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The number of nuclei of a given radioact...

The number of nuclei of a given radioactive sample at timet = 0 and t =T are `N_(0)` and `N_(0)`/n respectively. Obtain an expression for the half-life `(T_(1//2))` of the nucleus in terms of n and T.

Text Solution

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According to the law of radioactive decay ,
`N= N_(0) e^(-lambdat) , N = (N_(0))/(n)` and t =T
`:.` As we know `(N_(0))/(n) = N_(0) e^(-lambdaT)`
`implies n= e^(lambdaT) implies lambda= (log(n))/(T )`
`:.` Half - life ` T_(1//2) = (0.6931)/(lambda) = (0.693T)/("log"(n))`
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