By virtue of its charge and spin motion, an electron develops a magnetic field. It can be thought of as a small magnet (For more, see paramagnetic and diamagnetic substances). Spin is an intrinsic property of an electron (The intrinsic properties of an electron are charge, mass and spin).
The Magnetic quantum number or the third quantum number can be thought of [somewhat inaccurately] as the [quantised] projection of the angular momentum vector on the z-axis that runs from −l to l in integer units. (l is the Azimuthal quantum number).
Magnetic quantum number is used to indicate magnetic energy levels of the electron when an external magnetic field is applied (Hence the name magnetic quantum number). Incidently, it explains the Zeeman effect.
The expression of the separation constant in terms of this quantumnumber affects the form of the colatitude equation.
While the azimuthal dependence of the wavefunction only requires the quantumnumber to be an integer, the coupling to the colatitude equation further constrains that integer to be less than or equal to the orbital quantumnumber.
It is called the magneticquantumnumber because the application of an external magnetic field causes a splitting of spectral lines called the Zeeman effect.
In atomic physics, the magneticquantumnumber is the third of a set of quantumnumbers (the principal quantumnumber, the azimuthal quantumnumber, the magneticquantumnumber, and the spinquantumnumber) which describe the unique quantum state of an electron and is designated by the letter m.
The quantumnumber m refers, loosely, to the direction of the angular momentum vector.
The magneticquantumnumber determines the energy shift of an atomic orbital due to an external magnetic field, hence the name magneticquantumnumber (Zeeman effect).
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