Q91 / 180 · AIIMS 2018 (27 May) · Physics

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

  • Correct answer
    A
    $28$
  • B
    $56$
  • C
    $14$
  • D
    $7$

Solution

Here, $\lambda=0.05$ per year $\begin{aligned} & N=N_0-\frac{3 N_0}{4}=N_0 / 4, t=? \\ & \log _e \frac{N}{N_0}=\lambda t \\ & t=\frac{\log _e \frac{N_0}{N}}{\lambda}=\frac{\log _e 4}{0.05}=27.72 \text { year } \approx 28 \text { year }\end{aligned}$

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

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