A radioactive nucleus `X `decay to a nucleus `Y` with a decay with a decay Concept `lambda _(x) = 0.1s^(-1) , gamma ` further decay to a stable nucleus Z with a decay constant `lambda_(y) = 1//30 s^(-1)` initialy, there are only X nuclei and their number is `N_(0) = 10^(20)` set up the rate equations for the population of `X^9) Y and Z` The population of `Y` nucleus as a function of time is givenby `N_(y) (1) = N_(0) lambda_(x)l(lambda_(x) - lambda_(y))) (exp(- lambda_(y)1)) Find the time at which `N_(y)` is maximum and determine the populastion `X and Y` at that instant.