frac{15}{16}-th of a radioactive sample decay | vedclass

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(B) The fraction of the radioactive sample decayed is $\frac{15}{16}$.The fraction of the sample remaining is $N = 1 - \frac{15}{16} = \frac{1}{16}$.U

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$10$

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(B) The fraction of the radioactive sample decayed is $\frac{15}{16}$.The fraction of the sample remaining is $N = 1 - \frac{15}{16} = \frac{1}{16}$.Using the radioactive decay formula $N = N_0 (\frac{1}{2})^n$,where $n$ is the number of half-lives:$\frac{1}{16} = (\frac{1}{2})^n \implies (\frac{1}{2})^4 = (\frac{1}{2})^n \implies n = 4$.Since the total time $t = 40 	ext{ days}$ and $n = \frac{t}{T_{1/2}}$,we have $4 = \frac{40}{T_{1/2}}$.Therefore,the half-life $T_{1/2} = \frac{40}{4} = 10 	ext{ days}$.

$\frac{15}{16}$-th of a radioactive sample decays in $40$ days. The half-life of the sample is ...... days.

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