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Scientists prefer to use the term "spin" rather than angular momentum. However, if one were to view an electron as a charged particle, spinning about its axis, but changing the direction of its axis of rotation so rapidly that only a fraction of its angular momentum points in any one direction at any time, then we could say the TOTAL angular momentum is

sqrt(3) h-bar/2

where h-bar is Planck's Constant divided by 2 pi.

and the angular momentum along one specific, external axis would be

plus or minus h-bar over two.

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