The drift velocity of electrons in a typical electronic circuit might be measured in mm per second. In contrast, the thermal velocity of electrons is in the vicinity of km per second.
Because of the slow drift velocity, beginners in electronics sometimes get the mistaken impression that an electron leaving a battery's negative electrode and travelling through a circuit will only arrive at the battery's positive electrode after a relatively lengthy period of time.
Rather, I expect that the electron at one end of a wire, even with no applied electric field, will very rapidly move a short distance, (it's mean free path), have it's velocity and direction randomized, and then continue on in a random walk. At some point in it's random walk it will reach the other end of the wire. I am guessing that for relatively short lengths of wire, this could take less time than for an electron travelling directly at drift velocity.
My question is this.
On average, how long would it take for an electron to travel, via random walk, from one end of a wire of say 1 meter length to the other end? For your answer you may assume that the wire is copper (or anything else you choose), that the electrons are moving under thermal motion, with no drift velocity, that the temperature is any value you choose near 20 degrees Celsius. You may make any other assumptions you wish if you make them explicitly.
