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

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

MHT CETMHT CET 2010Atoms

Solution:

Time period of electron, $ T=\frac {4 \varepsilon_0^2n^3h^3}{mZ^2e^4} $
$ \therefore T \propto n^3 $
$ \therefore \frac {1}{\text{frequency} \, (f)} \propto n^3 $
or $ f \propto n^{-3} $