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Heisenberg's Uncertainty Principle

The half life...

Question

The half life of a radioactive sample is $T$ . If the activities of the sample at time t $_{1}$ and t $_{2}$ ( $t_{1} < t_{2}$ ) are $R_{1}$ and $R_{2}$ respectively, then the number of atoms disintegrated in time $t_{2} - t_{1}$ is proportional to

(

R_{1}

R_{2}

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(

R_{1}

R_{2}

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\frac{R_{1} R_{2}}{R_{1} + R_{2}} T

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\frac{R_{1} + R_{2}}{T}

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Solution

The correct option is B ( $R_{1}$ - $R_{2}$ )T
Activity of a radioactive sample is given as $a = λ N$

Activity at time $t_{1}$ $R_{1} = λ N_{1}$

Activity at time $t_{2}$ $R_{2} = λ N_{2}$

Then, the number of atoms disintegrated in time $t_{2} - t_{1}$ is $N_{1} - N_{2} = \frac{R_{1}}{λ} - \frac{R_{2}}{λ}$

Half life time period is: $T_{\frac{1}{2}} = \frac{ln 2}{λ}$

$N_{1} - N_{2} = (R_{1} - R_{2}) \frac{T}{ln 2}$

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The half life of a radioactive sample is $T$ . If the activities of the sample at time t $_{1}$ and t $_{2}$ ( $t_{1} < t_{2}$ ) are $R_{1}$ and $R_{2}$ respectively, then the number of atoms disintegrated in time $t_{2} - t_{1}$ is proportional to