Editing Free electron model (section)

{{short description|Simple model for the behaviour of valence electrons in a crystal structure of a metallic solid}}
{{about|the solid-state model for metals|the model of a free electron gas|Fermi gas}}In [[solid-state physics]], the '''free electron model''' is a [[Quantum mechanics|quantum mechanical]] model for the behaviour of [[charge carrier]]s in a [[metal]]lic solid. It was developed in 1927,<ref>{{Cite journal|last=Sommerfeld|first=Arnold|author-link=Arnold Sommerfeld|date=1928-01-01|title=Zur Elektronentheorie der Metalle auf Grund der Fermischen Statistik|journal=Zeitschrift für Physik|language=de|volume=47|issue=1–2|pages=1–32|doi=10.1007/bf01391052|issn=0044-3328|bibcode=1928ZPhy...47....1S}}</ref> principally by [[Arnold Sommerfeld]], who combined the [[Classical physics|classical]] [[Drude model]] with quantum mechanical [[Fermi–Dirac statistics]] and hence it is also known as the '''Drude–Sommerfeld model'''.<ref name=":1" group="Ashcroft & Mermin">{{Harvnb|Ashcroft|Mermin|1976|loc=Ch. 2 & Ch. 3}}</ref><ref name=":1" group="Kittel">{{Harvnb|Kittel|1972|loc=Ch. 6}}</ref>

Given its simplicity, it is surprisingly successful in explaining many experimental phenomena, especially
* the [[Wiedemann–Franz law]] which relates [[electrical conductivity]] and [[thermal conductivity]];
* the temperature dependence of the [[electron heat capacity]];
* the shape of the electronic [[density of states]];
* the range of binding energy values;
* electrical conductivities;
* the [[Seebeck coefficient]] of the [[thermoelectric effect]];
* [[thermionic emission|thermal electron emission]] and [[field electron emission]] from bulk metals.

The free electron model solved many of the inconsistencies related to the Drude model and gave insight into several other properties of metals. The free electron model considers that metals are composed of a quantum electron gas where [[ion]]s play almost no role. The model can be very predictive when applied to [[alkali metal|alkali]] and [[noble metal]]s.