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Ratio of the numbers of nuclei of two substances with different half-lives after a time

This type of question, asked 5 times: 2021 Paper 3, 14 Jun 2022, 29 Jul 2022, 29 Jan 2023, 23 Jan 2025. All 5 questions below, oldest first.

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  1. Question 1

    2021 Paper 3

    12
    Two radioactive substances XX and YY originally have N1N_{1} and N2N_{2} nuclei respectively. Half life of XX is half of the half life of YY. After three half lives of YY, number of nuclei of both are equal. The ratio N1 N2\frac{N_{1}}{{\text{ }N}_{2}} will be equal to:

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  2. Question 2

    14 Jun 2022

    116
    A sample contains 10−2 kg10^{- 2}\text{ }kg each of two substances AA and BB with half lives 4 s4\text{ }s and 8 s8\text{ }s respectively. The ratio of then atomic weights is 1:21:2. The ratio of the amounts of A and B after 16 s16\text{ }s is x100\frac{x}{100}. the value of xx is
  3. Question 3

    29 Jul 2022

    119
    Two radioactive materials AA and BB have decay constants 25λ25\lambda and 16λ16\lambda respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time 1aλ\frac{1}{a\lambda}. The value of a is
  4. Question 4

    29 Jan 2023

    91
    Substance AA has atomic mass number 16 and half-life of 1 day. Another substance BB has atomic mass number 32 and half life of 12\frac{1}{2} day. If both AA and BB simultaneously start undergo radio activity at the same time with initial mass 320 g320\text{ }g each, how many total atoms of A and B combined would be left after 2 days.

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  5. Question 5

    23 Jan 2025

    6
    A radioactive nucleus n2n_{2} has 3 times the decay constant as compared to the decay constant of another radioactive nucleus n1n_{1}. If initial number of both nuclei are the same, what is the ratio of number of nuclei of n2n_{2} to the number of nuclei of n1n_{1}, after one half-life of n1n_{1} ?

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