A radio nuclide with half-life T days em...

A radio nuclide with half-life `T` days emits `beta`-particles of average kinetic energy `E J`. The radionuclide is used as a source in a machine which generates electric energy with efficiency `25%`. The number of moles of the nuclide required to generate electrical energy at an initial rate `P` is `n=(yTP)/(EN ln(2))` where `'y'` is

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Let 'n' be the number of moles of the ratio nuclide number of nuclei in the nuclide `= n N, lambda=(ln(2))/(T)` ,
Rate of decay `A = lambda(nN)=(Nn ln(2))/(T)`
Rate of release of energy `=AE`
Rate of generate of electrical energy `P= eta AE`
`(25)/(100)(nNE ln(2))/(T) :. n=(4TP)/(NE ln(2))`

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