Q. The radioactivity isotope $X$ with a half-life of $10^{9}$year decays to $Y$ which is stable. A sample of rocks were found to contain both the elements $X$ and $Y$ in the ratio $1:7$. What is the age of the rocks?
A) $2 \times 10^{9}yr$
B) $3 \times 10^{9}yr$
C) $6 \times 10^{9}yr$
D) $7 \times 1^{9}yr$
Explanation
(b) $\frac{N}{N_{0}} = \frac{1}{1 + 7} = \frac{1}{8}$
$\frac{N}{N_{0}} = \left( \frac{1}{2} \right)^{n} = \frac{1}{8}$
$\therefore\ n = 3$
$t = nT = 3 \times 10^{9}\ yr$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.