Two radioactive materials X 1 and X 2 have decay constants 6 λ and 3 λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X 1 to that of X

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Two radioactive materials X 1 ​ and X 2 ​ have decay constants 6 λ and 3 λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X 1 ​ to that of X 2 ​ will be e 1 ​ after a time

TestHub · Accepted Answer

The ratio of number of nuclei of X 1 ​ to that of X 2 ​ after time t , N 2 ​ N 1 ​ ​ = e 1 ​ ∴ N 0 ​ e − 3 λ t N 0 ​ e − 6 λ t ​ = e 1 ​ ( ∵ N = N 0 ​ e − λ t ) or e 3 λ t 1 ​ = e 1 ​ or 3 λ t = 1 ∴ t = 3 λ 1 ​

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