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JEE Main 2019 (10 Apr, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2019 (10 Apr, Shift 2)

Q81JEE Main 2019 · 10 APR · SHIFT 2Medium

Law of Radioactive Decay

Two radioactive substances A and B have decay constants 5λ\lambda and λ\lambda respectively. At t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become (1e)2\left(\frac{1}{e}\right)^2 will be:

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Answer: (c)

  1. NANB=e−5λte−λt=e−4λt\frac{N_A}{N_B} = \frac{e^{-5\lambda t}}{e^{-\lambda t}} = e^{-4\lambda t}.
  2. e−4λt=e−2⇒t=12λe^{-4\lambda t} = e^{-2} \Rightarrow t = \frac{1}{2\lambda}.
  3. So the answer is (c) 12λ\frac{1}{2\lambda}.
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