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Sub-Atomic Particles

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 speciment is $T$ , the number of atoms that have disintegrated in the time $(T_{2} - T_{1})$ is equal to:

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

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(R_{1} - R_{2})

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

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\frac{(R_{1} - R_{2}) T}{0.693}

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Solution

The correct option is A $(R_{1} T_{1} - R_{2} T_{2})$
Radioactivity of a sample is : $R = λ N$
$R_{1} = λ N_{1}$ and $R_{2} = λ N_{2}$
No. of atoms disintegrated= $N_{1} - N_{2} = \frac{R_{1} - R_{2}}{λ}$
Now, $λ = \frac{I n 2}{T} = \frac{0.693}{T}$
$N_{1} - N_{2} = \frac{T (R_{1} - R_{2})}{0.693}$

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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 speciment is T, the number of atoms that have disintegrated in the time (T2−T1) is equal 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 speciment is $T$ , the number of atoms that have disintegrated in the time $(T_{2} - T_{1})$ is equal to: