How are the trends of atomic radius and ionization energy related? Explain in both groups and periods.

These trends are inverses of each other. As the size of the atom increases, the ionization energy (energy required to remove the electron) decreases because the electron being removed is farther from the nucleus in a larger atom.Less energy is required to remove an electron further from the nucleus. [AR increases down a group while IE decreases; AR decreases across a period while IE increases.]