
Edited on Mon Feb2105 07:37 AM by NNadir
I'm not sure exactly what you're refering to, but I don't see an error in this post.
The production rate and the decay rate are not related in any way. One is related to the fission yield, which is constant. The other is related to the amount of material that has accumulated. Radioactive equilibrium is established when the amount decaying is exactly equal to the amount decaying.
Actually the accumulated fission yields for Cs135 and Cs137 are very close for thermal neutrons fissioning U235. (Cs135, as noted above in another post is not a direct fission product, but is the most stable radioactive member of the 135 decay chain which usually starts with Te135.) Because of the short halflives of Te135 and Xe135, the fission yield for Cs135 can be considered as 6.53% of fissions. The fission yield for Cs137 is 6.27%, which is very close to that of its sister isotope. Therefore, before there has been much time to decay, the amounts of these two isotopes are very close.
The difference in the amount that can accumulate is a function of half life. This is because the competing process is radioactive decay. If the reactor is running at constant power (as I have assumed in this spreadsheet) the amount of cesium137 being formed remains constant. 6.27% of the fissions used to maintain the power result in a Cs137 nucleus. However, at more and more Cs137 accumulates, both inside the reactor in its fuel assembles and outside the reactor in spent and reprocessed fuel, the number of decays is actually rising. If we look at the radioactive decay law (dN = Nk dt) we see that the more stuff you have the more that decays per unit time. Eventually so much Cs137 will accumulate outside and inside the reactor that it will be decaying as quickly as it is formed. This second process, getting the decay to match production, is very slow for Cs135 and relatively faster for Cs137 because of their differening halflives.
In the spreadsheet, it looks as if the rate of accumulation of Cs135 has not changed at all, it is a constant 4.97 tons per year. This is because I've only used three significant figures. Actually, if I carried the calculation out for a hundred thousand years, this would not be the case. Doing the calculation at 100,000 years for instance, I have just seen that the new accumulation would fall to 4.82 metric tons per year.
Note that in my spreadsheet, I am not reporting total accumulation but rather new accumulation. In 233 years cesium137 is still being produced at the same rate, which is 6.74 X 10^20 atoms per second in the example I am using, but now so much has accumulated inside and outside the reactor that all but 22.7 kg is matched by Cs137 somewhere decaying in the 209 metric tons that have accumulated.
Please consider this and get back to me and let me know if I have clarified this in any way. I have a lot of respect for you. You think.
