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.

Explanation

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`

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.