As we know that the angular momentum of an electron is given by mvr = [nh]/ 2π ……………………………………………. [1]

Where

m = mass of the electron

v = velocity of the electron

r = radius of the orbit

h = Planck’s constant

According to the de Broglie’s Equation:

λ = h/mv

Where,

λ = wavelength of moving particle

m = mass of electron

v= velocity of particle

h= Planck’s constant [6.62× 10^-34]

mv = h / λ

Substituting the above value in [1]

[hr] / λ = [nh]/ 2π

2πr = nλ

Since we know that 2πr is the circumference of a circle, so it is proved in above equation that circumference of the Bohr’s orbit is an integral multiple of the de Broglie wavelength associated with the electron revolving around the orbit.