Why do empty electron orbits attract electrons from other atoms?

As I understand it, an atom with one or more empty slots in it’s electron orbits will (tend to) bond with other atoms (by sharing electrons) until they each have all their orbits full.

Since each atoms’s electrons are balanced by an equal number of oppositely charged protons, why are electrons attracted to these empty holes?

Keep in mind that the idea of electrons orbiting a nucleus is essentially a first approximation. It is the simplest model to help visualize what is going on. This is a very very crude picture in general.

That being said, think of it this way: each electron is attracted to the nucleus and repelled by every other electron. For atoms with an unfilled shell, an additional electron is still attracted to the nucleus but the other electrons in their orbits are far enough away that their repulsion doesn’t exactly cancel out the attraction to the nucleus.

For example, a neutral chlorine atom has 7 electrons in its outermost shell, which can hold 8 atoms. An extra electron is attracted to the nucleus. The other electrons in the outermost shell are far enough away from the orbit of the new electron that their repulsion isn’t enough to “push out” the new electron. Thus, chlorine is more stable as Cl- than as Cl.

Now consider an Na atom. Its outermost shell only has one electron in it. That means compared to all of the other electrons, it is farther away from the nucleus. It is also being pushed away from the nucleus by all of the other electrons, which all orbit closer to the nucleus. Thus, hopping into a Cl atom and filling its outermost orbital is lower in energy and, thus, more favorable. In this way, Na+ and Cl- is preferable to Na and Cl by themselves.

Don’t confuse atomic orbitals with molecular ones. Molecular orbitals are lower-energy, so atoms ‘want’ to form these bonds. They fill their outer shells, and are at lower energy, to boot!