In a certain hypothetical radioactive decay process, species A decays into spesies `B` and species `B` decays into` C` according to the reactions
`{:(A rarr 2B +"particles +energy"),(B rarr 2C+"particles +energy"):}`
The decay constant for species `B` is `lambda_(2)=100 s^(-1)`. Initially, `10^(4)` moles of species of `A` were present while there was no none of `B` and `C`. It was found that species `B` reaches its maximum number at a time `t_(0)=2 1n(10)s`. Calcualte the value of maximum number of moles of `B`.

Answer

`2`

Explanation

`(dN_A)/(dt) = - lambda_(1) N_(A), (dN_(B))/(dt)=2 lambda_(1) N_(A)-lambda_(2)N_(B)`
N_(B) =maximum rArr `(dN_(B))/(dt)=0`
`rArr 2 lambda_(1) N_(A)=lambda_(2)N_(B_(max))`
or `N_(B_(max))=(2 lambda_(1))/(lambda_(2)) N_(A)`
or `N_(B_(max)) =(2 lambda_(1))/(lambda_(2)) M_(0)e^(- lambda_(2)t )=2`.