Question

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 $1 : 15$ in a sample of a given rock. The age of the rock was estimated to be

• A. 150 years
• B. 200 years
• C. 250 years
• D. 100 years

Answer 1

Answer: (B)

200 years

Answer 2

$X \rightarrow Y$ $X : Y =1: 15$ A.P. $=\frac{1}{16}=\frac{1}{2^{ n }}$ No. of half life $n =4$ $t = n T _{1 / 2}=4 \times 50=200 \,yr$