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"Fermion" is the collective word for all quantum particles with half-integer spin, such as spin 1/2, 3/2 or 5/2.

Among elementary particles, fermions are the matter particles, for example electrons or quarks, while the carrier particles responsible for transmitting the elementary forces between particles belong to a different class - they are bosons.

Quite generally, fermions are subject to the Pauli exclusion principle. Roughly: no two electrons can rest at the same location. A bit more precisely: no two electrons can ever be in the same state. This property is decisive for what we call matter: Only the fact that it is impossible for all electrons of an atom to occupy the lowest energy state close to the atomic nucleus, but that instead the electrons have to spread out and occupy different states leads to the difference between atoms with different numbers of electrons and, in particular, to the fact that different elements have different chemical properties.