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Strontium 90 is one of the harmful nucli...

Strontium 90 is one of the harmful nuclides resulting from nuclear fission explosions.
Strontium 90 decays by beta particle emission with a half life of 28 years. How long (in years) would it take for 99.0% of a sample of strontium-90 released in an atmospheric test of an atomic bomb to decay? (log 2 = 0.30)

Text Solution

Verified by Experts

The correct Answer is:
186.67
The number of nuclei at time t, `N_(t)` is related to the number of nuclei present at `t = 0, N_(0)` by
`ln((No)/(N_(t))) = lambda t`, where `lambda` is activity constant
Half life `t_(1//2) = (ln 2)/(lambda), ((No)/(N_(t)) = 2), lambda = (ln 2)/(t_(1//2))`
If 99.0% sample has decayed, 1% is remaining so
`(No)/(N_(t)) = (100)/(1), ln((100)/(1)) = (ln 2)/("28 yrs") xx t` or `t = 186.666 = 186.67` years.
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