When a electron goes into a cable will the same electron come out the other end?

Answer 1

Almost certainly not for a wire of any length. The electrons that support current flow do so by something approximating "musical chairs" or the like. When an electron "goes into the wire" at one end, one "leaves the wire" at the other end. That's how current flow works. In a conductor like copper, there are an astronomical number of electrons all through the wire and at a Fermi energy level that will support conduction. The actual movement of a given electron in a wire is very slow. One source has it measured in centimeters per hour or the like for "normal" current flow. It is not much. If one is dead set on finding out an exact, or really scientific answer, you'll need to do a triple space integral for the copper wire and include a truck load of variables to "make it right" so the calculation will present an accurate picture of the movement of a given electron. And be advised that the whole of the experience is simply an exercise in probability and statistics. Current flow is not like the New York marathon where everyone who is running is wearing a number. Electrons are not wearing numbers, and what's more, they are all absolutely identical. You can't tell one from another when they are in free space.