Question

A freshly prepared radioactive source (half life $=4$ hrs) emits radiations of intensity which is $32$ times the permissible level.The minimum time (in hr) after which it would be safe to work with this source is

• A. $4$
• B. $8$
• C. $10$
• D. $20$

Answer 1

The correct option is D $20$

Activity of substance remaining $R=\frac{R_o}{2^n}$
where $n=\frac{t}{T_{1/2}}=\frac{t}{4}$
Permissible level $R=\frac{R_o}{32}$
$\therefore$ $\frac{1}{32}=\frac{1}{2^n}$
Or $2^n=32$
$⟹n=5$
Or $\frac{t}{4}=5$
$⟹t=5\times 4=20$ hrs
Correct answer is option D.