Which electron is, on average, further from the nucleus: an electron in a 3\(p\) orbital or an electron in a 4\(p\) orbital?

The principal quantum number, denoted as 'n', plays a crucial role in determining the properties of atomic orbitals, and consequently, the electron configuration of an atom. It is an integer starting from 1 and increasing in value as we move further away from the nucleus. Each quantum number corresponds to a different shell. For example, 'n=1' indicates the first shell, closest to the nucleus, while 'n=2' is the next shell outward, and so forth.

The value of 'n' also affects the orbital's energy level and size – higher values mean the orbital is larger and the electrons within have more energy, thus being further from the nucleus. This directly impacts how the elements behave chemically, since the 'n' value determines the most probable distance of an electron from the nucleus. In essence, 'n' is like the address of an electron, specifying a particular neighborhood (shell) inside the vast city that is an atom.

The term 'orbital energy levels' refers to the discrete amounts of energy that electrons in atoms can have. Electrons reside in regions known as orbitals, each with particular energy levels. These levels are often depicted as rungs on a ladder within each shell (principal quantum number, n), with electrons allowed to occupy only these specific rungs.

Several factors influence these energy levels, including the principal quantum number and the sublevels (s, p, d, f). Generally, energy levels increase with higher 'n' values; however, there can be overlaps between different shells, especially in larger atoms. Electrons naturally 'seek' the lowest energy states available according to the Aufbau principle, which states that electrons fill the lowest energy orbitals first. This orderly filling is what leads to the distinctive electron configurations of each element and is responsible for the unique chemical properties they exhibit.

Electron configuration is like a map that gives a detailed arrangement of electrons around a nucleus. It's built upon the Pauli Exclusion Principle and Hund's Rule, ensuring no two electrons in an atom have the same set of quantum numbers and that single electrons occupy each orbital of a subshell before pairing up.

Electron configurations are expressed using a notation that lists the principal quantum number followed by the letter of the subshell (s, p, d, f) and a superscript indicating the number of electrons in that subshell. For example, the electron configuration of oxygen is written as '1s² 2s² 2p⁴' telling us there are two electrons in the 1s orbital, two in the 2s, and four in the 2p orbitals. By understanding electron configuration, chemists can predict and explain a wide array of chemical behaviors and the formation of different molecules.