A radioactive isotope X with half-life `1.5xx10^(9)` yr decays into a stable nucleus Y .A rock sample contains both elements X and Y in the ratio 1 : 15. They age of the rock is

Options

A. `6 xx 10^(9)` yrs
B. `8 xx 10^(9)` yrs
C. `12 xx 10^(9)` yrs
D. `16 xx 10^(9)` yrs

Answer

A

Explanation

Here, `T_(1//2) = 1.5 xx 10^(9)` yrs
`X rarr Y` (stable)
`therefore" "(N)/(N_(0)) = (1)/(15 + 1) = (1)/(16)`
As per the radioactive decay law, `(N)/(N_(0)) = ((1)/(2))^(n)` where n is the number of half lives.
`therefore" "(1)/(16) = ((1)/(2))^(n) rArr ((1)/(2))^(4) = ((1)/(2))^(n) rArr n = 4`.
Let the age of rock be t yrs.
`therefore" "t = n T_(1//2) = (4) xx 1.5 xx 10^(9) = 6 xx 10^(9)` yrs.