Q. The half life of a radioactive isotope $X$ is 50 years. It decays to another element $Y$ which is stable. The two elements $X$ and $Y$ were found to be in the ratio of 1:16 in a sample of a given rock. The age of the rock was estimated to be
A) 100 years
B) 150 years
C) 200 years
D) 250 years
Explanation
(c) After $t$ second fractional amount of $X$ left is $\frac{1}{16}$ or $\left( \frac{1}{2} \right)^{4}$
$\therefore t = 4 \times T_{1/2} = 4 \times 50 = 200\ years$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.