Q140 / 180 · COMEDK 2019 · Physics

A count rate meter shows a count of 240 per min from a given radioactive source. One hour later the meter shows a count rate of 30 per min. The half-life of the source is

  • Correct answer
    A
    $20 \mathrm{~min}$
  • B
    $30 \mathrm{~min}$
  • C
    $80 \mathrm{~min}$
  • D
    $120 \mathrm{~min}$

Solution

Let $N$ be the amount of substance left, $N_{0}$ be the total amount of substance. The amount of substance left after $N$ half-life is given by $\quad \frac{N}{N_{0}}=\frac{1}{2^{n}}$ Hence, $\quad \frac{30}{240}=\frac{1}{2^{n}}$ (Since, decay rate proportional to amount of substance) $$ \Rightarrow \quad 2^{n}=8 \Rightarrow n=3 $$ Number of half-life passed $=3$ Time taken for the substance to decay from 240 count rate to 30 count rate $=1 \mathrm{~h}=60 \mathrm{~min}$ $$ \begin{aligned} \text { Half-life } &=\frac{\text { Total time }}{\text { Number of half - life }} \\ t_{1 / 2} &=\frac{60}{3}=20 \mathrm{~min} \end{aligned} $$

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

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