Atoms And Nuclei Question 363
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
Options:
A) $ 2\times 10^{9}years $
B) $ 4\times 10^{9}years, $
C) $ 6\times 10^{9}years $
D) $ 8\times 10^{9}years $
Show Answer
Answer:
Correct Answer: D
Solution:
- $ N_{x}=\frac{N_{0}}{2}{{e}^{-{\lambda_{1}}t}}=0.2N_{0},N_{y}=\frac{N_{0}}{2}{{e}^{-{\lambda_{2}}t}}=0.8N_{0} $ $ {{e}^{({\lambda_{1}}-{\lambda_{2}})}}=4\Rightarrow t=8\times 10^{9} $ years
