Question

A freshly prepared radioactive source of half life $2$ hours emits radiation of intensity which is $64$ times the permissible safe level. The minimum time after which it would be possible to work safely with the source is (in hrs.)

• A. 12
• B. 12.0
• C. 12.00

Answer 1

Answer: (A), (B), (C)

Since, activity of a sample is given by,

$A=\lambda N$

Where,

$\lambda =$ decay constant

$N=$ Number of active nuclei

To reach the safety limit, intensity (or activity) has to become $\frac{1}{64}$ times of the initial intensity.

Hence, the number of active nucleus should also decrease by a factor of $\frac{1}{64}$

Let us suppose, this process takes $n$ half lifes

$2^n=64\Rightarrow n=6$

$t=2\times 6=12\text{hrs}$