clancy688 said:
I think this question fits here best...
Since there are several estimates of released radioactivity, I would like to try converting "released radioactivity of isotope x" into "released mass of isotope x". I think this would help in imagining, how much of the reactor's inventory is gone.
But how do I do this?
My approach would be the following, but I'm not sure if it's right, if it's an okay estimate or if it's total ********. So please give me some feedback. ^^;
[...]
How much Cäsium-137 is there in Fukushima overall in all damaged reactors? (1-4)
You have the right basic idea, but you're missing a factor of log(2), I think.
Bq is the number of decays per second. So to get number of atoms that produces x decays per second, you take x Bq and divide by the decay constant (the probability of decay of 1 atom per second).
The Cs-137 half-life is 30.1 years, so the relation of half-life to decay constant is: lambda = ln(2)/tau ~ 0.693/30.17 years = 7.285 x 10^-10/s.
So 10 PB (that was released to the atmosphere) amounts to 1.373 x 10^25 atoms of Cs-137: mass of Cs-137 atom is 136.9 u x 1.660 x 10^-27 kg / u ~ 3.11 kg.
A guess at the total inventory of Cs-137 in cores 1-3 at Fukushima could be based on an ORNL study of the inventory of Cs-137 for a fully radiated core (Cs-137 takes a while to build up to an equilibrium value) at the Brown's ferry nuclear plant (a BWR like Fukushima with power rating of 1065 MWe: which gave 273 PBq, or 850 kg of Cs-137.
http://www.scribd.com/doc/51577387/MARK-I-Reactor-Meltdown-Analysis
(see page 84 for the initial Cs-137 inventory).
Scaling this number by power ratios to the Fukushima cores 1-3, I get about 1600 kg of Cs-137, and another 630 kg or so from
core 4, which was in the spent fuel pool ... so ~ 2200 kg Cs-137 total might have been available for release. I'm not sure of the total content of the spent fuel pool at unit 4, though ...