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What is spin quantization?

Updated: 12/13/2022
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Electron Spin:

An electron spin s = 1/2 is an intrinsic property of electrons. Electrons have intrinsic angular momentum characterized by quantum number 1/2. In the pattern of other quantized angular momenta, this gives total angular momentum

Spin "up" and "down" allows two electrons for each set of spatial quantum numbers.

The resulting fine structure which is observed corresponds to two possibilities for the z-component of the angular momentum.

This causes an energy splitting because of the magnetic moment of the electron

Two types of experimental evidence which arose in the 1920s suggested an additional property of the electron. One was the closely spaced splitting of the hydrogen spectral lines, called fine structure. The other was the Stern-Gerlach experiment which showed in 1922 that a beam of silver atoms directed through an inhomogeneous magnetic field would be forced into two beams. Both of these experimental situations were consistent with the possession of an intrinsic angular momentum and a magnetic moment by individual electrons. Classically this could occur if the electron were a spinning ball of charge, and this property was called "electron spin."

Quantization of angular momentum had already arisen for orbital angular momentum, and if this electron spin behaved the same way, an angular momentum quantum number s = 1/2 was required to give just two states. This intrinsic electron property

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