Electron Orbit Magnetic Moment

From the classical expression for magnetic moment, m = IA,an expression for the magnetic moment from an electron in a circular orbit around a nucleus can be deduced. It is proportional to the angular momentum of the electron. The effective current is

which can be rewritten as

so that the magnetic moment is

Show quantized form

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Orbital Magnetic Moment

The magnetic moment associated with an electron orbit is given by

Taking into account the quantization of angular momentum for such orbits, the magnitude of the magnetic moment can be written

A unit of magnetic moment called the "Bohr magneton" is introduced here.

The z-component of the magnetic moment is given by

Magnetic quantum numberZeeman effectElectron spin magnetic moment
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