Q. Half-life of radioactive sample, when activity of material initially was 8 counts and after 3 h it becomes 1 count, is
A) 2h
B) 1h
C) 3h
D) 4h
Explanation
(b) Here $A_{0}\ = \ 8$ counts, $A =$1 counts $t =$3h.
$\ \ \ \ \ \ \ \ \ \ \ \frac{A}{A_{0}} = \left( \frac{1}{2} \right)^{n}$
$\Rightarrow \ \ \ \ \ \ \ \ \frac{1}{8} = \left( \frac{1}{2} \right)^{n}$
or $\left( \frac{1}{2} \right)^{3} = \left( \frac{1}{2} \right)^{n} \Rightarrow n = 3$
So, $T_{1/2}\ = \ \frac{t}{n}\ = \ \frac{3}{3} = \ 1h$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.