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Fraction remaining or decayed after a number of half-lives

This type of question, asked 9 times: 4 May 2023 S2, 15 May 2023 S1, 14 May 2024 S2, 17 Apr 2026 S1, 18 Apr 2026 S2, 19 Apr 2026 S1, 20 Apr 2026 S2, 14 May 2026 S1, 19 May 2026 S1. All 9 questions below, oldest first.

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  1. Question 1

    4 May 2023 S2

    42
    Half-lives of two radioactive elements A and B are 30 minute and 60 minutes respectively. Initially the samples have equal number of nuclei. After 120 minute the ratio of decayed numbers of nuclei of B to that of A will be

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  2. Question 2

    15 May 2023 S1

    24
    A radioactive substance has half-life of 60 minute. During 3 hour, the amount of substance decayed would be

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  3. Question 3

    14 May 2024 S2

    24
    Half life of radio-active element is 1600 years. The fraction of sample remains undecayed after 6400 years will be

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  4. Question 4

    17 Apr 2026 S1

    147
    The half-life of the isotope 11Na24{}_{11}\mathrm{Na}^{24} is 15 hr. How much time does it take for (78)th\left(\dfrac{7}{8}\right)^{th} of a sample of this isotope to decay ?

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  5. Question 5

    18 Apr 2026 S2

    147
    Two samples A and B contain equal amount of radioactive substances. If (18)th\left(\dfrac{1}{8}\right)^{th} of sample A and (1128)th\left(\dfrac{1}{128}\right)^{th} of sample B, remain after 9 hours, then the ratio of half life period of B to that of A is

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  6. Question 6

    19 Apr 2026 S1

    147
    A radioactive sample has half-life of 55 years. The percentage of fraction decayed in 1010 years will be

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  7. Question 7

    20 Apr 2026 S2

    148
    Activity of a radioactive sample decreases to (14)th\left(\dfrac{1}{4}\right)^{th} of its original value in 4 days. Then in 16 days its activity will become xx times the original value. The value of xx is

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  8. Question 8

    14 May 2026 S1

    147
    Activity of a radioactive sample decreases to (13)rd\left(\dfrac{1}{3}\right)^{rd} of its original value in 33 days. Then in 99 days its activity will become

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  9. Question 9

    19 May 2026 S1

    147
    Initially 8×10108 \times 10^{10} atoms are present in a radioactive sample. The half-life of the sample is 1 hour. The number of atoms that will decay in the time interval t=2t = 2 hour to t=5t = 5 hour, is

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