Magnetic Quantum Number

The magnetic quantum number for an electron classifies which orientation its subshell shape is pointed. For each subshell in each shell, there are multiple directions in which the "lobes" can point, and these different orientations are called orbitals. For the first subshell (s; l=0), which resembles a sphere, there is no "direction" it can "point," so there is only one orbital. For the second (p; l=1) subshell in each shell, which resembles a dumbbell, there are three different directions they can be oriented (think of three dumbbells intersecting in the middle, each oriented along a different axis in a three-axis coordinate system).

Valid numerical values for this quantum number consist of integers ranging from -l to l, and are symbolized as m_l in atomic physics and l_z in nuclear physics. To calculate the number of orbitals in any given subshell, double the subshell number and add 1 (2l + 1). For example, the first subshell (l=0) in any shell contains a single orbital, numbered 0; the second subshell (l=1) in any shell contains three orbitals, numbered -1, 0, and 1; the third subshell (l=2) contains five orbitals, numbered -2, -1, 0, 1, and 2; and so on.

Like principal quantum numbers, the magnetic quantum number arose directly from experimental evidence: the division of spectral lines as a result of exposing an ionized gas to a magnetic field, hence the name "magnetic" quantum number.