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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 relat3d to the number of nuclei present at `t =0, N _(0)` by ln `((No)/(N_(t)))= lamda t,` where `lamda` is activity constant
Halflife `t _(1//2) = (ln 2)/(lamda ), ((No )/(N _(t))=2 ), lamda= (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 ) xxt or t = 185.85=185.85` years.
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