In solid-state physics, the free electron model is a quantum mechanical model for the behaviour of charge carriers in a metallic solid. It was developed in 1927, principally by Arnold Sommerfeld, who combined the classical Drude model with quantum mechanical Fermi–Dirac statistics and hence it is also known as the Drude–Sommerfeld model.
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;
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 ions play almost no role. The model can be very predictive when applied to alkali and noble metals.