Chapter 3 



Effects of Time and Mixing Characteristics 



35 



number of atoms of an individual fission prod- 

 uct present in the reactor at any time.- 



Integration v/ith appropriate hmits gives the 

 number of atoms of a given fission product in 

 the reactor as a function of time: 



N 



= ^(1 



') 



(1) 



where the build up factor (1— e"^^) varies 

 from to 1 as / varies from to infinity, and 

 gives the fraction of the equihbrium amount 

 attained at any time. At secular equilibrium in 

 the reactor, dN/dt=.0, and xN = fR; we then 

 have: 



N -B. 



^^eqlb — ^ 



(2) 



from which one sees that at any time in the 

 reactor, N = N,g,s (1-^-^0 • 



The assumed fission rate of 1000 tons U-^^/yr 

 is equivalent to 2.2 x lO*' megacuries of fission 

 (1 curie=3.7x 10^" 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 4.4x10^ by the average number of 

 radioactive members per fission chain. The 

 amount of an individual fission product would 

 be fR/k, 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: 



dt 



= [/,(! _^-V )+/,,] R_X,N, 



where fx and fy 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 U^^^/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 10^ 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 7.7 xlO^ 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 t^ 

 years, equivalent to any of the following physi- 

 cal interpretations: 



1. The reactors of the world are operated, on 

 the average, t^ years, then stripped down and 

 rebuilt. 



2. The reactor slugs are continuously pushed 

 through the reactors, each spending, on the 

 average, tj. years in the reactor. 



3. Continuous stripping into a holding tank 

 which is opened every t^. years for removal of 

 fission products. 



