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Alpha Decay

The radioacti...

Question

The radioactivity of a sample is $T_{1}$ at a time $R_{1}$ and at time $T_{2} i s R_{2}$ . If half-life of sample is $T$ , then in time $(T_{2} - T_{1})$ number of decayed atoms is proportional 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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(R_{1} - R_{2}) T

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Solution

The correct option is D $(R_{1} - R_{2}) T$
Radioactivity of sample at time $T_{1}$ is

$R_{1} = λ N_{1}$

Radioactivity of sample at time $T_{2}$ is

$R_{2} = λ N_{2}$

Number of atoms that have disintegrated in the time $(T_{2} - T_{1}) = N_{1} - N_{2}$

$= \frac{R_{1} - R_{2}}{λ}$

$λ = \frac{0.693}{T}$

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

$(T_{2} - T_{1}) \propto (R_{1} - R_{2}) T$

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The radioactivity of a sample is T1 at a time R1 and at time T2 is R2. If half-life of sample is T, then in time (T2−T1) number of decayed atoms is proportional to :

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