The radium and uranium atoms in a sample of uranium mineral are in the ratio of `12.8xx10^(6)`. If half life period of radium is 1620 years , the half life period of uranium will be

Options

A. `45.3xx10^(9)` years
B. `4.53 xx 10^(10)` years
C. `4.53 xx 10^(9)` years
D. `4.53 xx 10^(10)` years

Answer

C

Explanation

According to radioactive equilibrium,
`lambda_(A)N_(A)=lambda_(B)N_(B)`
or `(0.693 xx N_(A))/(t_(1//2)(A))=(0.693xxN_(B))/(t_(1//2)(B))[lambda=(0.693)/(t_(1//2))]`
Where `t_(1//2) (A)` and `t_(1//2) (B)` are half life periods of A and B respectively
`therefore (N_(A))/(t_(1//2)(A))=(N_(B))/(t_(1//2)(B))` or `(N_(A))/(N_(B))=(t_(1//2)(A))`
`therefore` At equilibrium , A and B are present in the ratio of their half lives.
`(1)/(2.8xx10^(6))=(1620)/("Half life of uranium")`
`therefore` Half life of uranium `=2.8xx10^(-6)xx1620`
`=4.53xx10^(9)` years