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

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$R_{1} T_{2} - R_{2} T_{1}$

$(R_{1} - R_{2}) T$

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

$R_{1} - R_{2}$

answer is B.

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Detailed Solution

$R_{1} = N_{1} λ$

$R_{2} = N_{2} λ$

$T = \frac{1}{λ}$

$(R_{1} - R_{2}) = (N_{1} - N_{2}) λ$

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

$∴ N_{1} - N_{2} = (R_{1} - R_{2}) T$

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