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Show that the circumference of the Bohr orbit for the hydrogen atom is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.

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According to de Broglie equation
`lambda=h/("mu")`
de-Broglie point out such closed orbits can exist only when the circumference of orbit equals to an integral multiple of the wavelength of electron as shown in figure.
i.e. , `2pir=nlambda`
image
Subtitute `lambda` from de Broglie equation
`2pir=nh/("mu")` or `"mur"=nh/(2pi)`
i.e., angular momentum is quantised for closed orbits. There is a stationary wave system for the de-Broglie waves for an electron in that orbit and the orbit must contain a whole number of electron waves as shown in figure. Clearly indicates `3` waves in third obit, `6` waves in sixths orbit and so on.

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