The half-life of a radioactive isotope `X` is `20 yr`. It decays to another element `Y` which is stable. The two elements `X` and `Y` were found to be in the ratio `1:7` in a sample of given rock. The age of the rock is estimated to be

Options

A. 40 yr
B. 60 yr
C. 80 yr
D. 100 yr

Answer

B

Explanation

Ratio of X and Y =1 :7
`m_(x)/(m_(y))=(1)/(7)" "m_(y)=7m_(x)` Let the initial total mass =m
`implies m_(x)+m_(y)=m`
`implies(m_(y))/(7)+m_(y)=m`
`(8m_(y))/(7)=mimpliesm_(y)=(7)/(8)m`
Only `((1)/(8))th` part remains undisintegrated, number of half-lives involve are three as
`1overset(T_(1//2))to(1)/(2)overset(T_(1//2))to(1)/(4)overset(T_1//2)to(1)/(8)`
So, total time taken to become `(1)/(8)` unstable part
`=3T_(1//2)=3xx20yr=60yr`