Q. A count rate meter shows a count of 240 per minute from a given radioactive source. One hour later the meter shows a count rate of 30 per minute. The half-life of the source is
A) $120\ min$
B) $80\ min$
C) $30\ min$
D) $20\ min$
Explanation
(d) $A = A_{0}\left( \frac{1}{2} \right)^{n} \Rightarrow 30 = 240\left( \frac{1}{2} \right)^{n} \Rightarrow \left( \frac{1}{2} \right)^{3} = \left( \frac{1}{2} \right)^{n} \Rightarrow n = 3$
$\therefore\frac{t}{T_{1/2}} = 3 \Rightarrow T_{1/2} = \frac{t}{3} = \frac{1}{3}hr = 20\ min$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.