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MHT CET 2026 (19 Apr, Shift 2) · Law of Radioactive Decay

Law of Radioactive Decay question from MHT CET 2026 (19 Apr, Shift 2)

Q4MHT CET 2026 · 19 APR · SHIFT 2Easy

Law of Radioactive Decay

A radioactive element has rate of disintegration 16,00016{,}000 disintegrations per minute at a particular instant. After four minutes, it becomes 20002000 disintegrations per minute. The decay constant per minute is

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Answer: (c)

  1. RR0=200016000=18=(12)3\frac{R}{R_0} = \frac{2000}{16000} = \frac{1}{8} = \left(\frac{1}{2}\right)^3, so 3 half-lives in 4 min.
  2. T1/2=43 minT_{1/2} = \frac{4}{3}\text{ min}.
  3. λ=ln⁡2T1/2=34ln⁡2=0.75log⁡e2 min−1\lambda = \frac{\ln 2}{T_{1/2}} = \frac{3}{4}\ln 2 = 0.75 \log_e 2\ \text{min}^{-1}.
  4. So the answer is (c) 0.75log⁡e20.75 \log_e 2.
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