A radioactive isotope `X` with a half-life of `1.37 xx 109` years decays to `Y` which is stable. A sample of rock from the moon was found to contain both the elements `X` and `Y` which were in the ratio of `1 : 7`. The age of the rock is.

Options

A. `1.96xx10^(8)yr`
B. `3.85xx10^(9)yr`
C. `4.11xx10^(9)yr`
D. `9.59xx10^(14)yr`

Answer

C

Explanation

If in the rack there is no Y element, then the time taken by element X to reduce to `1/8` th the initial value will be equal to
`1/8=((1)/(2))^(n)or n=3`
Therefore, from the beginning three half-life time is spent. Hence, the age of the rock is
`3xx1.37xx10^(9)=4.11xx10^(9)yr`