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Decay constant or mean life from two activity readings

This type of question, asked 2 times: 2021 Paper 26, 26 Jul 2022. All 2 questions below, oldest first.

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  1. Question 1

    2021 Paper 26

    6
    A radioactive sample is undergoing α\alpha decay. At any time t1t_{1}, its activity is AA and another time t2t_{2}, the activity is A5\frac{A}{5}. What is the average life time for the sample?

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  2. Question 2

    26 Jul 2022

    3
    The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is: (Take log⁡101.88=0.274\log_{10}1.88 = 0.274)

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