A radioactive nucleus n 2 has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n 1 . If initial number of both nuclei are the same, what is the ratio of

Question

A radioactive nucleus n 2 ​ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n 1 ​ . If initial number of both nuclei are the same, what is the ratio of number of nuclei of n 2 ​ to the number of nuclei of n 1 ​ , after one half-life of n 1 ​ ?

TestHub · Accepted Answer

​ N 2 ​ = N 0 ​ e − 3 λ t N 1 ​ = N 0 ​ e − λ t N 1 ​ N 2 ​ ​ = e − 2 λ t t half lifeofN ​ t t = λ ln 2 ​ n ​ 1 2 N 0 ​ ​ = N 0 ​ e − λ t ​ ​ λ t = ln 2 t = λ ln 2 ​ = e − 2 λ λ l n 2 ​ N 1 ​ N 2 ​ ​ = 4 1 ​ ​

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