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. 200 yr
B. 250 yr
C. 100 yr
D. 150 yr

Answer

A

Explanation

(a) We know that
`(N)/(N_0) = ((1)/(2))^(t//t_1//2) rArr (1)/(16) = ((1)/(2))^(t//50)`
`t = 4 xx 50 = 200 yr`.