A radioactive nucleus A can decay to P or Q with decay constant 2 λ and λ respectively. Another radioactive nucleus B decays into Q with decay constant 3 λ . Initially number of active nuclei of A and

Question

A radioactive nucleus A can decay to P or Q with decay constant 2 λ and λ respectively. Another radioactive nucleus B decays into Q with decay constant 3 λ . Initially number of active nuclei of A and that of B are equal ( N 0 ​ ). If at any later finite instant t > 0 the number of nuclei of A , B , P , Q which are N A ​ , N B ​ , N P ​ , N Q ​ obey N B ​ N A ​ ​ = r 1 ​ , N P ​ N Q ​ ​ = r 2 ​ then what is the value of r 1 ​ + r 2 ​ ?

TestHub · Accepted Answer

For A λ eq ​ = 3 λ . N A ​ = N 0 ​ e − 3 λ t decay of A in P = 3 2 N 0 ​ ​ ( 1 − e − 3 λ t ) , decay of A in Q = 3 N 0 ​ ​ ( 1 − e − 3 λ t ) decay of B in Q = N 0 ​ ( 1 − e − 3 λ t ) . So r 1 ​ = 1 , r 2 ​ = 2 .

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