Question

Why electrons in copper move toward the metal surface. Why do they not keep on going and leave the metal?

Answer 1

It should be given sufficient energy (heat, electric field, photon,etc) to escape from the metal. This energy for a particular metal is called its work function.

Imagine if you supplied energy less then required, as soon as it comes out of the surface of the metal un balance of charges happens in the conductor. Conductor have equal no of electrons and positive ions at normal conditions. If one electron leaves the metal it acquires net +ve charge and pulls electron back. If electron supplied with energy more than the work function it leaves the metal surface.

If metal finds another electron near its surface with less KE it pulls it into it becomes neutral