How does ionization energy affect atomic radius?
Perhaps you should ask how atomic radii affect ionization energy?
Ionization energy is the energy associated with the formation of 1 mole of gaseous cations, and 1 mole of electrons, from 1 mole of gaseous atoms.
The electron that is removed is the valence electron, i.e. the outermost electron that is MOST removed from the positively charged nucleus. It follows that large atoms with greater radii should have intrinsically lower ionization energies. And it is well known that ionization energies decrease down a Group, a column on Periodic Table.