Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0 , they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ( 1/ e 2 ) afte

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Two radioactive substances A and B have decay constants 5 λ and λ respectively. At t = 0 , they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be ( 1/ e 2 ) after a time

TestHub · Accepted Answer

At t = 0 , N = N 0 ​ for both the substances A and B ​ ∴ N A ​ = N 0 ​ e − λ A ​ t and N B ​ = N o ​ e − λ B t ​ N B ​ N A ​ ​ = e − λ B ​ t e − λ A ​ t ​ = e ( λ B ​ − λ A ​ ) t = e ( λ − 5 λ ) t = e − 4 λ t = ( e 1 ​ ) 4 λ t ​ As N B ​ N A ​ ​ = ( e 1 ​ ) 2 [According to question] ∴ 4 λ t = 2 or t = 4 λ 2 ​ = 2 λ 1 ​

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