Two radioactive nuclei `P` and `Q`, in a given sample decay into a stable nucleus `R`. At time `t = 0`, number of `P` species are `4 N_0` and that of `Q` are `N_0`. Half-life of `P` (for conversation to `R`) is `1mm` whereas that of `Q` is `2 min`. Initially there are no nuclei of `R` present in the sample. When number of nuclei of `P` and `Q` are equal, the number of nuclei of `R` present in the sample would be :

Options

A. `(5N_(0))/(2)`
B. `2N_(0)`
C. `3N_(0)`
D. `(9N_(0))/(2)`

Answer

D

Explanation

`(N_(0))_(P) = 4N_(0) , (N_(0))_(Q)= N_(0)`
`(T_(1//2))_(P) = 1"min" , (T_(1//2))_(Q)= 2`min
Given,
`(4N_(0))/(2^(t(T_(1//2))_(P)))= (N_(0))/((2)^(t//(T_(1//2))Q)) and N_(P)= (N_(0))/(4)`
Number of nuclei of R
`=(4N_(0)- (N_(0))/(4)) + (N_(0) - (N_(0))/(4)) = (9N_(0))/(2)`