Magnetic quantum number

In <a href="/facts/Atomic_physics/7Jlm4I7k">atomic physics</a>, a magnetic quantum number is a <a href="/facts/Quantum_number/AByP6F0y">quantum number</a> used to distinguish quantum states of an <a href="/facts/Electron/L0KBo5cW">electron</a> or other particle according to its <a href="/facts/Angular_momentum/7TuSVFxq">angular momentum</a> along a given axis in space. The orbital magnetic quantum number (ml or m) distinguishes the <a href="/facts/Atomic_orbital/tKhgl6mL">orbitals</a> available within a given <a href="/facts/Electron_shell/QxI30eh9">subshell</a> 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 <a href="/facts/Spin_(physics)/4Jvp7e8P">spin angular momentum</a> for a particle having <a href="/facts/Spin_quantum_number/5Nh2H8gr">spin quantum number</a> s. For an electron, s is 1⁄2, and ms is either +1⁄2 or −1⁄2, often called "spin-up" and "spin-down", or α and β. The term magnetic in the name refers to the <a href="/facts/Magnetic_dipole_moment/VpAQKJtr">magnetic dipole moment</a> associated with each type of angular momentum, so states having different magnetic quantum numbers shift in energy in a magnetic field according to the <a href="/facts/Zeeman_effect/A6NMlp2D">Zeeman effect</a>.
The four quantum numbers conventionally used to describe the quantum state of an electron in an atom are the <a href="/facts/Principal_quantum_number/8SzSWV6w">principal quantum number</a> n, the <a href="/facts/Azimuthal_quantum_number/vHSIzbFC">azimuthal (orbital) quantum number</a> 
 
 
 
 ℓ
 
 
 {\displaystyle \ell }
 
, 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 
 
 
 
 ℓ
 
 
 {\displaystyle \ell }
 
 (0, 1, 2, or 3). The orbital magnetic quantum number takes integer values in the range from 
 
 
 
 −
 ℓ
 
 
 {\displaystyle -\ell }
 
 to 
 
 
 
 +
 ℓ
 
 
 {\displaystyle +\ell }
 
, including zero. Thus the s, p, d, and f subshells contain 1, 3, 5, and 7 orbitals each. Each of these orbitals can accommodate up to two electrons (with opposite spins), forming the basis of the <a href="/facts/Periodic_table/umdGIfUb">periodic table</a>.
Other magnetic quantum numbers are similarly defined, such as mj for the z-axis component the <a href="/facts/Total_angular_momentum_quantum_number/onphLcJI">total electronic angular momentum</a> j, and mI for the <a href="/facts/Spin_quantum_number/5Nh2H8gr">nuclear spin</a> 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.

Magnetic quantum number open-in-new

Magnetic quantum number