A radioactive sample has a mass m, decay cosntant `lambda`, and molecular weight M. If the Avogadro number is `N_A`, then
(a) find the initial number of neclei present, (b) find the number of deacyed nuceli after a time t, (c ) find the activity of the sample after a time t,

Explanation

(a) The initial number of nuclei is `N_(0) =m(N_(A))/(M)`
(b) The number of undecayed nuclei after a time t is
`N=N_(0) e^(- lambda) =(m(N_(A))/(M)) e^(- lambda `t`)`
Therefore, the number of decayed nuclei is
`N' =N_(0) - N= (M(N_(A))/(M))(1-e^(_(lambda t))`
(c ) The activity of the sample is `A=A_(0) e^(- lambda t)=lambda N_(0) e^(-lambda t)`
`A=((m N_(A) lambda)/(M)) e^(-lambda t)`