A radio nuclide with half life T days emits β-particles of average kinetic energy E joule . This radionuclide is used as source in a machine which generates electric energy with efficiency η. The no.of moles of the nuclide required to generate electrical energy at an initial rate P is ( Avagadro no. =N)
PTηNE ln 2
If n = no. of moles
Rate of decay =λnN=nNln2T
Rate of release of energy =E[dNdt]P=ηE[dNdt]=ηnNEln2T