Derive the Bohr angular momentum from de Broglie’s relation

Let us consider an electron revolving around a nucleus of an atom. The wave train formed by it is as shown in figure. Now, for the wave to be in phase, the circumference of the orbit around the nucleus should be an integral multiple of the wavelength of the wave.

2Ωr=nλ,

where r is the radius of the orbit.

=nh/mν (from de Broglie’s equation)

Therefore,

Angular momentum; mνr=nh/2Ω, electron being revolving in nth orbit.

Category: Atomic Structure and Wave Mechanics

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