The Magnetic quantum number or the third quantum number can be thought of [somewhat inaccurately] as the [quantised] projection of the angular momentum vector on the z-axis that runs from −l to l in integer units. (l is the Azimuthal quantum number).
The magnetic quantum number determines the energy shift of an atomic orbital due to an external magnetic field, hence the name magnetic quantum number (Zeeman effect).
However, the actual magnetic dipole moment of an electron in an atomic orbital arrives not only from the electron angular momentum, but also from the electron spin, expressed in the spin quantum number.
