For the following first order parallel chain reaction. If the half-life of `A` is `25` seconds, then find out the half-life of `B,C` and `D`. Given that the rate of formation of `B` and `C` is `15%` and `30%` of the rate of decomposition of `A` respectively.

Explanation

Let the rate constants for the formation of `B, C` and `D` are `K_(1), K_(2), K_(3)` and overall rate constant is `K`.
`K=K_(1)+K_(2)+K_(3)`
`:' K=0.693/t_(1//2)=0.693/25 s^(-1)`
`:. K_(1)=0.15 K`
`K_(1)=0.15xx0.693/25`
`implies t_((1//2))=0.693/K_(1)=0.693/((0.15xx0.693)/(25))`
`implies t_((1//2))=25/0.15 s=166.66 sec`
Similarly, `t_((1//2)_(2))=25/0.3 s=333.33 sec`
and `t_((1//2)_(3))=25/0.55 s=45.45 sec`