What does the principal quantum number (N) define?

The principal quantum number (N) is a crucial descriptor in quantum mechanics that indicates the energy level and size of an atomic orbital. It is a positive integer (1, 2, 3, etc.) that corresponds to the main energy shell in which an electron resides. As the value of N increases, the energy of the electron increases, meaning that electrons in higher principal quantum levels have more energy compared to those in lower levels. Additionally, a larger principal quantum number implies that the orbital is larger, allowing electrons to be found further from the nucleus.

In this context, while the shape of the orbital is defined by the azimuthal quantum number (l), the spin orientation is described by the spin quantum number (s), and the magnetic properties of the atom are indicated by the magnetic quantum number (m). Each of these quantum numbers provides distinct information about the behavior and arrangement of electrons, but it is the principal quantum number that fundamentally relates to the energy and spatial extent of the orbital.