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

Answer

B

Explanation

Half-life of `X rArr T_(X)=20` years
`underset(1)overset("Active")X underset(" ")to underset(7)overset("Stable")Y`
`(N)/(N_(0))=(1)/(1+7)=(1)/(8)=(1)/(2^(n))=(1)/(2^(3))`
`n=3=(t)/(T)=(t)/(20)`
`t=60` years.