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Magnetic Quantum Number
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.


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