The half-life of a radioactive isotope `X` is `20` years. It decays to another element `Y` which is stable. The two elements `X` and `Y` were found to be in the ratio of `1 : 7` in a sample of a given rock. The age of the rock was estimated to be.

Options

A. 100 years
B. 40 years
C. 60 years
D. 80 years

Answer

C

Explanation

`X rarr Y` (stable)
`(N_(x))/(N_(y)) = (1)/(7) rArr (N_(x))/(N_(x) + N_(y)) = (N)/(N_(0)) = (1)/(8)`
Now, `N= N_(0) e^(-lamda t)`
`rArr (N_(0))/(8) = N_(0) e^(-lamda t) rArr t= 3 xx 20= 60` years