Which quantum number describes the orientation of an orbital?

The magnetic quantum number is the one that describes the orientation of an orbital within a given subshell. In quantum mechanics, each type of orbital (s, p, d, f) has a specific shape and orientation in space, which is dictated by this quantum number.

The magnetic quantum number can take on integer values ranging from -l to +l, where l is the azimuthal quantum number associated with the subshell type. For example, in a p subshell (l = 1), the magnetic quantum number can be -1, 0, or +1, corresponding to the three spatial orientations of the p orbitals (often visualized as three separate lobes). Thus, this quantum number is crucial for understanding how orbitals are oriented relative to each other in an atom and contributes to the overall electronic structure and behavior of atoms in chemical reactions.

In contrast, the principal quantum number defines the size and energy level of an orbital, the azimuthal quantum number determines the shape of the orbital, and the spin quantum number describes the intrinsic spin of electrons within the orbitals, not their orientation.