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.

Question

Philoid · Accepted Answer

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.