Pauli's exclusion principle¶

The Pauli exclusion principle states that in a single atom no two electrons will have an identical set or the same quantum numbers (\(n\), \(l\), \(m_l\), and \(m_s\)). To put it in simple terms, every electron should have or be in its own unique state (singlet state). There are two salient rules that the Pauli Exclusion Principle follows:

• Only two electrons can occupy the same orbital.
• The two electrons that are present in the same orbital must have opposite spins, or they should be antiparallel.

However, Pauli’s Exclusion Principle does not only apply to electrons. It applies to other particles of half-integer spin, such as fermions. It is not relevant for particles with an integer spin, such as bosons which have symmetric wave functions. Moreover, bosons can share or have the same quantum states, unlike fermions. As far as the nomenclature goes, fermions are named after the Fermi–Dirac statistical distribution that they follow. Bosons, on the other hand, get their name from the Bose-Einstein distribution function.