This "empty space" idea is a holdover from scattering experiments performed during the dawn of the 20th century. Most of the space in an atom is composed by the probability distribution of the electrons in the atom.
These experiments, if I am thinking of the same ones you are, more properly explain that most of the atom is "not the nucleus", not that most of the atom is "empty space". Of course, they still teach the Bohr model in schools, so it is no surprise that people get confused even after taking "some chemistry".
The atom is like a solar system. The nucleus is the sun and the electrons is the planets.