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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
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$20 \mathrm{~min}$
In radioactive decay, the decay rate is proportional to the amount of substance. So, for change of count rate from 240 per min to 30 per min, let $N$ be the number of half-life passed in one hour. Then,
$\frac{240}{2^{N}}=30$
$\Rightarrow \quad 2^{N}=8$
$\Rightarrow \quad N=3$
Half-life, $t_{1 / 2}=\frac{1 h}{3}=\frac{60}{3} \mathrm{~min}=20 \mathrm{~min}$
$\frac{240}{2^{N}}=30$
$\Rightarrow \quad 2^{N}=8$
$\Rightarrow \quad N=3$
Half-life, $t_{1 / 2}=\frac{1 h}{3}=\frac{60}{3} \mathrm{~min}=20 \mathrm{~min}$
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