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

Answer

C

Explanation

Fraction of nuclei remaining
`(1)/(16) = ((1)/(2))^(t//T_(1//2)) rArr 4= (t)/(T_(1//2)) rArr t= 4 xx 50 = 200` years