Bateman equation derivation

A general equation for the amount of any nuclide present at a time t after removal from the reactor can be derived by using the Bateman equation (2.17). Consider a time variable t, such that when 0 < t < T the number of atoms of the first member of the chain produced during any interval dt is P dt. The relevant time scale is shown below ... 

Kinetic equations for such a scheme were first derived by Bateman (1910) and Lowry John (1910) and used more specifically by Rutherford, Chadwick Ellis (1930) for the interpretation of their experiments on radioactive decay... 

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