Why does the periodic trend of atomic radius happen?

Radius is determined by a balance between attraction toward the nucleus, repulsion by other electrons, and the energy levels of the orbitals. The protons attract the electrons, but the electrons repel each other. so they find a place where attraction equals repulsion, and that is enforced by the energy level of the orbital they are in. If an electron is lost, then the number of negative charges no longer equals the number of positive charges and the entire molecule (now an ion) shrinks due to electric attraction.