Q. A radioactive isotope X with a half-life of $1.37 \times 10^{9}$ years decays to Y which is stable. A sample of rock from the moon was found to contain both the elements $X$ and $Y$ which were in the ratio 1:7. The age of the rock is
A) $1.96 \times 10^{8}years$
B) $3.85 \times 10^{9}years$
C) $4.11 \times 10^{9}years$
D) $9.59 \times 10^{9}years$
Explanation
(c) If in the rock there is no $Y$ element, then the time taken by element $X$ to reduce to $\frac{1}{8}th$ the initial value will be equal to $\frac{1}{8} = \left( \frac{1}{2} \right)^{n}$ or $n = 3$
Therefore, from the beginning three half life time is spent. Hence the age of the rock is
$= 3 \times 1.37 \times 10^{9} = 4.11 \times 10^{9}years$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.