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JEE Main 20209 JanuaryMorning Shift
Exam
JEE Main
Year
2020
Date
9 January
Shift
Morning Shift
Subject
Chemistry
Chapter
Structure of Atom

JEE Main 2020 · 9 January · Morning Shift · Chemistry · Structure of Atom

The de Broglie wavelength of an electron in the 4 ^ th Bohr orbit...

The de Broglie wavelength of an electron in the 4th{4}^{th} Bohr orbit is:

Options

  1. A2πa02\pi{a}_{0}
  2. B4πa04\pi{a}_{0}
  3. C6πa06\pi{a}_{0}
  4. D8πa08\pi{a}_{0}

Correct answer

D. 8πa08\pi{a}_{0}

Step-by-step solution

2\pir=nλ2\pir = n\lambda
2π×n2Za0=nλ2\pi \times \dfrac{{n}^{2}}{Z}{a}_{0} = n\lambda
2π×421a0=nλ2\pi \times \dfrac{{4}^{2}}{1}{a}_{0} = n\lambda
λ=8πa0\lambda = 8\pi{a}_{0}
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