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JEE Main 20236 AprilEvening Shift
Exam
JEE Main
Year
2023
Date
6 April
Shift
Evening Shift
Subject
Chemistry
Chapter
Structure of Atom

JEE Main 2023 · 6 April · Evening Shift · Chemistry · Structure of Atom

If the radius of the first orbit of hydrogen atom is a _ 0 , then...

If the radius of the first orbit of hydrogen atom is a0{a}_{0}, then de Broglie’s wavelength of electron in 3rd{3}^{rd} orbit is

Options

  1. Aπa06\dfrac{\pi{a}_{0}}{6}
  2. Bπa03\dfrac{\pi{a}_{0}}{3}
  3. C6πa06\pi{a}_{0}
  4. D3πa03\pi{a}_{0}

Correct answer

C. 6πa06\pi{a}_{0}

Step-by-step solution

According to Bohr's angular momentum equation,

mvr=nh2πmvr = \dfrac{nh}{2\pi}

The angular momentum equation for third orbit is

mvr=3h2πmvr = \dfrac{3h}{2\pi}

2\pir3=hmv\dfrac{2\pir}{3} = \dfrac{h}{mv}

According de Broglie's equation

λ=hmv\lambda = \dfrac{h}{mv}

∴λ=2π9a03=6πa0∴ \lambda = \dfrac{2\pi9{a}_{0}}{3} = 6\pi{a}_{0}

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