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Question

The angular momentum of an electron in a Bohr's orbit of hydrogen atom is 4.218×1034 kgm2s1. Calculate the wavelength of the spectral line emitted, when electrons falls from this level to the next lower level.

A
1.876×104 cm
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B
1.876×104 m
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C
1.786×104 cm
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D
1.786×104 m
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Solution

The correct option is A 1.876×104 cm
Angular momentum of an electron in a Bohr's orbit of H-atom.
mvr=nh2π
4.218×1034=n×6.626×10342×227
n=4.218×1034×2×226.626×1034×7=4
Now,
ν=1λ=109678(1n211n22) cm1
The spectral lines when electron falls from 4th level to 3rd level,
1λ=109678(132142) cm1
1λ=109678(1699×16) cm1
1λ=109678(79×16) cm1
λ=9×16109678×7=1.876×104 cm

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