Question

A freshly prepared radioactive source of half-life 2 h 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 this source is

• A. 6h
• B. 12 h
• C. 24 h
• D. 128 h

Answer 1

The correct option is B 12 h

Let's say the permissible level of intensity of radiation, that is Activity is A, so initially we have 64A activity.

We need to calculate the time taken to drop the activity from 64A to A.
We know, A = $A_0{e}^{-\lambda t}$
$A_{0}is64A$ here. So after subtituting this we get,
$e^{-\lambda t}=\frac{1}{64}$
Or,
$e^{\lambda t}=64$.
Which gives,
$\lambda t=In64.$
Or,
$t=\frac{In64}{\lambda }\dots \dots \dots 1)$
Now we have half-life,$t_{1/2}$ = 2h
Which gives, $\lambda$ = $\frac{In2}{t_{1/2}}$= $\frac{In2}{2h}$
Now putting this value in equation 1)
t = $\frac{In64}{\lambda }=\frac{In64}{In2}\times 2h$
Or,
t = $\frac{6In2}{In2}\times 2h=12h$.