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NEET 2022
Exam
NEET
Year
2022
Subject
Physics
Chapter
Nuclear Physics

NEET 2022 · Physics · Nuclear Physics

At any instant, two elements X_1 and X_2 have same number of...

At any instant, two elements X1X_1 and X2X_2 have same number of radioactive atoms. If the decay constant of X1X_1 and X2X_2 are 10λ10 \lambda and λ\lambda respectively. Then the time when the ratio of their atoms becomes 1e\frac{1}{e} respectively will be:

Options

  1. A111λ\frac{1}{11 \lambda}
  2. B19λ\frac{1}{9 \lambda}
  3. C16λ\frac{1}{6 \lambda}
  4. D15λ\frac{1}{5 \lambda}

Correct answer

B. 19λ\frac{1}{9 \lambda}

Step-by-step solution

By radioactivity law, we have, N=Noe−λt\mathrm{N}=\mathrm{N}_o e^{-\lambda t} (where, the symbols have their usual meanings) Hence, for two elements, N1 N2=Noe−10λt Noe−λt=1e\frac{\mathrm{N}_1}{\mathrm{~N}_2}=\frac{\mathrm{N}_o e^{-10 \lambda t}}{\mathrm{~N}_o e^{-\lambda t}}=\frac{1}{e} Hence, e−9λt=ee^{-9 \lambda t}=e t=19λt=\frac{1}{9 \lambda}
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