, the magnetic dipole moment is given by Here is the orbital angular momentum, , , and are the principal, azimuthal, and magnetic quantum numbers respectively. The component of the orbital magnetic dipole moment for an electron with a magnetic quantum number ℓ is given by History The electron magnetic moment is intrinsically connected to electron spin and was first hypothesized during the early models of the atom in the early twentieth century. The first to introduce the idea of electron spin was Arthur Compton in his 1921 paper on investigations of ferromagnetic substances with X-rays. In Compton's article, he wrote: "Perhaps the most natural, and certainly the most generally accepted view of the nature of the elementary magnet, is that the revolution of electrons in orbits within the atom give to the atom as a whole the properties of a tiny permanent magnet." That same year Otto Stern proposed an experiment carried out later called the Stern–Gerlach experiment in which silver atoms in a magnetic field were deflected in opposite directions of distribution. This pre-1925 period marked the old quantum theory built upon the Bohr-Sommerfeld model of the atom with its classical elliptical electron orbits. During the period between 1916 and 1925, much progress was being made concerning the arrangement of electrons in the periodic table. In order to explain the Zeeman effect in the Bohr atom, Sommerfeld proposed that electrons would be based on three 'quantum numbers', n, k, and m, that described the size of the orbit, the shape of the orbit, and the direction in which the orbit was pointing. Irving Langmuir had explained in his 1919 paper regarding electrons in their shells, "Rydberg has pointed out that these numbers are obtained from the series . The factor two suggests a fundamental two-fold symmetry for all stable atoms." This configuration was adopted by Edmund Stoner, in October 1924 in his paper 'The Distribution of Electrons Among Atomic Levels' published in the Philosophical Magazine. Wolfgang Pauli hypothesized that this required a fourth quantum number with a two-valuedness. Electron spin in the Pauli and Dirac theories Starting from here the charge of the electron is . The necessity of introducing half-integral spin goes back experimentally to the results of the Stern–Gerlach experiment. A beam of atoms is run through a strong non-uniform magnetic field, which then splits into parts depending on the intrinsic angular momentum of the atoms.