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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:

λB=λG/3

λB=2λG

λB=3λG

λB=λG/2

Solution:

The correct option is D λB=3λG
de- Broglie wavelength λ=h/mv
By conservation of angular momentum, mvr=nh/2π
h/mv=2πrn/n
λ=2πr
r=a₀n²/Z
λ=2πa₀n/Z
As the atom is hydrogen Z=1
λB=2πa₀(3)/1
λG=2πa₀(1)/1
λB=3λG