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 theory
`mvr=n h/(2pi)`
According to de-Broglie equation
`lambda=h/(mv)`
From eqs (i) and (ii) we have
`2pi r=n (h)/(mv)=n lambda`
`2pir` represents the circumference of the Bohr.s orbit. Thus, for hydrogen atom, circumference of Bohr orbit is an integral multiple of de-Broglie wavelength.