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  4. 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

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

AIPMTAIPMT 2011Nuclei

Solution:

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