# Why don't free electrons fall from metals if shaken?

This is a question we were asked at a physics lecture.

• If you shake it hard enough ... – Sridhar Oct 17 '14 at 9:04
• @sridhara Imagine the work function is just 1ev, from simple calculation you can see that you need to shake at a speed of 6*10^5 m/s – 喵喵是我的猫猫 Oct 17 '14 at 9:13
• They're not that free :D They still have a lower energy state when "in" the metal, so at the very least, you need to be able to give them enough energy to offset the potential energy they have in the EM field of their neighbourhood. Since the electromagnetic force is rather strong, this works out to rather non-trivial amount of work for all the electrons. And of course, the metal would then tend to attract electrons from afar, since it'd be quite positive, restoring the balance fast (think static electricity). – Luaan Oct 17 '14 at 14:30
• I expect that even once an electron separates from a piece of metal, it wouldn't be particularly likely to "fall", per se, given how tiny the force of gravity on an electron is. – Kyle Strand Oct 17 '14 at 21:32
• @buzhidao: What do you mean by "shake at a speed" haha... shouldn't the speed be an acceleration instead? – Mehrdad Jul 16 '17 at 4:08

## 2 Answers

Because there is an energy barrier between the metal and vacuum. Consider the ions in the metal as a uniformly distributed positive charge. Near the metal surface, the free electron wave function spread out a little into the vacuum, thus near the surface of metal the electric dipole forms with the electric field points to vacuum. Thus a gradual potential barrier will form.

Also think classically, when an electron near the surface of metal, it creates an positive image charge, which pull electron back to metal.

Finally, what we are talking about is called work function.

Because the electrical force on an electron is around 10^39 times that of gravity. Given the equivalence between gravitational and acceleration forces, you would have to shake it quite hard. Before you got to the point where an electron would drop out the entire material would disintegrate and all kinds of other phenomena would take precedence over you finding those spare electrons.