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Concept
Magnetic quantum number
Summary
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 , and ms is either + or −, 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 , and the magnetic quantum numbers ml and ms. Electrons in a given subshell of an atom (such as s, p, d, or f) are defined by values of (0, 1, 2, or 3). The orbital magnetic quantum number takes integer values in the range from to , including zero. Thus the s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals each, with values of ml within the ranges 0, ±1, ±2, ±3 respectively. Each of these orbitals can accommodate up to two electrons (with opposite spins), forming the basis of the periodic table.
Other magnetic quantum numbers are similarly defined, such as mj for the z-axis component the total electronic angular momentum j, and mI for the nuclear spin I. Magnetic quantum numbers are capitalized to indicate totals for a system of particles, such as ML or mL for the total z-axis orbital angular momentum of all the electrons in an atom.
There is a set of quantum numbers associated with the energy states of the atom.
Official source
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