A radio isotope `X` with a half-life `1.4 xx 10^9` years decays of `Y` which is stable. A sample of the rock from a cave was found to contain `X` and `Y` in the ratio `1 : 7`. The age of the rock is.

Options

A. `1.96 xx 10^9 years`
B. `3.92 xx 10^9 years`
C. `4.20 xx 10^9 years`
D. `8.40 xx 10^9 years`

Answer

C

Explanation

( c) As `(N_x)/(N_y) = (1)/(7)` (Given)
`rArr (N_x)/(N_x + N_y) = (1)/(8) = ((1)/(2))^3`
`rArr 3 half-lives`
Therefore, age of the rock
`t = 3 T_(1//2) = 3xx 1.4 xx 10^9 yrs = 4.2 xx 10^9 yrs`.