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JEE Main 2022 (29 Jul, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2022 (29 Jul, Shift 2)

Q50JEE Main 2022 · 29 JUL · SHIFT 2Medium

Law of Radioactive Decay

Two radioactive materials A and B 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 _________.

Numerical answer type. Work it out, then open the answer.

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Answer: 9

  1. NBNA=e−16λte−25λt=e9λt\frac{N_B}{N_A} = \frac{e^{-16\lambda t}}{e^{-25\lambda t}} = e^{9\lambda t}.
  2. e9λt=e⇒t=19λe^{9\lambda t} = e \Rightarrow t = \frac{1}{9\lambda}.
  3. So a=9a = 9.
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