mechanics that atomic spectra measured in an external magnetic field (see Zeeman effect) cannot be predicted with just , , and . In January 1925, when Ralph Kronig was still a Columbia University PhD student, he first proposed electron spin after hearing Wolfgang Pauli in Tübingen. Werner Heisenberg and Pauli immediately hated the idea. They had just ruled out all imaginable actions from quantum mechanics. Now Kronig was proposing to set the electron rotating in space. Pauli especially ridiculed the idea of spin, saying that "it is indeed very clever but of course has nothing to do with reality". Faced with such criticism, Kronig decided not to publish his theory and the idea of electron spin had to wait for others to take the credit. Ralph Kronig had come up with the idea of electron spin several months before George Uhlenbeck and Samuel Goudsmit. Most textbooks credit these two Dutch physicists with the discovery. Pauli subsequently proposed (also in 1925) a new quantum degree of freedom (or quantum number) with two possible values, in order to resolve inconsistencies between observed molecular spectra and the developing theory of quantum mechanics. Shortly thereafter Uhlenbeck and Goudsmit identified Pauli's new degree of freedom as electron spin. Electron spin A spin-1/2 particle is characterized by an angular momentum quantum number for spin s of 1/2. In solutions of the Schrödinger-Pauli equation, angular momentum is quantized according to this number, so that total spin angular momentum The hydrogen spectrum fine structure is observed as a doublet corresponding to two possibilities for the z-component of the angular momentum, where for any given direction z: whose solution has only two possible z-components for the electron. In the electron, the two different spin orientations are sometimes called "spin-up" or "spin-down". The spin property of an electron would give rise to magnetic moment, which was a requisite for the fourth quantum number. The electron spin magnetic moment is given by the formula: where is the charge of the electron is the Landé g-factor and by the equation: where is the Bohr magneton. When atoms have even numbers of electrons the spin of each electron in each orbital has opposing orientation to that of its immediate neighbor(s). However, many atoms have an odd number of electrons or an arrangement of electrons in which there is an unequal number of "spin-up" and "spin-down" orientations. These atoms or electrons are said to