Q. The masses of two radioactive substances are same and their half-lives are 1 yr and 2 yr respectively. The ratio of their activities after 4 yr will be
A) 1:4
B) 1:2
C) 1:3
D) 1:6
Explanation
(a) Let initial activity of both substances are same.
$\ \ \ \ \ \ \ \ R = \ R_{0}\left( \frac{1}{2} \right)^{n} = {R_{0}\left( \frac{1}{2} \right)}^{t/t_{1/2}}$
$\therefore\ \ \ \frac{R_{1}}{R_{2}} = \frac{\left( \frac{1}{2} \right)^{4/1}}{\left( \frac{1}{2} \right)^{4/2}} = \frac{\left( \frac{1}{2} \right)^{4}}{\left( \frac{1}{2} \right)^{2}} = \left( \frac{1}{2} \right)^{2}$
$\Rightarrow \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{R_{1}}{R_{2}} = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.