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Question

The de-Broglie wavelength (λB) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (λG) by :
  1. λB=λG/3
  2. λB=λG/2
  3. λB=2λG
  4. λB=3λG

A
λB=λG/3
B
λB=2λG
C
λB=λG/2
D
λB=3λG
Solution
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The correct option is D λB=3λG
de- Broglie wavelength λ=hmv

By conservation of angular momentum, mvr=nh2π

hmv=2πrn

λ=2πrn

r=a0n2Z

λ=2πa0nZ

As the atom is hydrogen Z=1

λB=2πa03Z

λG=2πa0Z

λB=3λG

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