Let's consider a block of carbon. Its density is 2.25, and its gram molecular weight is 12, meaning that 12 grams, or 5.33 cubic cm, contains Avagadro's number, or 6 x 10^23 atoms. Then the "volume" of 1 atom of carbon is 8.88 x 10^-24 cubic cm, equivalent roughly to a cube 2.07 x 10^-8 cm on a side. But the carbon nucleus is perhaps a "sphere" with a radius of about 2 x 10^-13 cm. Thus the ratio of atom dimension to nucleus dimension is about 100,000 to 1. The volume ratio is about 10^15 to 1. Most of the mass of the carbon atom is in the nucleus, with 6 electrons "filling" the rest of the space. For most purposes this space is empty, except that very close to the nucleus, the electric field is very high. This high field occasionally produces virtual electrons and positrons, meaning that they exist only for very short times, and disappear as quickly as they were created. So yes, there is a lot of empty space in atoms, and no, the vacuum is not completely empty.