A radio isotope `X` with a half life `1.4xx10^(9)` yr 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. `4.2 xx 10^(9)` years
B. `9.8 xx 10^(9)` years
C. `1.4xx 10^(9)` years
D. `10xx 10^(9)` years

Answer

a

Explanation

At present,
`("Number of K atoms")/("Number of Ar atoms")=(1)/(7)`
Let age of rock be n half-lives of K-nuclides. Then,
`((1)/(2))^(n) =("Number of K-atoms presnet now")/("Number of K-atoms present initially")` =`(1)/(1+7)`
where number of `K` atoms present initallly =Number of K-atoms + Number of Ar atoms present now.
`:. n=3`
So, age of rock is `3` half-lives of K nuclides, i.e., `4.2 xx10^(9)` years .