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A radioactive nucleus X decays to nucleus Y with decay constant x = 0.1s -1 .Y further decays to a stable nucleus Z with a decay constant y = 1 / 30 s -1 . Initially there are only X nuclei and there number is N 0 = 10 20 . Set up the rate equations for the populations of X, Y and Z . The population of Y nucleus as a function is given by N y = N 0 x * ( e - y t - e - x t ) whole divided by x - y . Find the time at which N y is maximum and determine the populations of X and Y at that instant .


A radioactive nucleus X decays to nucleus Y with decay constant x = 0.1s-1.Y further decays to a stable nucleus Z with a decay constant y = 1 / 30 s-1.
Initially there are only X nuclei and there number is N0 = 1020 . Set up the rate equations for the populations of X, Y and Z . The population of Y nucleus as a function is given by Ny  = N0 x  * ( e-y t  - e-xt ) whole divided by x  - y .
Find the time at which Ny is maximum and determine the populations of X and Y at that instant .


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