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Radioactive contamination at ChernobylOne of the most dangerous radioactive isotopes released by the Chernobyl disaster in 1986 was ^{90}Sr, whose halflife is 28 years. (a) How long will it be before the contamination is reduced to one tenth of its original level? (b) If a total of 10^{27} atoms was released, about how long would it be before not a single atom was left? (a) We want to know the amount of time that a ^{90}Sr nucleus has a probability of 0.1 of surviving. Starting with the exponential decay formula, surv = 0.5^{t/t1/2} , we want to solve for t. Taking natural logarithms of both sides,
so
Plugging in P = 0.1 and t_{1/2} = 28 years, we get t = 93 years. (b) This is just like the first part, but P = 10^{27} . The result is about 2500 years.


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