Can a single atom on its own be either a solid, liquid, or a gas? Or is it none of them?
This answer has been written so it hopefully can be understood by people that do not have a degree. If something is not correct, let me know, but be aware that throwing around fancy words will not help anyone understanding this any better. Consider the other posts here concerning liquids and solids, I don't want to be redundant and repeat what has been said already.
The answer is a bit complicated. One would intuitively say no, but that doesn't tell the whole story.
Take the interstellar medium. We have about 1 atom per cm³ in there and it is called a "gas". Now that's what I would call an isolated atom in the gas phase.
An atom is an object that belongs into the realms of quantum mechanics. A solid, liquid or gas is something that belongs into our classical world. If you zoom in close enough, that means if we look at a problem microscopically, words like "solid" or "liquid" no longer make sense. If you now begin to zoom out, the quantum effects vanish. This is sometimes called quantum decoherence and we enter the world of classical physics where solids and and liquids exist again.
So I would argue it all depends on how closely you look at the problem. Isolated atoms in a large volume? A gas if you ask me. But if you have to zoom in to talk about an individual atom within a larger compound consisting of many more atoms, let's say one atom within a piece of iron, you no longer can say that this single atom is "solid".
Think of it like this:
Can a single person have a political system?
Yes, why not. I can proclaim my own nation and be the only person in it. But mostly, a nation is something that many people form together. If you look at one individual person, you are in the realm of psychology (or biology). If you look at an entire state, you are in the realm of (for example) politics. If you zoom in at one individual person, you can no longer say that person has a certain political system. But if you zoom out far enough, you suddenly get a political system. Zooming out of course is a bit more abstract here, but, as I said, this is the realm of psychology/politics ...
Both the liquid and solid phases are, on a molecular level, defined by some kind of regular arrangement. Solid phases typically have short-distance and long-distance regular arrangements (think the periodicity of a crystal), while liquid phases only have short-distance arrangements. This can be modelled in various computer simulations and I myself have done so in a physics practical course.
Gases are then defined as phases without any type of arrangement; neither short- nor long-distance.
A single atom of course has no arrangements of other atoms around it, so it cannot be considered a liquid or a solid. One would, most likely, consider it a gas — but remember that ‘gas’ is a macroscopic term and one may equally consider a single atom as ‘just a single atom’.