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Half-life from the fraction of a sample left after a given time

This type of question, asked 5 times: 2021 Paper 12, 2021 Paper 15, 27 Jul 2022, 28 Jul 2022, 8 Apr 2023. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 12

    16
    An element has 116th \frac{1}{16}^{\text{th~}} of initial activity in 20sec20sec. Half life of the nuclei is

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  2. Question 2

    2021 Paper 15

    11
    A radioactive nucleus decays so that after 30 years, only 18th \frac{1}{8}^{\text{th~}} of the initial sample is active. What is the half-life of sample?

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  3. Question 3

    27 Jul 2022

    18
    What is the half-life period of a radioactive material if its activity drops to 1/16th 1/16^{\text{th~}} of its initial value in 30 years?

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  4. Question 4

    28 Jul 2022

    108
    A radioactive sample decays 78\frac{7}{8} times its original quantity in 15 minutes. The half-life of the sample is

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  5. Question 5

    8 Apr 2023

    96
    A radio-active material is reduced to 1/81/8 of its original amount in 3 days. If 8×10−3 kg8 \times10^{- 3}\text{ }kg of the material is left after 5 days. The initial amount of the material is

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