Free electron model

The free electron model describes metal conduction electrons as mobile particles moving through a fixed lattice of positive ions. It neglects electron interactions and the lattice’s periodic potential.

Drude model: A classical theory that treats conduction electrons in metals as particles undergoing random collisions. It supplies the classical collision-based account of transport within the free-electron picture.
Conduction electron: An electron in a solid that can move through the material and contribute to electrical conduction. The model treats these electrons, rather than bound electrons, as its mobile particles.
Nearly free electron model: A band theory that treats electrons as nearly free while including a weak periodic crystal potential. It restores the lattice’s periodic potential to explain energy bands and band gaps.
Alkali metals: The metallic elements in Group 1, excluding hydrogen, characterized by a single outer s electron. Their relatively simple valence-electron structure makes them natural cases for free-electron estimates.
Paul Drude: A German physicist who developed a classical electron theory of electrical and thermal conduction in metals. His theory established the classical free-electron approach to metallic transport.
Sommerfeld model: A quantum version of the free-electron model that applies Fermi–Dirac statistics to conduction electrons. It replaces classical electron statistics with quantum statistics while retaining free motion.
Metallic bonding: Chemical bonding in which delocalized electrons bind a lattice of positive atomic cores. It provides the physical setting of mobile electrons and fixed positive ions.
Tight-binding model: A model of electrons in solids built from atomic orbitals with hopping between neighboring sites. It describes electrons localized near atoms, opposite the free model’s extended states.
Hall effect: The production of a transverse voltage when current flows through a conductor in a magnetic field. Its carrier-sign and density predictions can be compared with the model’s electron assumptions.
Hendrik Antoon Lorentz: A Dutch physicist who extended the classical electron theory of metals and developed the Lorentz electron theory. His work refined the classical model and exposed its limits against measured properties.

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