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

Answer

C

Explanation

`{:("P",,"Q"),(4N_0,,N_0),("1min",,"2min"):}`
`T_(1//2)`
`N_P=N_Q`
`(4N_0)/(2^(t//1))=(N_0)/(2^(t//2))`
`4=2^(t//2)`
`2^2=2^(t//2)`
`t/2=2impliest=4min`
Disactive nucleus or Nuclei of R
`=(4N_0-(4N_0)/(2^4))+(N_0-(N_0)/(2^2))`
`=4N_0-N_0/4+N_0-N_0/4=5N_0-N_0/2`
`=9/2N_0`