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 $

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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


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