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JEE Main 201910 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
10 April
Shift
Evening Shift
Subject
Physics
Chapter
Nuclear Physics

JEE Main 2019 · 10 April · Evening Shift · Physics · Nuclear Physics

Two radioactive substances A and B have decay constants 5λ and λ...

Two radioactive substances AA and BB have decay constants 5λ5\lambda and λ\lambda respectively. Att=0t = 0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become {\left(\dfrac{1}{e}\right)}^{2} will be

Options

  1. A1λ\dfrac{1}{\lambda}
  2. B12λ\dfrac{1}{2\lambda}
  3. C2λ\dfrac{2}{\lambda}
  4. D14λ\dfrac{1}{4\lambda}

Correct answer

B. 12λ\dfrac{1}{2\lambda}

Step-by-step solution

Using the decay equation, N=N0e−\lambdatN = {N}_{0}{e}^{- \lambdat}
For radioactive substance AA, N1=N0e−5\lambdat{N}_{1} = {N}_{0}{e}^{- 5\lambdat} ...........(i)
For radioactive substance BB, N2=N0e−\lambdat{N}_{2} = {N}_{0}{e}^{- \lambdat} ............(ii)
From equation (i) and (ii)
N1N2=e−5\lambdate−\lambdat\dfrac{{N}_{1}}{{N}_{2}} = \dfrac{{e}^{- 5\lambdat}}{{e}^{- \lambdat}}
(1e)2=e−4\lambdat{\left(\dfrac{1}{e}\right)}^{2} = {e}^{- 4\lambdat}
4\lambdat=24\lambdat = 2
Time taken, t=12λt = \dfrac{1}{2\lambda}
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