radioactivity and law of decay questions with solutions

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• NumericmediumNuclear physicsradioactivity and law of decay

  A radioactive isotope A decays into radioactive isotope B, which then decays into stable isotope C. Initially the sample contains 2000 nuclei of A and no B or C. The half-life of A is 2 h and the half-life of B is 4 h. Find the number of B nuclei present after 4 h.

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• NumericmediumNuclear physicsradioactivity and law of decay

  The measured total binding energy of a nucleus ᴬZX is 492 MeV. The total binding energy of the isotope (A-1)ZX obtained by removing one neutron is 484 MeV. If the neutron separation energy is N MeV, find N.

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• NumericmediumNuclear physicsradioactivity and law of decay

  Two radioactive samples X and Y initially have activities 800 Bq and 100 Bq. Their half-lives are 2 h and 6 h respectively. After how many hours will their activities become equal?

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• MCQmediumNuclear physicsradioactivity and law of decay

  A radioactive material has activity 5×10¹² Bq. Each disintegration releases 4 MeV of energy and all of that energy is absorbed within the sample. Take 1 eV = 1.6×10⁻¹⁹ J. The thermal power generated is:

  Options

  • Option A

    0.32 W

  • Option B

    1.6 W

  • Option C

    3.2 W

  • Option D

    32 W

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• MCQmediumNuclear physicsradioactivity and law of decay

  Which of the following represents the correct β⁻ decay of a neutron?

  Options

  • Option A

    n → p + e⁻ + ν

  • Option B

    n → p + e⁺ + ν̄

  • Option C

    n → p + e⁺ + ν

  • Option D

    n → p + e⁻ + ν̄

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  JEE Mains 2025 28 Jan Morning Shift

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• NumericmediumNuclear physicsradioactivity and law of decay

  A heavy nucleus of mass number 240 has binding energy per nucleon 7.6 MeV. It fissions into two fragments of mass numbers 100 and 140, whose binding energies per nucleon are 8.5 MeV and 8.3 MeV respectively. Neglect any emitted neutrons. If the energy released is N MeV, find N.

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• MCQeasyNuclear physicsradioactivity and law of decay

  A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of 2:1. After disintegration they will move :-

  Options

  • Option A

    In opposite directions with speed in the ratio of 1:2 respectively

  • Option B

    In opposite directions with speed in the ratio of 2:1 respectively

  • Option C

    In the same direction with same speed.

  • Option D

    In opposite directions with the same speed.

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• Multi-correctmediumNuclear physicsradioactivity and law of decay

  Nucleus X has A = 40 and total binding energy 336 MeV. Nucleus Y has A = 56 and total binding energy 492.8 MeV. Nucleus Z has A = 240 and total binding energy 1824 MeV. Which statements are correct?

  Select all that apply

  • Option A

    BE ÷ A for X is 8.4 MeV

  • Option B

    BE ÷ A for Y is 8.8 MeV

  • Option C

    BE ÷ A for Z is 7.6 MeV

  • Option D

    Among the three nuclei, Z is the most tightly bound per nucleon

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• Multi-correctmediumNuclear physicsradioactivity and law of decay

  A radioactive nucleus has decay constant λ. Which statements are correct?

  Select all that apply

  • Option A

    The probability of survival up to time t is exp(-λt)

  • Option B

    The probability of decay before time t is 1-exp(-λt)

  • Option C

    If the nucleus has survived up to some instant, the probability that it decays during a very small following interval dt is approximately λdt

  • Option D

    The probability per unit time of decay increases continuously as the nucleus becomes older

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• NumericmediumNuclear physicsradioactivity and law of decay

  A radioactive parent nucleus can disappear through two independent decay modes. If only mode 1 existed, the half-life would be 6 h. If only mode 2 existed, the half-life would be 3 h. When both modes are simultaneously possible, find the actual half-life of the parent in hours.

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