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Show that the decay rate R of a sample o...

Show that the decay rate R of a sample of radionuclide is related to the number of radioactive nuclei N at the same instant by the expression `R=lambdaN`.

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`N=N_0e^(-lambdat)` differentiating both sides we get `(dN)/(dt) =-lambdaN_0e^(-lambdat)=-lambdaN` i.e, decay rate
`R=- (dN)/(dt)=lambdaN`
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