Does a single molecule or atom have a density?

Question

In a science lab I did recently we placed wax candles into two different liquids to see if they would float or sink. In one liquid, the candle floated, and the other one it sunk. We swapped the candles to confirm it was caused by the difference in the density of the candles and the two liquids. We were given a brief amount of homework on this, of which my question orginated.

The homework question that got me thinking (This is not my question, it's what lead up to it) was asking if there was a limit to how small the candle could be made and still behave the same way in each of the liquids. I considered that if there were two or more molecules, the candle would still have density due to there being an amount of space between them, or a density, and thus behave the same way. However, I am unsure if a single molecule or atom would have a density or not, since it is a single particle in space with actual properties.

So, in simplicity, the question is the title. Does a single molecule/atom have a density to it? Why?

Answer 1

The vast majority of the mass of an atom (typically about $99.975$%) is in the nucleus, so when we consider the density of some material this is basically the number of nuclei per cubic metre (multiplied by the mass of a single nucleus).

For macroscopic lumps of solids, liquids and gases the average spacing between nuclei is well defined so the number of nuclei per cubic metre is a nice well defined quantity. So far so good.

For a single atom the number of nuclei is well defined, but how can we define the spacing between nuclei when there is only one nucleus? The nucleus itself is about a femtometre across, but if we calculate the density using this size we get an absurdly high density (about the density of a neutron star in fact). The electron cloud around the nucleus doesn't have a well defined edge, so there isn't any obvious size for the atom. Typically we would use the covalent radius, but this is just half the nuclear spacing in a solid/liquid so it's cheating. We're making the density of the atom the same as the density of the solid/liquid by definition.

So I think we'd have to conclude that the density of a single atom isn't a well defined quantity. On the one hand we can't define it at all if we insist that density means nuclei per unit volume, and on the other we can make it any value we want by choosing how we define the size of the atom.