is only 

 92 per cent of the parent activity. The activities 

 listed are beta activities only, for all isotopes 

 except Bais'"^, Tei^sm, and Cd^^m^ 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 K*" and Rb^^ 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 k^N^, where N,^ is the mass of 

 water in the mixed layer and k^ is the exchange 

 rate constant for transfer of material from the 

 mixed layer to the deep sea. In general, we 

 write ki as the fraction of material in reservoir 

 / removed per year. 



The residence time of a molecule in a reser- 

 voir, T, 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 Ng particular molecules in the reser- 

 voir, and at some later time /, we have N' of 

 these original Nq molecules still present. Then 

 we define the average life of a molecule in the 

 reservoir in the usual way, as 



/=co,N' = 





t = 0, N' = No 



where ni is the number of molecules of the 

 original Nq which remain in the reservoir for 

 each time /,-, and dN' is the number of mole- 



