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NEET 2007 (AIPMT) · Law of Radioactive Decay

Law of Radioactive Decay question from NEET 2007 (AIPMT)

Q107NEET 2007 · AIPMTMedium

Law of Radioactive Decay

Two radioactive substances A and B have decay constants 5λ\lambda and λ\lambda respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e)2 after a time interval

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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) 1/2λ1/2\lambda.
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