why does atomic radius change as it does?

Answer 1

Atomic radius increases, moving from top to bottom of a family, because each succeeding element has an additional level or shell of electrons. (Draw Bohr-Rutherford diagrams to show this.)
Each new level is shielded from the pull of the nucleus by the layers below it, so it it is further out from the nucleus, making the atom bigger.

Moving from left to right across a row, the atomic radius decreases. All of these atoms have their electrons in the same valence shell, but the number of protons increases, making the pull from the nucleus larger as you move from left to right.
The increased pull draws the electrons in closer, making the atom smaller.