A radioactive sample decays 7/8 times its original quantity in 15 minutes. The half-life of the sample is

Correct answer: (A) 5 min. Remaining amount of sample is=1-7/8=1/8 Using radioactive decay law N=N_02^(-tT12) We have, 2^tT12=N_0N=N_0N_08=8=2^3 Then, tT_12=3 Thus, half life of the sample is T_12=5 min.

Q78 / 90 · JEE Main 2022 (28 Jul Shift 2) · Physics

A radioactive sample decays $\frac{7}{8}$ times its original quantity in $15$ minutes. The half-life of the sample is

Correct answer
A
$5 \min$
B
$7.5 \min$
C
$15 \min$
D
$30 \min$

Solution

Remaining amount of sample is $= 1 - \frac{7}{8} = \frac{1}{8}$
Using radioactive decay law
$N = N_{0} {(2)}^{\frac{- t}{T_{\frac{1}{2}}}}$
We have, ${(2)}^{\frac{t}{T_{\frac{1}{2}}}} = \frac{N_{0}}{N} = \frac{N_{0}}{\frac{N_{0}}{8}} = 8 = {(2)}^{3}$
Then, $\frac{t}{T_{\frac{1}{2}}} = 3$
Thus, half life of the sample is $T_{\frac{1}{2}} = 5 \min$ .

Hence, the correct answer is option: 'A'.

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Solution

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A radioactive sample decays $\frac{7}{8}$ times its original quantity in $15$ minutes. The half-life of the sample is