Is a single radon-daughter atom in air, such as ${}^{218}\text{Po}$, a solid?

When the Wikipedia article says that radon daughters are "solids", the authors actually mean, "If you get a bunch of radon daughter atoms together, then they would form a solid." The state of matter is a property of a large number of atoms, so a single atom in isolation doesn't strictly have a well-defined state.

That said, states of matter are primarily a function of the interactions between atoms. Atoms that weakly interact* with themselves and their environment are likely to be gases, while atoms that strongly interact* with other atoms are likely to be liquids or solids. So Wikipedia appears to be using the state of matter as a shorthand for the strength of interactions. Essentially, radon daughters, unlike radon (which is a noble gas), stick to each other and to the walls, which is the same property that makes large collections of radon daughters solids.

*"weakly" and "strongly" don't refer to the fundamental weak and strong nuclear interactions here, of course, but to the general idea of having a small or large coupling constant in whatever interaction you're examining.

A single atom is not a solid, a liquid, or a gas. These three terms refer to how large numbers of atoms or molecules behave, and they have no meaning for a single atom.

After the decay of Rn-222 in air (i.e. not necessarily in case of Rn-222 that is trapped in minerals), the freshly generated Po-218 is neither a solid nor a gas in the usual sense. It is predominately present as positively charged ions. These ions are not stable and react quickly with atmospheric gases and form small clusters. Furthermore, the Po-218 ions can become neutralised by interactions with gases or other airborne substances, or Po-218 can attach to particulate aerosols.

The ionized form of radon progeny can be demonstrated in a simple experiment using a charged sheet of plastic that collects the ionized radon progeny from the air. The activity collected on the plastic can then be measured using a suitable radiation detector.

Finally, at normal atmospheric pressure and temperature, elemental polonium and typical polonium compounds are solids. After decay of Rn-222, however, there is not enough Po-218 present to form a discrete solid phase. The chemical concentrations of Po-218 are so low that the Po-218 atoms cannot find other Po-218 atoms. Thus, the Po-218 sticks to foreign material (usually first to particulate aerosols or other available surfaces).