At the level you're talking about, the idea of "empty space" barely even makes sense.

You probably think about particles as being little solid billiard balls that bounce off of each other. That model can work OK for thinking about some things, but once you get down to the scale of atoms, it breaks down fast.

The state of an electron in an atom isn't a ball orbiting a nucleus. Instead, an electron is smeared-out "cloud" with a particular sort of shape. You can think of this as the electron being a billiard ball that has a certain probability of being at any given point, but thinking of the cloud as the basic truth and the billiard ball as an approximation is closer to the reality. Insofar as the billiard ball model works, electrons (and all other elementary particles) have zero size, but clearly they are taking up space in some sense, so we need to set aside that model if we want to talk about ideas of taking up space.

Instead, when we think of space being occupied, we mean something like "if you try to put something else there, it'll push back". This is why you don't fall through your wall. And it's at the heart of your question.

The reason that your atoms do not fall through the wall's atoms is twofold:

• First, the electrons in your atoms and the electrons in the wall's atoms are both negatively charged, and they get close to each other before they get close to the positively charged protons in the other atoms. That creates an electric repulsion that stops the two from getting too close, or from your atoms passing through the wall's.

• Second, the electron clouds take up space, in the sense that compressing a cloud takes energy. When you get very close to the wall, the electron clouds in your atoms start to press against the electron clouds in the wall's atoms. The clouds resist compression, which can hold you up in much the same way that a spring can hold up a weight.

Both of these effects contribute a fair amount to the "solidness" of solid objects.