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

Answer

B

Explanation

Given, `T_(1//2)=50` yrs.
Let number of nuclei in element X be `N_x` and of Y be `N_(y)`.
`N_(x)/N_(y)=1/15`
`N_(x)/(N_(x) + N_(y)) =1/16 =(1/2)^(4)`
In the angle of rock, both X and Y are present.
n=4
Total time taken, `t=nT_(1//2)`
`rArr t= 4 xx 50 = 200` yrs.