# How was the value of the electron's spin ($\pm \frac{\hbar}{2}$) first determined?

The value of the electron's spin is $$\pm \frac{\hbar}{2}$$.

In the paper where Pauli introduces his Pauli matrices he already knows the value of spin.

I'd imagine it was through the Ster-Gerlach experiment or through spectral line-splitting, but those would depend on the electron's intrinsic magnetic moment instead of spin, and the magnetic moment to spin ratio is twice the magnetic moment to angular momentum value that would be classically expected.

If that's how it is, then how was it discovered?

• Are you asking about the 1/2 part (vs integral spin) or the exact magnitude in MKS units? Apr 4 '19 at 12:55
• The 1/2 part, since it has the same magnetic moment as if it had spin 1 but g-factor 1. Apr 5 '19 at 2:30