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.

Explanation

We know that,
`(0.693)/(t_(1//2)) = (2.303)/(t_("age")) log ((N_(0))/(N))`
`(0.693)/(1.37 xx 10^(9)) = (2.303)/(t_("age")) log_(10) ((1 + 7)/(1))`
`:. T_("age") = 4.11 x 10^(9)` years