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JEE Main 2017 · Law of Radioactive Decay

Law of Radioactive Decay question from JEE Main 2017

Q89JEE Main 2017Medium

Law of Radioactive Decay

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by:

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Answer: (d)

  1. NA=N0e−λtN_A = N_0 e^{-\lambda t}, NB=N0(1−e−λt)N_B = N_0(1 - e^{-\lambda t}).
  2. NBNA=eλt−1=0.3⇒eλt=1.3\frac{N_B}{N_A} = e^{\lambda t} - 1 = 0.3 \Rightarrow e^{\lambda t} = 1.3.
  3. t=ln⁡1.3λ=Tlog⁡1.3log⁡2t = \frac{\ln 1.3}{\lambda} = T\frac{\log 1.3}{\log 2}.
  4. So the answer is (d).
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