Almost all of the volume of an atom is empty space. For example, the hydrogen atom, which has one proton, one neutron and one electron, is 99.99 percent empty space, with just 0.0000000000004 percent of its volume occupied by subatomic particles.
To give some scale, if a hydrogen atom were the size of the Earth, its nucleus of a lone proton and neutron would be about 600 feet in diameter, leaving the rest of the Earth an empty vacuum. Electrons, while approximately 1800 times less massive than protons, have an unknown volume. Heavier elements have more subatomic particles and therefore a slightly higher ratio of subatomic material to empty space.