What is the scientific term for the amount of energy required to remove free electrons from the surface of a metal?
We know that, in general, electrons on the surface of a metal are mobile. And the fact that they’re free means that these electrons are untethered to any particular atom. That is to say, these electrons are in the conduction band, which implies a certain amount of energy for the electrons.
Though this energy level is high enough to let an electron roam freely across the surface of a metal, it’s not quite high enough to completely eject the electron from the surface. To reach that point, to completely escape the surface of the metal and reach the vacuum outside it, an electron will need a higher energy level.
We see then that there’s an energy gap between free electrons on the surface of the metal and electrons which have completely escaped that surface. This gap, which we could call Δ𝐸, is effectively a potential barrier that keeps electrons from leaving the surface. The term for this amount of energy is surface potential barrier. It represents how much energy we need to add to free electrons to completely remove them from the surface of a metal.