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Half-life or decay constant from activity readings at two times

This type of question, asked 5 times: 23 Apr 2025 S1, 25 Apr 2025 S1, 26 Apr 2025 S2, 17 Apr 2026 S2, 19 Apr 2026 S2. All 5 questions below, oldest first.

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  1. Question 1

    23 Apr 2025 S1

    10
    The activity of radioactive sample is measured as N0N_{0} counts per minute at time t=0t = 0, and N0e\frac{N_{0}}{e} counts per minute at time t=3t = 3 minute, The activity reduces to half its value in time (in minute)

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  2. Question 2

    25 Apr 2025 S1

    42
    A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is

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  3. Question 3

    26 Apr 2025 S2

    44
    A radioactive element has rate of disintegration 8000 disintegrations per minute at a particular instant. After four minutes it becomes 2000 disintegrations per minute. The decay constant per minute is

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  4. Question 4

    17 Apr 2026 S2

    147
    The activity of a radioactive sample is measured as N0N_0 counts per minute at time t=0t = 0 and N0e\dfrac{N_0}{e} counts per minute at time t=3t = 3 minute. The time (in minute) in which the activity reduces to half the value, is

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  5. Question 5

    19 Apr 2026 S2

    147
    A radioactive element has rate of disintegration 16,00016{,}000 disintegrations per minute at a particular instant. After four minutes, it becomes 20002000 disintegrations per minute. The decay constant per minute is

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