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JEE Main 201912 AprilEvening Shift
Exam
JEE Main
Year
2019
Date
12 April
Shift
Evening Shift
Subject
Physics
Chapter
Dual Nature of Matter

JEE Main 2019 · 12 April · Evening Shift · Physics · Dual Nature of Matter

Consider an electron in a hydrogen atom, revolving in its second...

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius 4.65A˚4.65\text{Å} ). The de-Broglie wavelength of this electron is:

Options

  1. A12.9A˚12.9\text{Å}
  2. B6.6A˚6.6\text{Å}
  3. C9.7A˚9.7\text{Å}
  4. D3.5A˚3.5\text{Å}

Correct answer

C. 9.7A˚9.7\text{Å}

Step-by-step solution

According to Bohr’s atomic model
mvr=nh2πmvr = \dfrac{nh}{2\pi}
And the de-Broglie wavelength
λ=hmv\lambda = \dfrac{h}{mv}
From the above two equations we can write, λ=2\pirn\lambda = \dfrac{2\pir}{n}
In the 2nd excited state
λ=2\pir3\lambda = \dfrac{2\pir}{3}
∴λ=23π×4.65Å=9.7Å∴ \lambda = \dfrac{2}{3}\pi \times 4.65Å = 9.7Å
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