Final answer:
In general, the energy of atomic orbitals increases with the principal quantum number (n), meaning that electrons in higher principal energy levels have more energy and are further away from the nucleus.
Step-by-step explanation:
The relationship between the principal energy levels of an electron and the principal quantum number is foundational to understanding atomic structures and electron configurations. The principal quantum number, denoted by n, signifies the main energy level occupied by an electron and implies how far an electron is likely to be from the nucleus. As n increases, so does the energy of the electron, which hence relates to the electron being in a higher energy level. In a hydrogen-like atom or a one-electron ion, these energy levels are quantized and each level is associated with a specific value of energy.
As we look into multi-electron atoms, subshells and electron repulsion play a significant role as well. In this context, orbitals are filled according to their energy which increases within a shell in the order of s, p, d, f. This arrangement affects the chemical properties of the atom. Furthermore, electron-electron interactions lift the degeneracy present in hydrogen-like atoms, creating a distinct energy for each subshell. It is crucial to remember that as the principal quantum number, n, increases, both the size of the orbital and the average distance of the electron from the nucleus increase. This leads to a weaker attraction to the nucleus and a subsequent increase in the orbital's energy.