Q. From a newly formed radioactive substance (Half life $2\ hours$), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is
A) $6\ hours$
B) $12\ hours$
C) $24\ hours$
D) $128\ hours$
Explanation
(b) $\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} \Rightarrow \frac{1}{64} = \left( \frac{1}{2} \right)^{6} = \left( \frac{1}{2} \right)^{n} \Rightarrow n = 6$
After 6 half lives intensity emitted will be safe
$\therefore$ Total time taken $= 6 \times 2 = 12hrs$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.