The Pauli Exclusion Principle, formulated by Wolfgang Pauli in 1925, is a fundamental rule in quantum physics which states that no two fermions (particles with half-integer spin, like electrons, protons, and neutrons) can occupy the same quantum state at the same time within a given quantum system.

In the context of electrons in an atom, each electron is described by a unique set of four quantum numbers:

1. Principal quantum number (n) – energy level,
2. Angular momentum quantum number (l) – shape of orbital,
3. Magnetic quantum number (mₗ) – orientation of orbital,
4. Spin quantum number (mₛ) – spin direction (+½ or –½).

According to the Pauli Exclusion Principle, no two electrons in an atom can have all four quantum numbers identical. This is why, for example, an atomic orbital can hold a maximum of two electrons with opposite spins.

This principle explains a wide range of physical phenomena:

• The structure of the periodic table: Electron arrangements are governed by this rule, leading to chemical properties of elements.
• The stability of matter: It prevents all electrons from collapsing into the lowest energy state, maintaining the structure of atoms.
• The behavior of white dwarfs and neutron stars: In these extreme objects, the pressure resisting gravitational collapse is due to the Pauli Exclusion Principle acting on electrons (in white dwarfs) or neutrons (in neutron stars).

In contrast, bosons (particles with integer spin) are not restricted by this principle and can occupy the same state, allowing phenomena like Bose-Einstein condensation.