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MHT CET 2023 (11 May, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from MHT CET 2023 (11 May, Shift 1)

Q32MHT CET 2023 · 11 MAY · SHIFT 1Easy

Law of Radioactive Decay

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time t=12λt = \frac{1}{2\lambda} is [λ=\lambda = decay constant]

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Answer: (b)

  1. N=N0e−λt⇒N0N=eλtN = N_0 e^{-\lambda t} \Rightarrow \frac{N_0}{N} = e^{\lambda t}.
  2. At t=12λt = \frac{1}{2\lambda}: N0N=e1/2=e\frac{N_0}{N} = e^{1/2} = \sqrt{e}.
  3. So the answer is (b) e\sqrt{\text{e}}.
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