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

Answer

A

Explanation

Since, `N_(X) : N_(Y)= 1:7`
`rArr N_(X): (N_(X) + N_(Y)) = 1: 8`
i.e., `3T_(1//2)` (3 half life)
`therefore` Time `=3 xx 1.4 xx 10^(9) = 4.2 xx 10^(9)` years