Electrons in metals behave like a gas or a liquid

 Electrons in metals behave more like a liquid than an independent gas. While early theories treated them as a simple bouncing "gas," strong electrical repulsions mean they actually flow as a correlated fluid called a Fermi liquid. [1, 2, 3, 4]

The Electron Gas Model

The classical Drude-Sommerfeld model treats conduction electrons as a "free electron gas". [1, 2]

• How it works: Electrons move randomly in all directions, much like molecules in an ideal gas, but they do not bounce off one another.
• What it explains: It successfully predicts basic electrical and thermal conductivity, as well as the heat capacity of metals.
• Why it falls short: It ignores the fact that electrons are highly charged and repel each other. [1, 2, 3, 4, 5]

The Electron Liquid Model (Fermi Liquid Theory)

Because the concentration of electrons in a metal is incredibly high (roughly \(10^{29} \text{ per m}^3\)), they are constantly interacting via Coulomb forces. This requires a quantum fluid approach. [1, 2, 3, 4, 5]

• How it works: Electrons drag and coordinate with one another. Instead of moving independently, they flow collectively as a highly viscous, charged liquid. [1, 2, 3]
• What it explains: It accurately describes complex phenomena like superconductivity, specific types of resistance, and how electrons "screen" or hide the charge of impurities