How do trends in atomic radius relate to ionization energy?

The smaller the radius, the higher the ionization energy.

This is because the electrons are being held in closer to the protons, which have opposing charges and therefore hold on to them, in an atom with a small radius.

If the radius is larger, then those electrons on the outer edge of the atom aren't being held in so close and are easier to lose - requiring a lower amount of energy to ionize.

Factors are more shielding (from core electrons) in those lower down in a family making electrons easier to leave. For those in a period, the effective nuclear charge increases as you go across a period (more protons, but no more energy levels, so the electrons are the same distance from the nucleus). This makes the electrons held in closer (smaller radius) and higher energy is required to ionize them.