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JEE Main 2019 (10 Apr, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2019 (10 Apr, Shift 1)

Q82JEE Main 2019 · 10 APR · SHIFT 1Medium

Law of Radioactive Decay

Two radioactive materials A and B have decay constants 10λ\lambda and λ\lambda, respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time:

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Answer: (a)

  1. NANB=e−10λte−λt=e−9λt\frac{N_A}{N_B} = \frac{e^{-10\lambda t}}{e^{-\lambda t}} = e^{-9\lambda t}.
  2. e−9λt=e−1⇒t=19λe^{-9\lambda t} = e^{-1} \Rightarrow t = \frac{1}{9\lambda}.
  3. So the answer is (a) 1/9λ1/9\lambda.
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