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JEE Main 201815 AprilEvening ShiftOnline
Exam
JEE Main
Year
2018
Date
15 April
Shift
Evening Shift
Mode
Online
Subject
Physics
Chapter
Atomic Physics

JEE Main 2018 · 15 April · Evening Shift · Online · Physics · Atomic Physics

Muon (μ^ -1 ) is negatively charged (|q|=|e|) with a mass m_μ=200...

Muon (μ−1)\left(\mu^{-1}\right) is negatively charged (∣q∣=∣e∣)(|\mathrm{q}|=|\mathrm{e}|) with a mass mμ=200 me\mathrm{m}_\mu=200 \mathrm{~m}_{\mathrm{e}}, where me\mathrm{m}_{\mathrm{e}} is the mass of the electron and e is the electronic charge. If μ−1\mu^{-1} is bound to a proton to form a hydrogen like atom, identify the correct statements (A) Radius of the muonic orbit is 200 times smaller than that of the electron (B) the speed of the μ−1\mu^{-1} in the nnth orbit is 1200\frac{1}{200} times that of the election in the nth orbit (C) The lonization energy of muonic atom is 200 times more than that of an hydrogen atom (D) The momentum of the muon in the nth orbit is 200 times more than that of the electron

Options

  1. A(A), (B), (D)
  2. B(B), (D)
  3. C(C),(D)
  4. D(A), (C), (D)

Correct answer

D. (A), (C), (D)

Step-by-step solution

 (A) Radius of muon = Radius of hydrogen 200 Radius of H atom =r=∈0n2h2πme2 Radius of muon =rμ=∈0n2h2π×200me2rμ=r200\begin{aligned}&\text{ (A) Radius of muon }=\frac{\text{ Radius of hydrogen }}{200}\\ &\text{ Radius of } \mathrm{H} \text{ atom }=r=\frac{\in_0 n^2 h^2}{\pi m e^2}\\ &\text{ Radius of muon }=r_\mu=\frac{\in_0 n^2 h^2}{\pi \times 200 m e^2}\\ &r_\mu=\frac{r}{200} \end{aligned}(B)Velocityrelationgiveniswrong(C)IonizationenergyinB) Velocity relation given is wrong (C) Ionization energy ine^{-} \mathrm{H}atomE=atom E=\frac{+m e^4}{8 \epsilon_0^2 n^2 h^2}Eμ=E_\mu=\frac{200 m e^4}{8 \epsilon_0^2 n^2 h^2}=200E(D)Momentumof200 E (D) Momentum of\mathrm{H}−atommvr=-atom m v r=\frac{n h}{2 \pi}$Hence (A), (C), (D) are correct.
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