The orbital frequency of an electron in the hydrogen atom is proportional to

Question

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Answer 1

For Bohr's model of hydrogen atom,
$m v r = \frac{n h}{2 π}$
and $\frac{k Z e ^{2}}{r ^{2}} = \frac{m v ^{2}}{r}$
Time period of revolution of electron $= T = \frac{2 π r}{v} = \frac{4 ϵ _{0}^{2} n ^{3} h ^{3}}{m Z ^{2} e ^{4}} \propto n^{3}$
Thus frequency of revolving electron $= \frac{1}{T} \propto n^{- 3}$

Answer 2

For Bohr's model of hydrogen atom,

m v r = \frac{n h}{2 π}

and

\frac{k Z e ^{2}}{r ^{2}} = \frac{m v ^{2}}{r}

Time period of revolution of electron

= T = \frac{2 π r}{v} = \frac{4 ϵ _{0}^{2} n ^{3} h ^{3}}{m Z ^{2} e ^{4}} \propto n^{3}

Thus frequency of revolving electron

= \frac{1}{T} \propto n^{- 3}