What is the difference between fermions and bosons?

Fermions are particles with half-integer spin, while bosons have integer spin.

Fermions and bosons are two types of particles that make up the universe. Fermions have half-integer spin, meaning their spin is a multiple of 1/2 (e.g. 1/2, 3/2, 5/2). Examples of fermions include electrons, protons, and neutrons. Fermions obey the Pauli exclusion principle, which states that no two fermions can occupy the same quantum state simultaneously. This is why electrons in an atom must occupy different energy levels.

Bosons, on the other hand, have integer spin, meaning their spin is a multiple of 1 (e.g. 0, 1, 2). Examples of bosons include photons, gluons, and W and Z bosons. Bosons do not obey the Pauli exclusion principle, which means that many bosons can occupy the same quantum state simultaneously. This is why lasers can produce coherent light, as many photons can occupy the same energy level.

The difference in spin between fermions and bosons has important implications for their behaviour. Fermions are subject to the Fermi-Dirac statistics, which describe their behaviour in a system with many particles. Bosons are subject to the Bose-Einstein statistics, which describe their behaviour in a system with many particles. This leads to different properties for these particles, such as the fact that fermions make up matter while bosons are responsible for mediating the fundamental forces of nature.