Calculate the time taken to decay `100` percent of a radioactive sample in terms of (a) half- life T and
(b) mean-life `T_(av)`

Explanation

We know that `N=N_(0) e^(_lambda t)`, where `lambda =((In 2)/(T)) =(1)/(T_(av))`
Here, `N=(1-eta)N_(0)`
` (1-eta)N_(0)=N_(0) e^(-lambda t)`
`t=(1)/(lambda)1n|(1)/((1-eta))|`
(a) Thus, `t=(T)/(1n2)[1n|(1)/(1-eta)|]=(T)/(0693)In|(1)/(1- eta)|`
`t=T_(av) In|(1)/(1-eta)|`.