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MHT CET 2026 (13 May, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from MHT CET 2026 (13 May, Shift 2)

Q10MHT CET 2026 · 13 MAY · SHIFT 2Medium

Law of Radioactive Decay

Two radioactive substances AA and BB have decay constant 5λ5\lambda and λ\lambda respectively. At t=0t = 0, they have the same number of nuclei. The ratio of number of nuclei of AA to those of BB will be (1e)2\left(\frac{1}{e}\right)^2 after a time interval

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Answer: (d)

  1. NANB=N0e−5λtN0e−λt=e−4λt\frac{N_A}{N_B} = \frac{N_0 e^{-5\lambda t}}{N_0 e^{-\lambda t}} = e^{-4\lambda t}.
  2. e−4λt=e−2⇒4λt=2⇒t=12λe^{-4\lambda t} = e^{-2} \Rightarrow 4\lambda t = 2 \Rightarrow t = \frac{1}{2\lambda}.
  3. So the answer is (d) 12λ\frac{1}{2\lambda}.
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