
A model of free electrons in a metal, treated as a gas of charged particles.The electron gas model treats the free electrons in a metal as a gas of charged particles, ignoring the periodic lattice of positive ions except as a uniform background. This simplification captures the essential physics of electrical and thermal conductivity, and explains why metals are shiny and malleable. It is the starting point for understanding more complex phenomena like superconductivity and magnetism.
The model was developed by Paul Drude in 1900, shortly after the discovery of the electron, and later refined by Hendrik Lorentz and Arnold Sommerfeld.
In a metal, the outermost electrons of atoms are loosely bound and can move freely throughout the material. The electron gas model assumes these electrons behave like a classical ideal gas, colliding with each other and with the lattice ions, but otherwise moving independently. This allows the use of statistical mechanics to derive properties like the Drude conductivity, which relates the electrical current to the applied electric field.
It is used to estimate the electrical and thermal conductivity of metals, and to understand the behavior of electrons in semiconductor devices and plasma physics.
The electron gas model predicts that the heat capacity of a metal should be much larger than it actually is, a discrepancy that was only resolved with the advent of quantum mechanics.


