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Question

How many revolutions does an electron complete in one second in the first orbit of hydrogen atom?

A
6.5 x 1015
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B
6.5 x 1013
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C
1000
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D
6.5 x 1014
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Solution

The correct option is B 6.5 x 1015
The orbital frequency is given by:
ν=v2πr .....................(1)
The velocity of revolving electron is:
v=e22nhϵ0
The radius of an orbit of revolution of electron is:
r=n2h2ϵ0πme2
Using these values in (1) we get:
ν=e22nhϵ02π(n2h2ϵ0πme2)
ν=12π(e22nhϵ0)(πme2n2h2ϵ0)
ν=me44ϵ20n3h3
For n=1,
ν=9.1×1031×(1.6×1019)44×(8.85×1012)2×13×(6.6×1034)3
ν=59.63×1010791179.3×10126
ν=6.539×1015Hz

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