Radioactive contamination at Chernobyl

One of the most dangerous radioactive isotopes released by the Chernobyl disaster in 1986 was ⁹⁰Sr, whose half-life 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 10²⁷ 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 ⁹⁰Sr 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.