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