Over the last hundred years or so, our understanding of atoms has changed drastically. Since the ancient Greeks, people have speculated that matter might be made up of atoms. However, our modern understanding of the structure of atoms began with the discovery of the electron and the proton, a little over one hundred years ago. After those discoveries, people began to propose models for what atoms might look like, and how the positive protons and the negative electrons might be arranged. As time went on and more experiments were performed, the models describing the atoms were updated to be consistent with the experimental results. For example, the neutron was discovered!

Eventually, a model was proposed in which the protons and neutrons were concentrated in a tiny core at the center of the atom, with electrons orbiting around the core like planets in our solar system orbiting around the sun.

To describe the motion of the electrons and the behavior of atoms in general, a new branch of physics was developed: quantum mechanics. This model did describe atoms as containing mostly empty space. However, experiments continued to be performed, and this model for the atom, and the quantum mechanics describing it, continued to be updated.

Today, we still agree that protons and neutrons are located at the center of atoms, but the locations of electrons are much less clearly defined. In fact, one of the core principles of quantum mechanics is that electrons don’t actually have a defined position. Instead, if you perform an experiment to look for the location of an electron in an atom, you will sometimes find it in one location, and sometimes in another, and you will never be able to predict exactly where you will find it. Instead, you can only specify the probability that you will find the electron at a certain location.

Therefore, atoms can’t be said to contain a vacuum inside, since at any location there is some probability that an electron will be there. So, if you are looking for a vacuum, you need to find a place where there are no atoms at all!

Sincerely,

p.s.
To complicate things, some people believe that electrons actually do have a defined position, and we just haven’t been able to perform the right measurements to find them. This is an area of open research.