One of the main contaminants of a nuclear accident, such as that at Chernobyl, i

Question

One of the main contaminants of a nuclear accident, such as that at Chernobyl, is strontium-90, which decays exponentially at an annual rate of approximately 2.2% per year Write the percent of strontium-90 remaining, P, as a function of years, t, since the nuclear accident. Estimate the half-life of strontium-90. After the Chernobyl disaster, it was predicted that the region would not be safe for human habitation for 94 years. Estimate the percent of original strontium-90 remaining at this time.

Explanation / Answer

After one year, fraction remaining = (1 - 0.022) = 0.978
After two years, fraction remaining = 0.978 x 0.978
After three years, fraction remaining = 0.978 x 0.978 x 0.978
and so on.

So after t years, fraction remaining = 0.978^t

or, as a percentage, = 0.978^t x 100


Half life is the time for the remainder to drop to 0.5

So

0.978^t = 0.5

t * log 0.978 = log 0.5

t = log 0.5 / log 0.978 = 31.1 588 years


At t = 94 years

P = 0.978^94 = 0.12355

12.35 %

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