relaxation time
/ ree-lak-SAY-shun time /
Picture an electron drifting through a metal under a voltage, gradually building up speed in one direction — until, bump, it scatters off something and its sense of direction is wiped clean. The relaxation time is the average stretch of time it gets to travel between such direction-erasing collisions: how long, on average, the electron "remembers" which way it was supposed to be going.
It's the central clock of the Drude and Sommerfeld models. A long relaxation time means electrons coast a good while before being knocked off course, building up a healthy drift and so a high conductivity. A short one means constant interruptions and a sluggish, resistive metal. Almost every transport number in the free-electron model traces back to this single timescale.
It matters because it bundles all the complicated scattering — off vibrating atoms, off impurities, off defects — into one tidy average. The honest caveat: that's also its weakness. By hiding the real causes behind one number, it can't by itself explain why the relaxation time changes with temperature or purity; for that you must look at what the electrons are actually colliding with.
In ordinary copper at room temperature the relaxation time is only about a hundredth of a trillionth of a second. Cool the copper down and purify it, and that time stretches out — the electrons travel farther between mishaps, and the metal conducts better.
Cooling and purifying copper lengthens the relaxation time, so it conducts better.
Relaxation time (a duration) and mean free path (a distance) are two sides of one coin: multiply the relaxation time by the electron's speed and you get the mean free path. In a metal that speed is the fast Fermi velocity, not the slow drift.