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When was the fact that a spin could only have values $S = n/2$? I cannot find any source that says when.

The Bosco
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The experiment of Stern and Gerlach showed that the spin of atomic silver was 1/2. This experiment was "simplified" by Phipps and Taylor to hydrogen atoms so as to eliminate any possible ambiguities on the spin-1/2 nature of the electron.

ZeroTheHero
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