Half lives of two isotpers X and Y are know to be `2xx10^(9)` years and `4xx10^(9)` years of these isotopes and currntly the meterical has 20% of X and Y 80% by number on the plabnet. The current age of the planet is

Options

A. `2 xx 10^(9)` years
B. `4 xx 10^(9)` years
C. `6 xx 10^(9)` years
D. `8 xx 10^(9)` years

Answer

D

Explanation

`N=(N_(0))/(2).e^(-lamda_(1)t)=0.2 N_(0)`
`N_(y) =(N_(0))/(2) e^(-lamda_(2) t) = 0.8 N_(0)`
`e^((lamda_(1)-lamda_(2)))=4 rArr t=8xx10^(9)` years