The magnetic quantum number for an electron classifies which orientation its subshell shape is pointed. The “lobes” for subshells point in multiple directions. These different orientations are called orbitals. For the first subshell (s; l=0), which look like a sphere pointing in no “direction”, so there is only one orbital. For the second (p; l=1) subshell in each shell, which bear a resemblance to dumbbells point in three possible directions.
Valid numerical values for this quantum number consist of integers ranging from -1 to 1 and are symbolized as m in atomic physics and Iz in nuclear physics. To calculate the number of orbitals in any given subshell, double the subshell number and add 1 i.e. (2.l + 1), for instance, 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) comprises of five orbitals, numbered -2, -1, 0, 1, and 2, etc.
The magnetic quantum number stem from experimental evidence: the Zeeman Effect, the division of spectral lines by exposing an ionized gas to magnetic field, hence the name “magnetic” quantum number.
Related: Principal Quantum Number
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