Atoms are made of electrons and a positively charged nucleus. The nucleus, however, only takes a tiny fraction of the atom's space. Hence, one could say that for a small object, an atom is 'nearly empty'.
When you send alpha particles on a sheet, most of them will go through the sheets, as they'll travel through the atom's 'empty' zone. Only a small fraction will actually meet the nuclei; as they are both charged positively, the alpha particles will undergo a repulsive force, and thus be deflected.
