The rate at which a particular decay process occurs in a radio active sample, is proportional to the number of radio active nuclei present. If N is the number of radio active nuclei present at some instant, the rate of change of N is `(dN)/(dt) = - lambdaN`.

Consider radioavtive decay of A to B which may further decay, either to X or to Y, `lambda_(1),lambda_(2)` and `lambda_(3)` are decay constants for A to B decay, B to X decay and B of Y decay respectively. If at `t = 0` number of nuclei of A, B, `X` and Y are `N_(0), N_(0)`, zero and zero respectively and `N_(1),N_(2),N_(3),N_(4)` are number of nuclei `A,B,X` and `Y` at any intant.
At `t = oo`, which of the following is incorrect ?

Options

A. `N_(2) = 0`
B. `N_(3) = (N_(0)lambda_(2))/(lambda_(2) + lambda_(3))`
C. `N_(4) = (2N_(0)lambda_(3))/(lambda_(2) + lambda_(3))`
D. `N_(3) + N_(4) + N_(1) + N_(2) = 2N_(0)`

Answer

B

Explanation

`N_(2)=0, N_(1)=0` as both will decay completely :
`N_(3)=(2N_(0) lambda_(2))/(lambda_(2)+N_(3))` therefore B is incorrect