We have two radioactive nuclei `A` and `B`. Both convert into a stable nucleus `C`. Nucleus `A` converts into `C` after emitting two two `alpha`-particles and three `beta`-particles. Nucleus `B` converts into `C` after emitting one.
`alpha`-particle anf five `beta`-particles. A time `t = 0`, nuclei of `A` are `4N_(0)` and that of `B` are `N_(0)`. Half-life of `A`(into the conversion of `C`) is `1min` and that of `B` is `2min`. Initially number of nuclei of `C` are zero.
If atomic numbers and mass numbers of `A` and `B` are `Z_(1),Z_(2),A_(1)` and `A_(2)` respectively. Then

Options

A. `Z_(1)-Z_(2)=4`
B. `A_(1)-A_(2)=4`
C. both (a) and (b) are correct
D. both (a) and (b) are wrong

Answer

C

Explanation

For `A rarr C, A_(Z_(1))^(A_(1))rarrC_(Z_(1-3))^(A_(1-8))+2_(2)He^(4)+3_(-1)e^(0)`
For `B rarrC, A_(Z_(2))^(A_(2))rarrC_(Z_(2)+3)^(A_(2)-8)+_(2)He^(4)+5_(-1)e^(0)`
Hence `A_(1)-8=A_(2)-4` and `z_(1)-3=z_(2)+3`