36 



Atomic Radiation and Oceanography and Fisheries 



From these sources, the fission products are 

 assumed to enter the coohng 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: 



A ^ 



-X?,- 



(3) 



Assuming for the moment no coohng time, the 

 fission products are stripped out every t^ years 

 and dumped into the sea. Thus the introduc- 

 tion rate into the sea of a given fission product 

 is equal to its activity Ag in the sea at steady 

 state, and is given by Nt,./tr or: 



.=£(.-. 



) 



(4) 



where /^ denotes the coohng time, here assumed 

 to be 0. 



The activity of the fission products in the 

 world reactors at any time, A,., may be evaluated 

 in the following way. The fission products are 

 stripped out every /,. years, and N,., the amount 

 in the reactors, varies from to N(,. in cycles, 

 as / varies from to t^. For many reactors 

 operating independently (the sum of the fission 

 rates being R) with random distribution on the 

 /,. cycle, we take the average of N^ consistent 

 with R by integrating equation (1) from to 

 /,. and dividing by /,.; i.e., the steady state value 

 of N,. is: 



N.= 



fR 



(l-e-^*)dt 



Performing the integration, and setting A,.z= 

 \Nr, we have for the steady state activity of a 

 fission product in the reactors of the world: 



AJ~lXt,-(l-e^^'r>^-] 



A',- 



(5) 



and from equations (4) and (5) we see that 

 Ng + N^ = fR/X = N,,j,f„ 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,/Np^,5 = /l.,/^c,^;b =Fg, 

 and: 



Fmif-o)-. 



(1 



-xf, 



Xtr 



(6) 



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 t^, as given below. 



Equation (6) shows the following character- 

 istics: 



For long half-lives (A/r small): Fg = \ — -^ 



. . .(approaching 1). 

 For short half-lives (A/;.>5): Fg = 



Xtr 



For /,. = 1 year, and for any isotope with a half- 

 life of less than 60 days: 

 Fg = 0.4/^/0 (where /i/., 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: 



N, = Ntre~^'<' 



and from (4), the steady state activity of a 

 given fission product in the sea, equal to its 

 introduction rate, now becomes: 



■ A/, ^ 

 and F, is reduced to 



A. = l^ {I -e-''r>^{e -'''=) (7) 



>-t r\ /^->''( 



F,= 



Xfr 



(8) 



III. Fission product concentration in the sea as 

 a junction 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 



