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 Bohr.s postulation of angular momentum
`mvr = (nh)/(2pi) " or " 2pi r = n h/(mv) " " (i)`
According to de Broglie equation, `lambda = h/(mv) " " …..(ii)`
From (i) and (ii) we get
`2 pi r = n lambda`
Thus, the circumference `(2 pi r)` of Bohr orbit for H-atom is an integral multiple of de Broglie wavelength.