Q177 / 180 · COMEDK 2017 · Physics

Mean life of a radioactive sample is $100 \mathrm{~s}$. Then, its half-life (in min) is

  • A
    $0.693$
  • B
    1
  • C
    $10^{-4}$
  • Correct answer
    D
    $1.155$

Solution

Given, mean life of radioactive sample, $\tau=100 \mathrm{~s}=\frac{100}{60} \mathrm{~min}=\frac{5}{3} \mathrm{~min}$ We know that, $\begin{aligned} \tau &=1.44 T_{1 / 2} \\ \Rightarrow \quad T_{1 / 2} &=\frac{\tau}{1.44}=\frac{5 / 3}{1.44}=\frac{5}{3 \times 1.44}=1.157 \mathrm{~min} \\ & \simeq 1.155 \mathrm{~min} \end{aligned}$

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

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