# Bohr magneton

The value of Bohr magneton
system of units value unit
SI[1] Template:Val J·T−1
CGS[2] Template:Val Erg·G−1
eV[3] Template:Val eV·T−1
atomic units Template:Frac none

In atomic physics, the Bohr magneton (symbol μB), also known as the Bohr-Procopiu magneton is a physical constant and the natural unit for expressing an electron magnetic dipole moment. The Bohr magneton is defined in SI units by

${\displaystyle \mu _{\mathrm {B} }={\frac {e\hbar }{2m_{\mathrm {e} }}}}$

and in Gaussian CGS units by

${\displaystyle \mu _{\mathrm {B} }={\frac {e\hbar }{2m_{\mathrm {e} }c}}}$

where

e is the elementary charge,
ħ is the reduced Planck constant,
me is the electron rest mass and
c is the speed of light.

The magnitude of an electron's spin magnetic moment is approximately one Bohr magneton.[4]

## History

The idea of elementary magnets is due to Walter Ritz (1907) and Pierre Weiss. Already before the Rutherford model of atomic structure, several theorists commented that the magneton should involve Planck's constant h.[5] By postulating that the ratio of electron kinetic energy to orbital frequency should be equal to h, Richard Gans computed a value that was twice as large as the Bohr magneton in September 1911.[6] At the First Solvay Conference in November that year, Paul Langevin obtained a submultiple.[7] The Romanian physicist Ştefan Procopiu obtained for the first time its value in 1911;[8][9] the value is referred to as the "Bohr–Procopiu magneton" in Romanian scientific literature.[10]

The Bohr magneton is the magnitude of the magnetic dipole moment of an orbiting electron with an orbital angular momentum of one ħ. According to the Bohr model, this is the ground state, i.e. the state of lowest possible energy.[11] In the summer of 1913, this value was naturally obtained by the Danish physicist Niels Bohr as a consequence of his atom model,[6][12] and also published independently by Procopiu using directly Max Planck's quantum theory.[9] In 1920, Wolfgang Pauli gave the Bohr magneton its name in an article where he contrasted it with the magneton of the experimentalists which he called the Weiss magneton.[5]