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Free electrons are electrons that are not bound to any specific atom and are free to move throughout a material. In metals, they arise from the outermost electrons of metallic atoms that are delocalized over the entire crystal lattice. These electrons form an electron gas that can flow under an applied electric field, giving metals their characteristic electrical conductivity. The density of free electrons in a metal is typically on the order of 10^29 per cubic meter, and their motion is described by the Drude free‑electron model in classical physics and the nearly free electron model in quantum mechanics.

In semiconductors and insulators, free electrons can be generated by doping, thermal excitation, or photon absorption. When an electron transitions from the valence band to the conduction band, it leaves behind a hole that behaves as a positive charge carrier. The number of free electrons in a semiconductor depends on temperature and impurity concentration, and it determines the material’s conductivity. In alloys and composites, free electrons can be localized or delocalized depending on the electronic structure of the constituent elements.

Free electrons are also key to phenomena such as the photoelectric effect, where incident photons impart sufficient energy to release electrons from a metal surface. They contribute to the behavior of plasmas, where electrons and ions coexist in a quasi‑neutral gas. In metals, the scattering of free electrons by phonons, impurities, and defects limits conductivity; this scattering is quantified by the relaxation time in transport theory. Understanding and controlling free‑electron behavior is essential for advancements in electronic devices, power transmission, and the development of conductive materials.