Fermi–Dirac statistics apply to particles called fermions, which obey the Pauli exclusion principle—meaning no two identical fermions can occupy the same quantum state simultaneously. This restriction leads to unique distribution behaviors, especially at low temperatures.
Fermions have half-integer spin values (e.g., 1/2, 3/2) and include fundamental particles like electrons, protons, neutrons, and quarks. Their statistical behavior is crucial in determining the structure and properties of matter.
Key Features:
- Governed by the Fermi–Dirac distribution function, which describes the probability of a quantum state being occupied by a fermion at a given energy and temperature.
- At absolute zero, fermions fill up energy states starting from the lowest, forming what is called a Fermi sea.
- Lead to the concept of Fermi energy—the highest occupied energy level at zero temperature.
Examples:
- Electron configurations in atoms are determined by Fermi–Dirac statistics and the Pauli exclusion principle.
- White dwarfs and neutron stars are supported against gravitational collapse by degeneracy pressure, a direct consequence of Fermi–Dirac behavior.
- Electrical conductivity in metals is explained using a Fermi gas model of free electrons.
Fermi–Dirac statistics are essential for understanding the quantum behavior of matter, particularly in solid-state physics, nuclear physics, and astrophysics.