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Rutherford's Set up and Predictions

The activity ...

Question

The activity of a radioactive sample is $A_{1}$ at time $t_{1}$ and $A_{2}$ at time $t_{2}$ . If $T_{a v}$ is the average life time of the radioactive sample, then the number of atoms that decay during interval $(t_{2} - t_{1})$

A

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B

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C

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D

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Solution

The correct option is B

$A c t i v i t y, A = λ N \Rightarrow A_{1} = λ N_{1} = \frac{1}{T_{a v}} N_{1}; A_{2} = \frac{N_{2}}{T_{a v}} ∴ (N_{1} - N_{2}) = (A_{1} - A_{2}) T_{a v}$

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