Question

Suppose the daughter nucleus in a nuclear decay is itself radioactive. If λ_d and λ_m, denote the decay constants of daughter and mother nuclei and N_d and N_m, the numbers of daughter and mother nuclei present at a time, then the number of daughter nuclei becomes constant when 

(a) λ_m N_m = λ_d N_d

(b) λ_m N_d = λ_d N_m

(c) N_m - N_d = λ_m -  λd

(d) N_m + N_d = λ_m +  λd

Answer 1

The correct option is (a) λ_m N_m = λ_d N_d

Explanation:

The number of mother nuclei decaying in a short time interval dt is N_m λ_m dt But death of a mother nucleus implies the birth of a daughter nucleus. 

The number of daughter nuclei decaying in the same time interval is N_d λ_d dt. 

The number of daughter nuclei will remain constant when

N_m λ_m dt  = N_d λ_d dt

λ_m N_m = λ_d N_d