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 :
λB=λG/3
λB=λG/2
λB=2λG
λB=3λG
A
λB=λG/3
B
λB=2λG
C
λB=λG/2
D
λB=3λG
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Solution
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The correct option is DλB=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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