The half-life of a radioactive isotope `X` is `50` 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 : 15` in a sample of a given rock. The age of the rock was estimated to be

Options

A. 150 years
B. 200 years
C. 250 years
D. 100 years

Answer

B

Explanation

Let number of atoms in `X = N_(X)`
Number of atoms in Y = `N_(Y)`
By question
`(N_(X))/(N_(Y)) = (1)/(15)`
`therefore` Part of `N_(X) = (1)/(16) (N_(X) + N_(Y)) = (1)/(2^(4)) (N_(X) + N_(Y))`
So , total 4 half lives are passed , so , age of rock is `4 xx 50` = 200 years