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MHT CET 2021 (22 Sep, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from MHT CET 2021 (22 Sep, Shift 2)

Q67MHT CET 2021 · 22 SEP · SHIFT 2Medium

Law of Radioactive Decay

Two radioactive materials X1X_1 and X2X_2 have decay constants '5λ5\lambda' and 'λ\lambda' respectively. Initially, they have the same number of nuclei. After time 'tt', the ratio of number of nuclei of X1X_1 to that of X2X_2 is 1e\frac{1}{e}. Then tt is equal to

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Answer: (d)

  1. N1N2=e−5λte−λt=e−4λt\frac{N_1}{N_2} = \frac{e^{-5\lambda t}}{e^{-\lambda t}} = e^{-4\lambda t}.
  2. e−4λt=e−1⇒t=14λe^{-4\lambda t} = e^{-1} \Rightarrow t = \frac{1}{4\lambda}.
  3. So the answer is (d) 14λ\frac{1}{4\lambda}.
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