Particle Spin
By the early 1920s, scientists had developed a reasonably satisfactory model of the atom. That model required three quantum numbers in order to explain the location and properties of the electrons in an atom. At this point, however, there remained a small number of observed properties that could not be explained by means of this model. For example, the number of spectral lines observed for an element was always twice what it ought to be, as predicted by the model.
In 1925, Wolfgang Pauli announced a method for dealing with this problem. He suggested adding a fourth quantum number to those already used in the atomic model. This new quantum number, he said, could have only two possible values. The inclusion of this new factor in existing equations, Pauli was able to show, explained the observed properties of spectral lines and resolved other remaining empirical difficulties. The only problem was that Pauli had little or no idea as to what physical meaning this new quantum number had. He had suggested it primarily because it made his equations turn out correctly!
At nearly the same time that Pauli was working on his theoretical model, two Dutch graduate students, Samuel Goudsmit and George Uhlenbeck, were attacking the problem of spectral line doubling from an experimental standpoint. Eventually, the two researchers realized that line doubling could be explained if the electron were considered to be a particle that was spinning on its own axis. They suggested that the electron have two possible spin directions, clockwise and counter-clockwise. They assigned the numerical values of +1/2 and-1/2 to the two possible spin directions. These two options, Goudsmit and Uhlenbeck pointed out, were comparable to the double-valued factor proposed by Pauli.
As fortunate as the Goudsmit-Uhlenbeck discovery was, yet another problem remained. There was no sound theoretical reason to explain why an electron would spin. This problem was attacked by Paul Dirac in 1928. Dirac began by re-working Erwin Schrödinger's wave equation and introducing relativistic corrections (which Schrödinger himself had not done). As he developed these revised equations, he found that they predicted that electrons exist in two energy states that can be represented with angular momenta of +[frac12] or-[frac12]. That is, a set of equations correctly representing the energy states of an electron require that it have the property of spin observed by Goudsmit and Uhlenbeck and predicted by Pauli.
Over time, it has become apparent that all fundamental particles have the property of spin. Some particles, like the proton, neutron, muon, and neutrino also have spins of +[frac12] or-[frac12]. Other particles have different spins. For example, the photon and pi meson have spins of zero, while the rho particle and the psi/J (J/) particle have spins of 1 and the particle has a spin of 3/2.
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