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Two radioactive samples with decay constants k times lambda and lambda: time for a given ratio of nuclei

The same question, asked 3 times: 16 May 2023 S2, 21 Apr 2025 S1*, 13 May 2026 S2. Every wording below, oldest first.

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  1. Question 1

    16 May 2023 S2

    37
    Two radioactive substances A and B have decay constants 5λ5\lambda and λ\lambda respectively. At t=0t=0, they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be 1e2\frac{1}{e^2} after a time interval

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  2. Question 2

    21 Apr 2025 S1

    32
    Two radioactive materials A and B having decay constant ' 7λ7\lambda ' and ' λ\lambda ' respectively, initially have same number of nuclei. The time taken to have the ratio of number of nuclei of material B to that of A as ' e ' is

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  3. Question 3

    13 May 2026 S2

    147
    Two radioactive substances AA and BB have decay constant 5λ5\lambda and λ\lambda respectively. At t=0t = 0, they have the same number of nuclei. The ratio of number of nuclei of AA to those of BB will be (1e)2\left(\dfrac{1}{e}\right)^2 after a time interval

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