Steven Dutch, Professor Emeritus, Natural and Applied Sciences, University of Wisconsin - Green Bay
Above is a scale drawing of a unit cell of sodium chloride (Table Salt). Sodium atoms are gold, chlorine atoms green. Sodium entirely loses its 3s electron. Chlorine acquires a final 3p electron, which doesn't change its electron configuration much. Orbitals are shown to scale, with the ionic radii colored.
Below is a scale drawing of a unit cell of copper. Copper atoms are, well, copper, with the layer behind in a lighter hue. Orbitals are shown to scale, with the metallic radii colored. Copper has two electrons in its 4s shell but on the average only one becomes a free electron, so the 4s shell is shown. Note that it pretty much accounts for the atomic radius.
Perhaps the most striking thing about these diagrams is that the ionic radii of the atoms is so much larger than the orbitals. Why?
It's been said that "time is God's way of keeping everything from happening all at once." We might also say the Pauli Exclusion Principle is "God's way of keeping everything from happening all in the same place." The Pauli Exclusion Principle says that two fermion (most particles) wave functions cannot occupy the same space if they have identical quantum numbers. For electrons orbiting atoms, those numbers describe the electron shell, the type of orbital, the specific orbital the electron occupies, and the spin. (The principle also applies to particles in the nucleus, but that won't affect interactions between atoms.)
The electrons around a particular atom sort themselves out to avoid any conflicts. But when the electrons around an atom encounter another atom, there will be conflict. The conflicting electron shells resist overlapping very hard. The atoms feel a repulsive force, entirely apart from whatever electrostatic forces may exist between the atoms. This repulsive force, called the Born Repulsion, is a short range force that can be approximated as 1/rn, where r is the distance between nuclei, and n is an exponent with values typically between 5 and 12. If n =5, a decrease of 10 per cent in r results in a 60 per cent increase in the repulsion. For n = 12, the repulsion more than triples. The effect of a large exponent n is to make the atoms behave as if they are rigid, incompressible spheres of a fixed size. However, a large enough force can overcome the Born repulsion. The simplest response is simply for the atoms to collapse to a denser arrangement. At higher pressures, electrons can be squeezed off to become free electrons.
So there's a very strong repulsive force between atoms, but it drops off very sharply with distance. There's a weaker electrostatic force that drops off more slowly. If the electrostatic force is attractive, there's a point where it reaches a maximum value as r decreases, before the Born repulsion takes over. That distance basically defines the ionic radii of the atoms.
Note also, that the Pauli Exclusion Principle applies only between electrons with identical quantum states. Electrons in Shell 1 don't care about any other shells. 3d electrons don't care about electrons in any other shells or orbitals. They don't even care about other 3d electrons in different suborbitals, or even in the same orbital if the spin is different. And 1s electrons in sodium will repel 1s electrons in chlorine, but not 2s electrons.
Actually, calling the Pauli interaction "repulsive" is a little misleading. It conveys the impression there's some kind of Pauli "field" that reaches out, like an electric field. But the Born repulsion is simply a mathematical description of the way electrons of identical quantum state resist being superimposed. It has a large exponent because the repulsion kicks in very abruptly and very strongly. In NaCl, the 1s, 2s and 2p electrons of adjacent Na and Cl atoms refuse to be suprimposed. The 3s and 3p electrons of chlorine don't care (sodium has given up its 3p electron).
Copper is a metal and has free electrons wandering around between the atoms. What effect do they have? On the atoms themselves, none. The free electrons generally come off the outermost shell, so they don't share the same quantum numbers as the inner electrons. But once they're free, they're all effectively identical, and that means no two of the free electrons can have the same quantum numbers. So they occupy every possible energy level from zero up to some maximum value. Above the maximum are other energy levels that are vacant. This means a photon can always find an electron to kick up to an available energy level. So metals are opaque, because a photon never gets very far before finding an electron to excite. (The only exception is extremely thin layers, like gold leaf, where some photons can get through.) The excited electron soon drops back, spitting out an identical photon. So metals are reflective.
What Do Atoms Really "Look Like?"
What Atoms of Hydrogen Through Xenon Really "Look Like"
What Atoms of the Heavy Elements Really "Look Like"
Scale Drawings of Atoms and Orbitals: Hydrogen Through Krypton
Scale Drawings of Atoms and Orbitals: Rubidium Through Xenon
Scale Drawings of Atoms and Orbitals: Cesium Through Radon
Scale Drawings of Atoms and Orbitals: Francium Through Lawrencium
What the Atomic Structures of Some Simple Materials Really "Look Like"
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Created 20 September 2005, Last Update