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  4. In the radioactive decay of an element it is found that the count rate reduces from 1024 to 128 in 3 minutes. Its half life will be

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Q. In the radioactive decay of an element it is found that the count rate reduces from $1024$ to $128$ in $3$ minutes. Its half life will be

Nuclei

Solution:

$\frac{R}{R_{0}}=\frac{128}{1024}$
$\frac{R}{R_{0}}=\frac{1}{8}$
or $ \frac{R}{R_{0}}=\left(\frac{1}{2}\right)^{3} $
$\therefore n=3$
$3$ half lives in $3$ minutes,$ 1$ half life in $1$ minute