Energy spacing in the description of energy bands.

[dvurger]

"The electrons of a single isolated atom occupy atomic orbitals, which form a discrete set of energy levels. If several atoms are brought together into a molecule, their atomic orbitals split, as in a coupled oscillation. This produces a number of molecular orbitals proportional to the number of atoms. When a large number of atoms (of order ×1020 or more) are brought together to form a solid, the number of orbitals becomes exceedingly large. Consequently, the difference in energy between them becomes very small." -Wikipedia on energy bands.

I don't understand that implication between the number of orbitals and the energy spacing converging to 0.

 

[TeethWhitener]

The energy splitting induced between two atoms can be thought of as a measure of how strongly those atoms interact. So the stronger the interaction, the bigger the energy splitting.

For two atoms close together, they interact relatively strongly, so the energy splitting is large. But for a big molecule, two atoms at opposite ends of the molecule barely interact at all, so their energy splitting is very small. So as the number of atoms in a system increases, the energy levels get closer together until finally, in an infinite crystal, the energy levels are continuous—that is, infinitely close together.