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The activity of a sample of a radioactive material is A at tim

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

A_{1} t_{1} = A_{2} t_{2}

A_{1} - A_{2} = t_{2} - t_{1}

A_{2} = A_{1} e^{(t_{1} - t_{2}) / T}

A_{2} = A_{1} e^{(t_{1} / t_{2}) / T}

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Updated on: Feb 1, 2023

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The activity of a sample of a radioactive material is

A

at time

t_{1}

and

A_{2}

at time

t_{2} (t_{2} > t_{1}) .

If its mean life is

T

, then

5 mins ago

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5 mins ago

Text solutionVerified

A = A_{0} e^{- λ t} = A_{0} e^{- t / τ};

where

τ =

mean life
So

A_{1} = A_{0} e^{- t_{1} / T}

\Rightarrow A_{0} = \frac{A _{1}}{e ^{- t / T}} = A_{1} e^{t_{1} / T}

∴ A_{2} = A_{0} e^{- t / T} = (A_{1} e^{t_{1} / T}) e^{- t_{2} / T}

\Rightarrow A_{2} = A_{1} e^{(t_{1} - t_{2}) / T}

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Question Text	The activity of a sample of a radioactive material is $A$ at time $t_{1}$ and $A_{2}$ at time $t_{2} (t_{2} > t_{1}) .$ If its mean life is $T$ , then
Updated On	Feb 1, 2023
Topic	Nuclei
Subject	Physics
Class	Class 12
Answer Type	Text solution:1 Video solution: 4
Upvotes	366
Avg. Video Duration	10 min

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

Text solutionVerified

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