The count rate of a Geiger- Muller counter for the radiation of a radioactive ma

Question

The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of 30 minutes decreases to

5 s^{- 1}

after 2 hours. The initial count rate was

Options:

A . 25 s−1

B . 80 s−1

C . 625 s−1

D . 20 s−1

Answer: Option B
:
B

A = A_{0} {(\frac{1}{2})}^{t / T_{1 / 2}} \Rightarrow 5 = A_{0} {(\frac{1}{2})}^{\frac{2 \times 60}{30}} = \frac{A_{0}}{16} \Rightarrow A_{0} = 80 s e c^{- 1}

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