Final answer:
The principal quantum number (n) labels the basic states of a system and determines the energy level and distance of an electron from the nucleus.
Step-by-step explanation:
The principal quantum number (n) in quantum mechanics labels the basic states of a system. It tells the average relative distance of an electron from the nucleus. The allowed values for n are 1, 2, 3, and so on, increasing by integers.
For example, if n = 1, the electron is in the first energy level or shell closest to the nucleus. If n = 2, the electron is in the second energy level or shell, and if n = 3, the electron is in the third energy level or shell, and so on.
The principal quantum number determines the energy level of an electron and its distance from the nucleus.