Free Electron Gas in a Metal

Metal

Applied Field & Temperature

Electric field E 5.0 V/m

Lattice temperature T 300 K

Live Readouts

Drift velocity v_d— mm/s

Current density J— A/mm²

Conductivity σ— MS/m

How it works

The Drude model treats conduction electrons as a classical gas that flies freely between random collisions with the vibrating lattice ions. Between collisions each electron accelerates under the field E; at a collision its velocity is randomised, erasing the memory of that acceleration. Averaged over the whole gas this gives a small net drift on top of a much larger, essentially random, thermal motion:

a = eE/m                (free acceleration between collisions)
v_d = eEτ/m              (mean drift velocity)
J = n·e·v_d = σE          (current density, Ohm's law)
σ = n·e²·τ/m              (conductivity)
τ(T) ≈ τ₃₀₀·(300/T)       (scattering time falls as the lattice gets hotter)

n — conduction-electron density (fixed per metal, from its known valence and atomic density).
τ — mean free time between scattering events, back-derived per metal from its measured room-temperature resistivity, then scaled with temperature.
Metal — swaps n and τ₃₀₀: silver scatters least (longest τ, highest σ), iron scatters most.
E field / Temperature sliders and the Reverse Field button feed directly into the equations above — the drift velocity, current density and conductivity readouts are computed analytically from them, not measured off the animation.
The 3D scene shows the same mechanism qualitatively: electrons (small spheres) fly ballistically, scatter off the fixed ion lattice at a rate set by 1/τ, and pick up a slight bias toward the field direction between scatters. In reality that drift is thousands of times smaller than the electrons' thermal speed — the animation exaggerates it so the bias is visible.

Conduction electrons Lattice ions

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Free Electron Gas in a Metal — Drude Model