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Fraction left, or time for a sample or its activity to fall to a fraction, given the half-life

This type of question, asked 7 times: 2021 Paper 20, 29 Jun 2022, 27 Jul 2022, 28 Jul 2022, 29 Jan 2023, 10 Apr 2023, 15 Apr 2023. All 9 questions below, oldest first.

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  1. Question 1

    2021 Paper 20

    2
    There are 101010^{10} radioactive nuclei in a given radioactive element, Its half-life time is 1 minute. How many nuclei will remain after 30 seconds? (2=1.414)(\sqrt{2}= 1.414)

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  2. Question 2

    29 Jun 2022

    118
    The half -life of a radioactive substance is 5 years. After xx years a given sample of the radioactive substance gets reduced to 6.25%6.25\% of its initial value. The value of xx is
  3. Question 3

    29 Jun 2022

    3
    The activity of a radioactive material is 2.56×10−32.56 \times10^{- 3} Ci. If the half life of the material is 5 days, after how many days the activity will become 2×10−5Ci2\times10^{- 5}Ci ?

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  4. Question 4

    27 Jul 2022

    108
    The activity of a radioactive material is 6.4×10−46.4 \times10^{- 4} curie. Its half life is 5 days. The activity will become 5×10−65 \times10^{- 6} curie after:

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  5. Question 5

    28 Jul 2022

    18
    The half-life period of a radioactive substance is 60 days. The time taken for 78\frac{7}{8} th of its original mass to disintegrate will be:

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  6. Question 6

    28 Jul 2022

    22
    A freshly prepared radioactive source of half life 2 hours 30 minutes emits radiation which is 64 times the permissible safe level. The minimum time, after which it would be possible to work safely with source, will be________ hours.
  7. Question 7

    29 Jan 2023

    11
    If a radioactive element having half-life of 30 min⁡30\text{ }\min is undergoing beta decay, the fraction of radioactive element remains undecayed after 90 min⁡90\text{ }\min. will be

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  8. Question 8

    10 Apr 2023

    92
    The half-life of a radioactive substance is TT. The time taken, for disintegrating 78\frac{7}{8} th part of its original mass will be:

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  9. Question 9

    15 Apr 2023

    5
    The half-life of a radioactive nucleus is 5 years, the fraction of the original sample that would decay in 15 years is:

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