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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 $T_{2} - T_{1}$ is proportional to

T_{2} - T_{1} α (R_{1} - R_{2}) T

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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 $T_{2} - T_{1} α (R_{1} - R_{2}) T$
$\begin{matrix} R_{1} = λ N_{1} R_{2} = λ N_{2} \end{matrix}$
Number of atoms disintegrated in time
$\begin{matrix} T_{2} - T_{1} = N_{1} - N_{2} = \frac{R_{1} - R_{2}}{λ} λ = \frac{0.693}{T} T_{2} - T_{1} = \frac{R_{1} - R_{2} \times T}{0.693} T_{2} - T_{1} α (R_{1} - R_{2}) T \end{matrix}$

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The radioactivity of a sample is R1at 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 T2−T1 is proportional to

The correct option is B T2−T1α(R1−R2)TR1=λN1R2=λN2Number of atoms disintegrated in time T2−T1=N1−N2=R1−R2λλ=0.693TT2−T1=R1−R2×T0.693T2−T1α(R1−R2)T

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 $T_{2} - T_{1}$ is proportional to