Question

Using the equation `N = N_0e^(-lambdat)` obtain the relation between half-life (T) and decay constant (`lambda`) of a radioactive substance.

Answer 1

A relation between half-life (T) and decay constant(`lambda`) of a radioactive substance.

`N = N_o^(e^(-lambdat))`

when t = T

`N = N_o/2`

`:. N_o/2 = N_o^(e^(-lambdaT))`

`1/2 = e^(-lambdaT)`

`2/1 = e^(lambdaT)`

`Log_e 2 = lambdaT`

`T = (log_e 2)/lambda`

`T = 0.6931/lambda`