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Radioactive decay by two simultaneous processes (effective half-life)

This type of question, asked 4 times: 2021 Paper 9, 2021 Paper 11, 26 Jun 2022, 30 Jan 2023. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 9

    10
    A radioactive sample disintegrates via two independent decay processes having half-lives T1/2(a)T_{1/2}^{(a)} and T1/2(b)T_{1/2}^{(b)} respectively. The effective half-life T1/2T_{1/2} of the nuclei is:

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  2. Question 2

    2021 Paper 11

    19
    A radioactive material is undergoing simultaneous disintegration into two different products with half-lives 1400 years and 700 years respectively. Find the time taken by the sample to decay to one third of its initial value

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  3. Question 3

    26 Jun 2022

    108
    A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half- life of the nucleus will be:

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  4. Question 4

    30 Jan 2023

    114
    A radioactive nucleus decays by two different process. The half-life of the first process is 5 minutes and that of the second process is 30 s30\text{ }s. The effective half-life of the nucleus is calculated to be α11 s\frac{\alpha}{11}\text{ }s. The value of α\alpha is______