in solid-state physics, representation of a metallic solid as a container filled with a gas composed of free electrons (i.e., those responsible for high electrical and thermal conductivity). The free electrons, considered identical to the outermost, or valence, electrons of free metal atoms, are presumed to be moving independently of one another throughout the entire crystal.

The free-electron model was first proposed by the Dutch physicist Hendrik A. Lorentz (Lorentz, Hendrik Antoon) shortly after 1900 and was refined in 1928 by Arnold Sommerfeld (Sommerfeld, Arnold) of Germany. Sommerfeld introduced quantum-mechanical concepts, most notably the Pauli exclusion principle. Although the model provided a satisfactory explanation for certain properties (e.g., conductivity and electronic specific heat) of simple metals such as sodium, it had some serious shortcomings. It did not, for example, take into account the interaction of free electrons with the metal ions. Researchers soon recognized that a broader system was needed to explain the behaviour of complex metals and semiconductors. By the mid-1930s the free-electron model was largely superseded by the band theory of solids.