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Question: Answered & Verified by Expert
In \( \mathrm{H} \)-atom, if ' \( \mathrm{x} \) ' is the radius of the first Bohr orbit, de Broglie wavelength of an electron in the \( 3^{\mathrm{rd}} \) orbit is:
ChemistryStructure of AtomJEE Main
Options:
  • A \( 3 \pi \mathrm{x} \)
  • B \( 6 \pi \mathrm{x} \)
  • C \( \frac{9 x}{2} \)
  • D \( \frac{x}{2} \)
Solution:
1067 Upvotes Verified Answer
The correct answer is: \( 6 \pi \mathrm{x} \)

According to the Bohr model, the first radius for hydrogen atom:

r1=0.529A°=x

The third radius of the Bohr model:r3=0.529  n2 A° = 0.52932A°=9x

Hence, the de Broglie wavelength:

λ=2πr3n=2×π×(9x)3=6πx

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