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JEE Main 2021 (20 Jul, Shift 1) · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2021 (20 Jul, Shift 1)

Q72JEE Main 2021 · 20 JUL · SHIFT 1Difficult

Law of Radioactive Decay

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains? (Take ln 3 = 1.1)

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Answer: (a)

  1. For two simultaneous decay modes: λ=λ1+λ2=ln⁡21400+ln⁡2700=3ln⁡21400\lambda = \lambda_1 + \lambda_2 = \dfrac{\ln 2}{1400} + \dfrac{\ln 2}{700} = \dfrac{3\ln 2}{1400}
  2. N=N03⇒t=ln⁡3λ=1.1×14003×0.693N = \dfrac{N_0}{3} \Rightarrow t = \dfrac{\ln 3}{\lambda} = \dfrac{1.1 \times 1400}{3 \times 0.693}
  3. t≈740t \approx 740 years
  4. So the answer is (a) 740 years.
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