Question

Half lives of two isotopes X and Y of a material are known to be $2\times {10}^9$ years and $4\times {10}^9$ 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

• A. $2\times {10}^9$ years
• B. $4\times {10}^9$ years
• C. $6\times {10}^9$ years
• D. $8\times {10}^9$ years

Answer 1

Answer: (D)

$8\times {10}^9$ years

Given:

$t_X=2\times {10}^9$ Years

$t_Y=4\times {10}^9$ Years

$N_x=\frac{N_0}{2}.e^{-{\lambda }_{1}t}=0.2N_0$........(1)

$N_y=\frac{N_0}{2}.e^{-{\lambda }_{2}t}=0.8N_0$.............(2)

Ratio of both equation

$e^{t({\lambda }_1-{\lambda }_2)}=4\Rightarrow t=8\times {10}^{9}years$