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Physics - Modern Physics Question with Solution | TestHub

PhysicsModern PhysicsRadioactivityEasy2 minPYQ_2020

PhysicsEasysingle choice

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:

Answer:

Solution:

We know that

$λ_{1} = \frac{\ln 2}{T_{\frac{1}{2}}} = \frac{\ln 2}{2 \times 10^{9}}$

$λ_{2} = \frac{\ln 2}{T_{\frac{1}{2}}} = \frac{\ln 2}{4 \times 10^{9}}$

$N_{x} = N {.e}^{- λ_{1} t} = 0.2 N_{0}$

$N_{y} = N {.e}^{- λ_{2} t} = 0.8 N_{0}$

Solving above equations, we get,

$e^{t (λ_{1} - λ_{2})} = 4 \Rightarrow t = 8 \times 10^{9} years$

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Modern PhysicsSubtopic:Radioactivity

⏱ 2mℹ️ Source: PYQ_2020

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