ABSTRACT
In section 3.2, we stated the Pauli exclusion principle and it is part of the more general fifth postulate of quantum mechanics. To state this postulate, it is necessary to differentiate between two classes of particles: fermions and bosons. A fermion is a particle for which the spin angular momentum quantum number (called s for an electron and I for a nucleus in section 3.2) has a half-integer value, and a boson is a particle for which the spin angular momentum quantum number has an integer value. Electrons have s = 1/2 and are fermions. The nuclei 1H, 3He, 13C, 15N and 19F with I = 1/2, the nuclei 7Li, 9Be, 11B and 21Ne with I = 3/2, and the 17O nucleus with I = 5/2, are all fermions. In contrast, the nuclei 4He, 12C, 16O, 18O, 20Ne and 22Ne with I = 0, 2H (= D), 6Li and 14N with I = 1, and 10B with I = 3, are all bosons.
It is an empirical fact that the complete internal wavefunction Φ (including spin) of a system of particles is changed in sign by an interchange of two identical fermions in the system but is unchanged by the interchange of two identical bosons. The statistical-mechanics treatment of many-body systems is affected by this (particularly the calculation of entropy) and it is said that fermions obey Fermi–Dirac statistics, whereas bosons obey Bose–Einstein statistics. This is the full statement of the fifth postulate of quantum mechanics.
