A radioactive nucleus X decays to nucleus Y whichfurther decays to a stable nucleus Z as given belowX overset(lamda_(x) = 0 , 1 sec^(-1))rarr Y overset(lamday=(1)/30sec^(-1))rarrZ (stable). Initially the sample contains nuclei of X only and its population is N_(0) = 10^(20) . Further the population of Y as function of time is given by N_(Y)(t) = (N_(0)lamdaX)/(lamda_(X) - lamda_(Y)) (e^(-lamda)y^(t) -e^(-lamda)x^(t)) (a) If N_(X),N_(Y) and N_(Z) represent population of X, Y and Z respectively at any instant of time t . Find (dN_Y)/(dt) (b) Find the time at which population of Y is maximum (c) Find the population of X at instant when N_Y is maximum

A radioactive nucleus X decays to nucleus Y whichfurther decays to a s

1.	A radioactive nucleus X decays to nucleus Y whichfurther decays to a stable nucleus Z as given belowX overset(lamda_(x) = 0 , 1 sec^(-1))rarr Y overset(lamday=(1)/30sec^(-1))rarrZ (stable). Initially the sample contains nuclei of X only and its population is N_(0) = 10^(20) . Further the population of Y as function of time is given by N_(Y)(t) = (N_(0)lamdaX)/(lamda_(X) - lamda_(Y)) (e^(-lamda)y^(t) -e^(-lamda)x^(t)) (a) If N_(X),N_(Y) and N_(Z) represent population of X, Y and Z respectively at any instant of time t . Find (dN_Y)/(dt) (b) Find the time at which population of Y is maximum (c) Find the population of X at instant when N_Y is maximum
Answer» Answer :(a) `0.1N_(x)-(N_Y)/30 ` (B) `15 In 3` (c) `(10^(20)SQRT3)/9`

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