Magnetic Moment of an Electron

Consider the simplest model of an electron revolving around a proton. The ratio of its circumference to its velocity is the period of its revolution.

The electron's orbital motion creates a current loop, which, in turn, generates a magnetic dipole moment. Now, the product of the current and the orbital area gives the orbital magnetic dipole moment.

The revolving electron also creates an orbital angular momentum equal to the product of the electron's momentum and the orbital radius.

So, the magnetic moment can be expressed in terms of the angular momentum. Considering the electron's negative charge, the magnetic moment is antiparallel to the orbital angular momentum.

Further, the angular momentum is quantized in multiples of the reduced Planck's constant.

So, the magnitude of the electron dipole moment is simplified in terms of the fundamental unit of the dipole moment, known as the Bohr magneton.

This constant has a magnitude of 9.27 X 10^-24 Am².

Similar to the charge quantization, the dipole moment is quantized in terms of the Bohr magneton.