Atoms really have no true structure. They consist of a nucleus (protons and neutrons) that is surrounded by a cloud of electrons. The electrons do not orbit the central nucleus. Instead they inhabit orbitals of probability around the nucleus. The relationship between structure and valency is that (1) the higher energy valent electrons tend to be further from the nucleus, so (2) the valency of an element can determine the general size of the atomic radius. In other words, the more valent electrons that an atom has in its outermost shell the larger the atomic radius of the atom is. This is why atomic radii tend to increase going to the right and down on the periodic table.