Dirac Equation Solves Spin
When the idea of electron spin was first introduced in 1925, even Wolfgang Pauli had trouble accepting Ralph Kronig's model. The problem was not that a rotating charged particle would have given rise to a magnetic field but that the electron was so small that the equatorial speed of the electron would have to be greater than the speed of light for the magnetic moment to be of the observed strength.
In 1930, Paul Dirac developed a new version of the Wave Equation which was relativistically invariant (unlike Schrödinger's one), and predicted the magnetic moment correctly, and at the same time treated the electron as a point particle. In the Dirac equation all four quantum numbers including the additional quantum number, s arose naturally during its solution.
Read more about this topic: Spin Quantum Number
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