We have two radioactive nuclei A and B. Both convert into a stable nucleus C. Nucleus A converts into C after emitting two α -particles and three β -particles. Nucleus B converts into C after emitting one α -particle and five β -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 1 min and that of B is 2 min. Initially number of nuclei of C are zero.
(i) If atomic numbers and mass numbers of A and B are Z 1 , Z 2 , A 1 and A 2 respectively. Then –
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Ans.
(i)
Sol. Z 1 – 2 × 2 + 3 × 1 = Z 2 – 2 × 1 + 5 × 1 = Z c
⇒ Z 1 – Z 2 = 4
A 1 – 4 × 2 = A 2 – 1 × 4 = A c
⇒ A 1 – A 2 = 4
(ii)
Sol. A : 4N 0 
2N 0 
N 0 
B : N 0 
After 4 minutes N A = N B = 
∴ N C = (4N C + N 0 ) – 
= 
(iii)
Sol. Given R A = R B λ A N A = λ B N B
or 
= N 0 
t = 6 min.
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