Question

A freshly prepared radioactive source of half life $2\text{hours}30\text{minutes}$ emits radiation which is $64\text{times}$ the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be hours.

Answer 1

Given: Half life of radioactive substance is:
$T_{\frac{1}{2}}=150\text{minutes}$

$A_0=64x,\text{where}x\text{is safe limit}$

From radioactive disintegration formula:
$x=64x\times 2^{-\frac{n}{T_{\frac{1}{2}}}}$

$\Rightarrow \frac{1}{64}=2^{-\frac{n}{T_{\frac{1}{2}}}}$

$\Rightarrow 2^{-6}=2^{-\frac{n}{T_{\frac{1}{2}}}}$

or $\frac{n}{T_{\frac{1}{2}}}=6$

$\Rightarrow n=6\times 150\text{minutes}$

$=15\text{hours}$