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. `19.6 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

`tau_(X)=1.4 xx 10^(9)` years
`N_(X)/N_(Y)=1/7`
`(N_(X))/(N_(X) + N_(Y)) =1/8 =(1/2)^(3) rArr n=3`
Total time `t=ntau_(x)=3 xx 1.4 xx 10^(9)`
`=4.2 xx 10^(9)` years.