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Half-life of a radioactive substance is ...

Half-life of a radioactive substance is T. At time t_1 activity of a radioactive substance is `R_1` and at time `t_2` it is `R_2`. Find the number of nuclei decayed in this interval of time.

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The correct Answer is:
A, B
Half-life is given by
`t_(1//2) = (1n2)/(lambda)`
:. `lambda = (1n2)/(t_(1//2))=1n2/T`
Activity `R= lambdaN`
:. `N=R/lambda=(RT)/(1n2)`
When activity is `R_1`, numbers of nuclei are
`N_1 =(R_1T)/(1n2)`
Similarly, `N_2 = (R_2T)/(1n2)`
:. Numbers decayed `=N_1-N_2 = ((R_1-R_2)T)/(1n2)`
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