The magnetic quantum number (often denoted as “m”) is a quantum number used to describe the orientation of atomic orbitals within a subshell and the direction of an electron’s angular momentum relative to an external magnetic field. It provides information about the spatial distribution of electrons within an orbital and helps in defining the orientation of the orbital in three-dimensional space.

Key points about the magnetic quantum number:

1. Values: The magnetic quantum number can take integer values ranging from -l to +l, where “l” is the azimuthal quantum number. For a given subshell with a specific value of “l,” there are (2l + 1) possible values of “m.”
2. Orbital Orientation: Each value of “m” corresponds to a specific orbital orientation within a subshell. When plotted, the orientation of the orbitals resembles the orientation of different axes in space.
3. Number of Orbitals: The number of possible values of “m” determines the number of orbitals within a subshell. For example, an “s” subshell (l = 0) has only one orbital (m = 0), while a “p” subshell (l = 1) has three orbitals (m = -1, 0, +1).
4. Electron Pairing: According to the Pauli exclusion principle, each orbital can hold a maximum of two electrons with opposite spins. When an orbital is occupied by a single electron, it has a specific value of “m.” The second electron in the same orbital has the opposite spin and maintains the same value of “m.”
5. Energy Order: Within a given subshell (same “l” value), orbitals with different “m” values have the same energy level. However, as “m” changes, the spatial orientation of the orbitals changes.
6. Magnetic Behavior: The orientation of atomic orbitals and the magnetic quantum number contribute to the magnetic properties of atoms, particularly in external magnetic fields.
7. Subshell Labels: The values of “m” help label individual orbitals within a subshell. For example, the three “p” orbitals are labeled as px (m = -1), py (m = 0), and pz (m = +1).

The magnetic quantum number, along with the principal quantum number (n) and azimuthal quantum number (l), helps describe the arrangement and orientation of electrons within orbitals and subshells. It is a crucial component of the quantum mechanical model of atoms and is fundamental to understanding atomic structure and behavior.