Q. The half-life of a radioactive substance is 48 hours. How much time will it take to disintegrate to its $\frac{1}{16}th$ part
A) $12\ h$
B) $16\ h$
C) $48\ h$
D) $192\ h$
Explanation
(d) $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{t/T} \Rightarrow \frac{1}{16} = \left( \frac{1}{2} \right)^{t/48}$
$\Rightarrow \left( \frac{1}{2} \right)^{4} = \left( \frac{1}{2} \right)^{t/48} \Rightarrow t = 192\ hours$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.