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  4. If decay constant of a radioactive sample is 0.05 per year, then find the time (in year) for which sample will decay by 75%.

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Q. If decay constant of a radioactive sample is 0.05 per year, then find the time (in year) for which sample will decay by 75%.

AIIMSAIIMS 2018

Solution:

Here, $\lambda$ = 0.05 per year
$N=N_{0}-\frac{3N_{0}}{4}=N_{0}/4, t=?$
log$_{e} \frac{N}{N_{0}}=\lambda t$
$t=\frac{log_{e} \frac{N_{0}}{N}}{\lambda}=\frac{log_{e} 4}{0.05}=27.72$ year $\approx28$ year