Since atoms are mostly "empty space,"

[eppur_se_muova]

19. Well, that's what keeps the electrons in atoms from collapsing inward ...

otherwise all atoms would be smaller than hydrogen, and there would be no Periodic Table.

But I was trying to anwer the question with the simplest picture possible -- and that meant sweeping QM under the rug.




In any case ...

Whether you're talking about an atom or a star, there are several types of forces involved, so I don't like to see any one factor given as the "cause" for their stability; it is a balance of these forces with/against each other that leads to a stable system. My impression of Dyson's work (he talked about this in one of his books, IIRC, my memory is not clear after all these years) was that he discovered that no one had ever proved fermionic matter -- and hence the Universe -- is overall stable, and he provided the proof. I would think fermionic degeneracy pressure would be part of that proof.

Ironically, we're no longer certain that the majority of the Universe consists of matter, much less fermionic matter. So in some sense, the proof went to waste.

I can't agree with the conclusion in your first para -- any single electron in any atom has, strictly speaking, non-zero density even as the distance goes to infinity -- that's reflected in the exponential part of the hydrogen-like atom wavefuntion, e^-Zr/na_μ. As long as there is a single electron in a single atom in the Universe, no point in the Universe is completely devoid of electron density(except for nodal surfaces of the wavefunction, but that's only in a non-relativistic approximation).

I think the reason people have a hard time grasping the idea of solid matter being made up of tiny, swiftly moving particles is that they don't realize how much stronger the electrostatic force between such particles is than the forces we experience directly -- what we sense is the combined effect of many repulsive forces (between particles of like charge) and many attractive forces (between particles of opposite charge), which largely cancel each other out, except for some tiny, tiny residual imbalance due to the inhomogeneous distribution of charges in normal matter.

In a four kilogram (~1 gallon) jug of water there are

2.1 x 10⁸Coulombs

of total electron charge. Thus, if we place two such jugs a meter apart, the electrons in one of the jugs repel those in the other jug with a force of

4.1 x 10²⁶Newtons

This is larger than what the planet Earth would weigh if weighed on another Earth. The nuclei in one jug also repel those in the other with the same force. However, these repulsive forces are cancelled by the attraction of the electrons in jug A with the nuclei in jug B and the attraction of the nuclei in jug A with the electrons in jug B, resulting in no net force. Electromagnetic forces are tremendously stronger than gravity but cancel out so that for large bodies gravity dominates.

http://en.wikipedia.org/wiki/Fundamental_interaction#Overview

Note that the electrostatic interaction between these two jugs of water, even at close range, is immeasurably small, but that the gravitational attraction of two bodies of approximately that size is within the range of measurement -- even though gravity is ~10³⁸ times stronger than the electrostatic force.