Question

A freshly prepared radioactive source of half life 2 hrs emits radiation of intensity which is 32 times the permissible safe value of intensity. Which of the following is the minimum time after which it would be possible to work safely with this source?

• A. 16 hrs
• B. 5 hrs
• C. 10 hrs
• D. 32 hrs

Answer 1

The correct option is C 10 hrs

Given : $T_{1/2}=2hrs$
Amount of radioactive substance left $N=\frac{N_o}{2^n}$
where $n=\frac{t}{T_{1/2}}$
$\therefore$ $\frac{N_o}{32}=\frac{N_o}{2^n}$
We get $2^n=32=2^5$
or $n=5$
$⟹t=5T_{1/2}=5\times 2=10hrs$