Half lives of two isotopes X and Y of a material are known to be `2 xx 10^(9)` years and `4 xx 10^(9)` years respectively. If a planet was formed with equal number of these isotopes, then the current age of planet, given that currently the material has 20 % of X and 80 % of Y by number, will be

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