A radioactive isotope `X` with a half-life of `1.37 xx 109` 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 of `1 : 7`. The age of the rock is.

Options

A. `1.96 xx 10^8 years`
B. `3.85 xx 10^9 years`
C. `4.11 xx 10^9 years`
D. `9.59 xx 10^9 years`

Answer

C

Explanation

( c) If in the rock there is no `Y` element, then the time taken by element `X` to reduce to `(1)/(8) th` the initial value will be equal to `(1)/(8) = ((1)/(2))^n` or `n = 3`
Therefore, from the beginning three half life time is spent. Hence, the age of the rock is
=`3 xx 1.37 xx 10^9 = 4.11 xx 10^9 years`.