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. `3.0xx10^(9)yr`
B. `4.5xx10^(9)yr`
C. `6.0xx10^(9)yr`
D. `9.0xx10^(9)yr`

Answer

C

Explanation

Initially whole isotope was X `" "[thereforeX:Y=1:15]`
i.e., `N_(0)=1+15=16` and after decaying into Y
`implies"We have",N=N_(0)e^(-lamdat)implies1=16e^((0.693)/(15xx10^(9))xxt)`
`implies " " 1n ((1)/(16))=e^((1n2)/(t//2))`
`implies "The age of the rck,"t=6.00xx10^(9)yr`
So, to convert 16 to 1, a four half-lives is required.