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

Explanation

`(N)/(N_(0))=((1)/(2))^(n)`
where n is number of half lives
`therefore" "(1)/(16)=((1)/(2))^(n) or ((1)/(2))^(4)=((1)/(2))^(n) or n = 4`
Let the age of rock be t years.
`because n =(t)/(T_(1//2)) or t =nT_(1//2)=4xx"50 years "="200 years"`