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The half -life of a radioactive nucleus ...

The half -life of a radioactive nucleus is 50 days. What is the time interval `(t_2-t_1)` between the time `t_2` when `2/3` of it has decayed and the time `t_1` when `1/3` of it had decayed ?

Text Solution

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From the law of nuclear decay, `N=N_0e^(-lambdat)`
If `1/3`rd of nucleus decays in time `t_1, 1/3N_0=N_0e^(-lambdat_1)` and if `2/3`rd of nucleus decays in time `t_2, 2/3N_0=N_0e^(-lambdat_2)`
`therefore (1/3N_0)/(2/3N_0)=e^(-lambdat_1)/e^(-lambdat_2)` or , `1/2 =e^(-lambda(t_2-t_1))`
or , `lambda(t_2-t_1)`=In2
Putting `lambda="In2"/T_(1//2)` and solving , we get `t_2-t_1 = T_(1//2)` = 50 days
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