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Fictitious assumption: 10 billion years ago there would have been 10 billion kg244Pu with a HWZ of 8.3·107 years.
How many nuclear power plants are today of the of origin 244Pu still present?
Solution: Number of cores originally in mol: n(Pu) = m/M = 1013kg / 0.244kg = 4.098·1013 mol
Real number of cores: 4.098·1013 mol · 6.022·1023 = 2.468·1037
N=No·2^(-t/T12) = 2.468·1037 · 2^(-1010/8.3·107) = 13.3 cores
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