**Bohr magneton**( symbol

*μ*B ) is a physical changeless and the lifelike unit for expressing the charismatic moment of an electron caused by either its orbital or spin angular momentum. [ 4 ] [ 5 ] The Bohr magneton is defined in SI units by μ B = einsteinium ℏ 2 thousand e { \displaystyle \mu _ { \mathrm { B } } = { \frac { e\hbar } { 2m_ { \mathrm { east } } } } } μ B = e ℏ 2 m east c { \displaystyle \mu _ { \mathrm { B } } = { \frac { e\hbar } { 2m_ { \mathrm { east } } hundred } } } and in gaussian CGS units by

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where

## history [edit ]

The idea of elementary magnets is ascribable to Walther Ritz ( 1907 ) and Pierre Weiss. Already before the Rutherford model of nuclear structure, several theorists commented that the magneton should involve Planck ‘s constant *h*. [ 6 ] By postulating that the ratio of electron kinetic energy to orbital frequency should be adequate to *h*, Richard Gans computed a value that was twice a large as the Bohr magneton in September 1911. [ 7 ] At the First Solvay Conference in November that class, Paul Langevin obtained a e ℏ / ( 12 molarity east ) { \displaystyle e\hbar / ( 12m_ { \mathrm { e } } ) } . [ 8 ] Langevin assumed that the attractive pull was inversely proportional to distance to the power n + 1, { \displaystyle n+1, } and specifically normality = 1. { \displaystyle n=1. } [ 9 ]

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The romanian physicist Ștefan Procopiu had obtained the expression for the magnetic moment of the electron in 1911. [ 10 ] [ 11 ] The value is sometimes referred to as the “ Bohr–Procopiu magneton ” in romanian scientific literature. [ 12 ] The Weiss magneton was experimentally derived in 1911 as a unit of charismatic moment equal to 1.53×10−24 joules per tesla, which is about 20 % of the Bohr magneton. In the summer of 1913, the values for the natural units of nuclear angular momentum and magnetic consequence were obtained by the danish physicist Niels Bohr as a consequence of his atom model. [ 7 ] [ 13 ] In 1920, Wolfgang Pauli gave the Bohr magneton its diagnose in an article where he contrasted it with the magneton of the experimentalists which he called the Weiss magneton. [ 6 ]

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## theory [edit ]

A magnetic consequence of a appoint particle can be generated by two ways. First, a moving electric charge forms a current, hence the orbital gesture of an electron around a nucleus generates a charismatic consequence by Ampère ‘s circuital law. Second, the implicit in rotation, or spin, of the electron has a spin magnetic moment. In Bohr ‘s atomic model, a natural unit for the orbital angular momentum of an electron was denoted *ħ*. The Bohr magneton is the order of magnitude of the magnetic dipole moment of an electron orbiting an atom with such angular momentum. According to the Bohr model, this is the ground submit, i.e. the state of lowest possible department of energy. [ 14 ] The spin angular momentum of an electron is 1/2 *ħ*, but the intrinsic electron charismatic moment caused by its spin is besides approximately one Bohr magneton since the electron spin *g* -factor, a agent relating spin angular momentum to corresponding magnetic moment of a atom, is approximately two. [ 15 ]