Which quantum number designates the orientation of an orbital?

The magnetic quantum number is the one that designates the orientation of an orbital within a given subshell. It provides information on the specific spatial orientation of an orbital in relation to the three axes in space (x, y, and z). For instance, in a p subshell (where the orbital quantum number l equals 1), there are three possible orientations corresponding to the values of the magnetic quantum number: -1, 0, and +1. This means there are three distinct p orbitals oriented along different axes.

In contrast, the principal quantum number indicates the overall energy level and size of the orbital, while the orbital quantum number describes the shape of the orbital. The spin quantum number relates to electron spin and does not provide information about orbital orientation. Therefore, the magnetic quantum number is crucial in determining how orbitals are aligned in a given atom.