magnetic quantum number

In atomic physics, a magnetic quantum number is a quantum number used to distinguish quantum states of an electron or other particle according to its angular momentum along a given axis in space. The orbital magnetic quantum number (ml or m) distinguishes the orbitals available within a given subshell of an atom. It specifies the component of the orbital angular momentum that lies along a given axis, conventionally called the z-axis, so it describes the orientation of the orbital in space. The spin magnetic quantum number ms specifies the z-axis component of the spin angular momentum for a particle having spin quantum number s. For an electron, s is 1⁄2, and ms is either +1⁄2 or −1⁄2, often called "spin-up" and "spin-down", or α and β. The term magnetic in the name refers to the magnetic dipole moment associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field according to the Zeeman effect.

The four quantum numbers conventionally used to describe the quantum state of an electron in an atom are the principal quantum number n, the azimuthal (orbital) quantum number