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Activity A = lambda N: compare two samples using half-lives and numbers of nuclei

This type of question, asked 3 times: 12 May 2024 S2, 15 Apr 2026 S1, 15 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    12 May 2024 S2

    24
    Two different radioactive elements with half lives 'T1T_1' and 'T2T_2' have undecayed atoms 'N1N_1' and 'N2N_2' respectively present at a given instant. The ratio of their activities at that instant is

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  2. Question 2

    15 Apr 2026 S1

    147
    Two different radioactive elements with half lives T1T_1 and T2T_2 have undecayed atoms N1N_1 and N2N_2 respectively, present at a given instant. The ratio of their activities at this instant is

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  3. Question 3

    15 May 2026 S1

    147
    A radioactive sample S1S_1 having activity A1A_1 has twice the number of nuclei as another sample of S2S_2 of activity A2A_2. If A2=2A1A_2 = 2A_1 then the ratio of half life of S1S_1 to the half life of S2S_2 is

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