What atomic property affects periodic trends down a group in the periodic table?

The phenomenon that comes into play as we go down toward the bottom of the periodic table through a group is electron screening. As we descend through a group, the atomic number of an atom increases, and so does the number of electrons shells. That means more electrons are between the nucleus (the positive charge) and the valence shell. You'll recall that the valence shell is the outer electron shell, and it is this shell and its population that largely determine the chemistry of an element. When atoms are larger with more electrons shells, the positive charge on the nucleus is "shielded" from the valence shell to a degree by the inner electron shells. That nucleus isn't "holding onto" the valence electrons as tightly. And in atoms that are electron "loaners" like those on the left side of the periodic table, the elements further down a group are "more willing" to loan out valence electrons. This means that they are more reactive. Electron screening serves to "interfere" with the grip the nucleus holds on the valence electrons for atoms farther down a group. On the right side of the periodic table, elements tend to be "borrowers" of electrons, and the translation of the effect of screening on the right is that the elements toward the bottom of a group are going to be less inclined to want to borrow an electron that elements higher up. Again, this is due to electron screening. If all of this is true, then the element of the bottom of Group 1, which is on the left of the table, will be the most reactive electron-loaning element. That's francium, and it is, indeed, the most reactive of the Group 1 elements. Conversely, on the right in the Group 17 elements (the halogens or halides), we'd expect the elements at the bottom to be less reactive than those at the top. And they are. The most reactive halogen is fluorine (at the top of the group), and it is the hungry wolf of the periodic table. Links are provided below.