principal quantum number (n)
The principal quantum number, written n, is a whole number — 1, 2, 3, and so on — that labels the main energy level of an electron in an atom. It is the single biggest factor deciding how tightly the electron is bound and, roughly, how far its cloud spreads from the nucleus. In hydrogen the energy depends only on n: the larger n, the higher (less negative) the energy and the bigger and looser the orbital.
Each value of n names a shell. The lowest, n equal to one, is the snug ground state where the electron sits closest to the nucleus and is hardest to remove. Higher shells lie at greater average distance and step closer together in energy, crowding toward the point where the electron breaks free of the atom altogether. The familiar energy ladder of hydrogen, with levels spaced by one over n squared, is entirely a story about n.
It pays to keep n in its place among the quantum numbers. By itself n fixes the energy in hydrogen and sets the overall scale, but it does not say what shape the orbital has or which way it points — those are the jobs of the other quantum numbers. Think of n as choosing the floor of a building; the remaining numbers then choose the room and its orientation on that floor.
Energy in hydrogen rises toward zero as one over n squared; larger n means a looser, larger orbital.
That energy depends on n alone is special to the pure 1/r potential of hydrogen. In multi-electron atoms the other quantum numbers also shift the energy, which is why their levels split.