Why do surfaces act like barriers for electrons?

Say you have a conductor, filled with free electrons. The nuclei have a weak pull on the valence electrons so they are moving around in the conductor.

But the electrons don't leave the solid. If you bring a positively charged object near the conductor, the electrons might move to the other side of the object, but won't leave it, almost as if there's a "wall" blocking it.

I have gotten the following explanations:

1) They are attracted by the nuclei so they are pulled back.

My problem with this: Conductors have a weak attraction force on the electrons, so why does it take an extremely large force to counteract the pull by the nuclei? And also what makes the boundary so special?

If the electron can move within the solid freely, what makes it so much harder to move outside the solid, since the force by the nuclei is the same?

2) Think of the electrons as being held by the nuclei by a string. If you pull on it, you might be able to move the electron away but you would need a stronger force to break the "string" of the nuclei.

My problem with this: This analogy doesn't work. Elastic strings follow Hooke's Law:

$$F = kr$$ where $k$ is a constant and $r$ is the distance. As the distance increases, the force pulling back increases.

Electromagnetic forces however follow Coloumb's Law:

$$F = \frac{kq_1q_2}{r^2}$$

As the distance increases, force pulling back decreases.

I am not looking for a mathematical proof. I am looking for an intuitive explanation. Something like an analogy would help a lot, but any other explanation you feel would be more helpful is welcome.

Also note that I know that you can get electrons to leave a conductor, but this requires a high voltage.

If you stopped me on the street and asked me, I would reason it's probably because inside the conductor, the attractive forces from the nuclei are fairly uniform, so motion in one direction is as easy as motion in any other. On the surface, however, there are only forces on one side of the the electron, namely from the nuclei on the surface of the conductor. The air molecules don't attract the electrons strongly enough to pull them away because they are either neutral or relatively weak dipoles. As a result, electrons are effectively bound to the surface of the conductor unless a sufficiently high voltage is applied to overcome the strong attractions of the conductor's nuclei.

Or so I would guess.

• But the pull on the nuclei is weak, so the difference between moving inside (where the forces are on both sides) and moving outside (where the force is on one side) isn't very different, since the forces are so weak.
– dfg
Jan 30 '14 at 4:56
• The conductor doesn't actually have a weak pull on the electrons. The reason the electrons can move freely throughout the material is because they are bound to the material as a whole. This requires a bit of quantum mechanics to explain quantitatively, but essentially the electrons occupy a bonding orbital that belongs to the entire conductor. Feb 1 '14 at 0:32

Let us not forget that when we are talking about electrons we are talking about elementary particles .

Elementary particles move within the confines of Quantum Mechanics always. In QM the electron sees a potential, i.e. attraction of the nucleus(nuclei) charges, and is either bound by it in an energy level or it is free. It can be bound to a single nucleus, to a molecule sharing the nuclei, to a crystal sharing order 10^23 nuclei. In a sense the latter is what is happening in metals.

The QM states are defined on the common potential of the nuclei in the lattice of the metal, a many body problem, still, the electrons are bound by a specific energy level defined by this potential; in metals, from the great number of nuclei in the lattice and the structure of the nuclei*, the outer electrons have available a a band of energy where the energy level differences of the many levels are very small.

Since two electrons cannot occupy the same state it means that for any change of direction some energy in the shape of virtual or real photons must be supplied to them for the necessary change in energy level occupation. Because this energy level differences within the band is small in the vertical direction to the surface, within the band only, they have the mobility that we measure in the metal and accumulate wherever the overall potential difference attracts them : i.e. jump energy levels absorbing energy as virtual photons from the potential within the band.

To get out of the band and the surface of the metal an electron has to absorb a virtual or real photon of much higher energy then the energy the virtual photons necessary for "motion" within the band. In a sense the band serves the role of the specific energy state of an electron in a hydrogen atom for example, as far as breaking out of the surface. The dipoles and higher moments of neutral molecules cannot supply that energy with off mass shell photons, cannot attract the electrons from the band enough to kick them out and bind them on the molecule.

In a nutshell, much more energy in the form of virtual or real photons has to be absorbed to get out of the band/surface than to move within the band. In a sense it is the band structure that exists in metals that is the unusual state of matter, since all matter gives up its electrons to the air with difficulty ( large energy virtual or real photons). The band structure allows the mobility in metal and is the unique characteristic needing explanation which I hope I gave.

• Nuclei have charges classified in the periodic table , the Z number. Depending on the number of such charges the energy levels available to be filled by electrons define the chemical and other macroscopic properties of matter, whether it is a metal or not for example.
• "the electron sees a potential" - whats a potential?
– dfg
Jan 30 '14 at 4:57
• A potential is what is giving the F force in your question above. Forces arise because of potentials. Jan 30 '14 at 5:06
• sorry, just saw that I had typed "potentials" instead of "electrons". age shows :( Jan 30 '14 at 5:10

Though I am really not well versed with these topics, I will attempt to answer your question in a fairly simple and non-mathematical language.

The barrier is not the wall of the conductor. Instead it is the air in between the charged body and the conductor. Electrons just cannot travel freely in the air unless there is really heavily charged body (that is what happens during lightning or sparking).

Now to the why part of your question. Electrons jump from atom to atom and then traverse. The atoms of the conductor allow that traversing of electrons but air doesn't because air does not have free electrons. So the electrons near the surface are not allowed to move further. And I think that in the and VINAY has given a good diagram to clear out my explanation.

In short, Inside the conductor the electrons can traverse but that cannot happen outside the conductor. I hope this clears out yourr doubt.