Well...Not quite. Atoms are actually packed quite close together, and in some sense touch one another. Now, in crude terms, the size of the NUCLEUS of an atom compared to the diameter of the 'First Bohr Orbit' can be about the scale of the solar system. The Nucleus is about 10^-14 centimeters across. The first Bohr orbit is about 1 angstrom across or 10^-8 centimeters, so the diameter of the atom is about 1 million times the diameter of an atomic nucleus. If the Earth is about 6500 kilometers in radius, then 6500 x 1 million is 6.5 billion kilometers or about 4 billion miles. This is about the orbital distance of Pluto. So the INTERIOR of an atom relative to the size of the NUCLEUS matches the solar system in scale, but the individual atoms themselves, using an atom as a measuring unit, is packed far denser.