`._(19)^(49)K` isotope of potassium has a half-life of `1.4 xx10^(9)` yr and decays to form stable argon, `._(18)^(40)Ar`. A sample of rock has been taken which contains both potassium and argon in the ratio `1:7`, i.e.,
`("Number of potassium `-14` atoms")/("Number of argon`-40` atoms")=(1)/(2)`
Assuming that when the rock was fromed no argon `-40` was present in the sample and none has escaped subssequently, determine the age of the rock.

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 .