Having been an undergraduate physics student, I can tell you that this is a problem that every undergraduate physics student has to solve. The answer is that all the free electrons in the conductor move. Since there's a lot of free electrons in the cross section of a piece of wire, they're not moving very fast. OTOH, 1 amp of current is 6x10^18 electrons flowing past a given point per second, which is an awful lot of electrons. So, they are moving much farther than some atomic diameters, but if they want to visit the power company, they're going to be disappointed. It's called "drift velocity".

73,
Josh W6XU

On 9/4/2017 7:09 PM, Dauer, Edward wrote:
Is it really the same electrons that flow from the municipal generator to our 
rigs and then back to the powerhouse again?  I would have guessed that any 
individual electron motivated by an applied voltage would simply have moved an 
atomic diameter or two to fill in a spot in an adjacent depleted valence shell, 
such that a current flow is actually a shuffling of electrons from one positive 
ion to the next, but that individual electrons really don’t move very far.  And 
then they all shuffle back the other way every one sixtieth of a second.

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