As the elements in Group 17 on the Periodic Table are considered from top to bottom what happens to the atomic radius and the metalic character ofeach successive element?
Atomic radii and metallic character both increase.
When going from top to bottom in any group of the periodic table, the atomic radius always tends to increase. This is due to the fact that with each successive period, elements have electrons that occupy a new energy shell more distant from the nucleus, and the nuclear force acting on these outer electrons decreases, meaning the nucleus (specifically the positively-charged protons) exerts less of a "pull" on the outer electrons, and thus are farther from the nucleus.
Metallic character tends to increase as one goes from top to bottom and from right to left on the periodic table. In this sense, "metallic character" means the ability to give up electrons to become cationic. This is due (as mentioned before) to the electrons being farther from the nucleus, and nucleus doesn't have enough of a "force" to keep the electrons in the atom's electron cloud, and are pulled away more easily. Going left to right, metallic character decreases because as atoms have more electrons in their outer shell, the more likely they are to gain an electron than to give one up to complete a fully occupied valence shell.