One of our consistent themes in this MCAT course is how helpful classical electrodynamics can be to understanding chemistry. While quantum electrodynamics provides a better model in many ways, plain old Coulomb's Law does provide useful insight into the periodic properties of atomic radius, ionization energy, and electron affinity. Without trying to be perfectly rigorous, imagine mechanical work against electrostatic force to visualize the energy transformations of the atom represented by each periodic property.
This is fine as long as one does not forget that the events are quantized. Atomic radius decreases as you move rightward on the table. Imagine the stronger, more positive nucleus, pulling the electrons tighter with a stronger electrostatic force. Ionization energy increases moving rightward. Imagine how it would take more work to pull an electron in a given shell away from a nucleus with more protons. You are using imaginative visualization to build your intuition.
The classical picture can help you as long as you know its limitations. Sometimes it is helpful to think about the periodic properties as if they were describing a simple electrostatic system as long as you don't forget that quantum electrodynamics provides a fuller picture.