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

The Bosco
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  • @Spencer That does not have anything to do with the history of spin. – HDE 226868 Dec 10 '16 at 14:39
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Quantization of spin was discovered experimentaly by Stern and Gerlach in 1922. See Wikipedia article "Stern-Gerlach experiment". The correct theoretical model for spin was constructed by Pauli and Dirac in 1928.

Alexandre Eremenko
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  • Although a shout-out to Samuel Goudsmit might also be in order for proposing intrinsic electron spin, not just atomic spin, in 1925 (published in Nature in 1926). – Jon Custer Dec 13 '16 at 18:40