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PhysicsModern PhysicsRadioactivityEasy2 minPYQ_2018

PhysicsEasysingle choice

The activity of a sample of radioactive material is $A_{1}$ at time $t_{1}$ and $A_{2}$ at time $t_{2} (t_{2} > t_{1})$ . If its mean life is $T$ , then

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Solution:

$A_{1} = (\frac{d N}{d t})_{1} = λ N_{1} = λ N_{0} e^{- λ t_{1}} A_{2} = (\frac{d N}{d t})_{2} = λ N_{2} = λ N_{0} e^{- λ t_{2}} ∴ \frac{A _{2}}{A _{1}} = \frac{e ^{- λ t_{2}}}{e ^{- λ t_{1}}} = e^{(t_{1} - t_{2}) λ} \frac{A _{2}}{A _{1}} = e^{(t_{1} - t_{2}) / T} or A_{2} = A_{1} e^{(t_{1} - t_{2}) / T}$

Stream:AIIMSSubject:PhysicsTopic:Modern PhysicsSubtopic:Radioactivity

⏱ 2mℹ️ Source: PYQ_2018

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