Drude model
/ DROO-duh /
Just three years after the electron was discovered, Paul Drude in 1900 made the simplest guess imaginable: treat the free electrons inside a metal exactly like the air molecules in a balloon — a gas of tiny balls zipping around, occasionally smacking into the fixed atoms and bouncing off in random directions.
Each electron flies in a straight line until it collides; the collisions reset its motion and cause electrical resistance. Switch on a voltage and the electrons drift slowly down the wire on top of their fast random jiggle, which is electric current. From this single picture Drude derived Ohm's law and a tidy relationship between how well a metal carries electricity and how well it carries heat.
It matters as the very first quantitative theory of metals, and parts of it survive today. But it has a serious flaw: it assumes electrons obey the ordinary rules of a hot gas, which badly overestimates how much heat they should store. Fixing that required quantum mechanics, and the repair is called the Sommerfeld model.
Think of electrons as pinballs and the atoms as the bumpers. Tilt the table (apply a voltage) and the balls drift steadily downhill even as they ricochet wildly — that steady drift through endless bouncing is exactly Drude's picture of electric current.
A pinball table: random bouncing plus a gentle tilt gives a steady drift — Drude's view of current.
A famous lucky accident: Drude's prediction for the heat-to-electricity conductivity ratio (the Wiedemann-Franz law) came out roughly right — but only because two of his errors happened to cancel. The quantum version gets the same answer for the right reasons.