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. `1.96xx10^(9)yr`
B. `3.92xx10^(9)yr`
C. `4.20xx10^(9)yr`
D. `8.40xx10^(9)yr`

Answer

C

Explanation

Here, `X/Y=1/7 :. X/(X+Y)=1/(1+7)=1/8=1/(2^(3))=(1/2)^(3)`
`n=3 or t/T=3`
`t=3T=3xx1.4xx10^(9)yrs =4.20xx10^(9)yrs`