Radioactive material A has decay constant 8λ and material B has decay constant λ Initially, they have same number of nuclei. After what time, the ratio of number of nuclei of material B to that A will be 1e?

(a) 1λ

(b) 17λ

(c) 18λ

(d)19λ

(b) Let initial number of nuclei in A and B is NO

Number of nuclei of A after time t is 

               NA=N0e-8λt                          ...(i)

Similarly, number of nuclei of A after time t is   

             NB=N0e-λt                          ...(ii)

It is given that 

NANB=1e                    NB>NA

Now,from Eqs.(i)  and (ii)

e-Bλte-λt=1e

Rearranging 

        e-1=e-7λt      7λt=1

    Time (t)=17λ

 

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