Free Electron Gas Model-Solid State Physics-Lecture Slides, Slides of Solid State Physics

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Free Electron Gas

 The behavior of free electron moving inside the metals is considered to be similar to that of atoms or molecules in a perfect gas  These free electrons in metals are referred to  “free electron gas”  And the theory is named as “free electron gas model”

Difference b/w Free Electrons and Atoms

 Free electron gas is differ to an ordinary gas with following aspects;  1) Free electron gas is negatively charged while the molecules of ordinary gas are neutral  2) The concentration of free electron gas is quite large with respect to concentration of atoms/molecules of ordinary gas  3) The valance electrons of free electron gas are also considered the conduction electrons while atoms/molecules in ordinary gas are neutral

Characteristics of Free Electrons Gas

 These electrons are responsible to conduction of electricity through metals  They obey the Pauli‟s exclusion principle  The conduction electrons move in a uniform electrostatic field of ion cores  Their potential energy remains constant and taken as zero  Therefore, the existence of ion cores can be ignored

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 This energy difference „Vo‟ serves as a potential barrier which stops the inner electrons from leaving the surface of the metal

 Thus, in free electron gas model, the movement of free electrons in a metal is equivalent to the movement of a free electron gas inside a potential energy box.

 Based on Drude considerations, the electron gas behaves a perfect gas

Lorentz-Model (1909)

 The electrons constituting the electron gas obey Maxwell- Boltzmann Statistics under equilibrium conditions  The combined idea of Drude and Lorentz constitutes  Drude-Lorentz Theory  As the theory is based on classical ideas of Maxwell- Boltzmann statistics, it is called “Classical theory”

SOMMERFELD QUANTUM THEORY

 Sommerfeld treated the problem quantum mechanically by using the Fermi-Dirac Statistics rather than the classical Maxwell-Boltzmann statistics  This can be explained in one-dimensional and three- dimensional cases

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