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MHT CET 2025 (25 Apr, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from MHT CET 2025 (25 Apr, Shift 1)

Q16MHT CET 2025 · 25 APR · SHIFT 1Medium

Law of Radioactive Decay

A radioactive element has rate of disintegration 9000 disintegration per minute at a particular instant. After two minutes it becomes 3000 disintegration per minute. The decay constant per minute is

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Answer: (a)

  1. R=R0e−λtR = R_0e^{-\lambda t}: 3000=9000 e−2λ3000 = 9000\,e^{-2\lambda}.
  2. e2λ=3⇒λ=12log⁡e3=0.5log⁡e3 min−1e^{2\lambda} = 3 \Rightarrow \lambda = \frac{1}{2}\log_e3 = 0.5\log_e3\text{ min}^{-1}.
  3. So the answer is (a) 0.5log⁡e30.5\log_e3.
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