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Law of Radioactivity

The radioacti...

Question

The radioactivity of a sample is $R_{1}$ at a time $T_{1}$ and $R_{2}$ at a time $T_{2}$ . If the half-life of the specimen is $T$ , the number of atoms that have disintegrated in the time $(T_{1} - T_{2})$ is proportional to

(R_{1} T_{1} - R_{2} T_{2})

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(R_{1} - R_{2})

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(R_{1} - R_{2})

T

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(R_{1} - R_{2})

T

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Solution

The correct option is B $(R_{1} - R_{2})$ $T$
Radioactivity at $T_{1}, R_{1} =$ $λ N_{1}$
Radioactivity at $T_{2}, R_{2} =$ $λ N_{2}$
$∴$ Number of atoms decayed in time $(T_{1} - T_{2})$ $= (N_{1} - N_{2})$

$= \frac{(R_{1} - R_{2})}{λ} = \frac{(R_{1} - R_{2}) T}{0.693} \propto (R_{1} - R_{2}) T$

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The radioactivity of a sample is R1 at a time T1 and R2 at a time T2. If the half-life of the specimen is T, the number of atoms that have disintegrated in the time (T1−T2) is proportional to

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The radioactivity of a sample is $R_{1}$ at a time $T_{1}$ and $R_{2}$ at a time $T_{2}$ . If the half-life of the specimen is $T$ , the number of atoms that have disintegrated in the time $(T_{1} - T_{2})$ is proportional to