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

B

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 = n T _(1//2) = 4 x 50` years = 200 years