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In atomic physics, the spin quantum number is a quantum number which describes the intrinsic angular momentum of an electron or other particle. The phrase was originally used to describe the fourth of a set of quantum numbers , which completely describe the quantum state of an electron in an atom. The name comes from a physical spinning of the electron about an axis, as proposed by Uhlenbeck and Goudsmit. The value of ms is the component of spin angular momentum parallel to a given direction , which can be either +1/2 or –1/2.
However this simplistic picture was quickly realized to be physically impossible because it would require the electrons to rotate faster than the speed of light. It was therefore replaced by a more abstract quantum-mechanical description. This description technically involves two spin quantum numbers ms and s, where s is related to the magnitude of the electron spin. However s is always +1/2 for an electron, so it is not necessary to include its value in the set of quantum numbers describing the state of each electron in an atom.
At an elementary level, ms is described as the spin quantum number, and s is not mentioned since its value 1/2 is a fixed property of the electron. At a more advanced level where quantum mechanical operators are introduced, s is referred to as the spin quantum number, and ms is described as the spin magnetic quantum number or as the z-component of spin sz.