I can't say confidently that an atom is mostly vacuum, but I am somewhat sure of it because electrons and nucleons cover little space, and everything other than these elementary particles in an atom is vacuum.
Why is everything around us rigid even if the atom is mostly vacuum?
EDIT
The question over which this question is marked duplicate has a completely different premise as compared to this question as this question asks about rigidity of materials around us rather than interaction between things around us and their subsequent behavior that they do not pass through each other.
