Bohr magneton

The value of Bohr magneton

system of units	value	unit
SI	9.27400968(20)×10−24	J·T−1
CGS	9.27400968(20)×10−21	Erg·G−1
eV	5.7883818066(38)×10−5	eV·T−1
atomic units	​1⁄2	$\frac{e \hbar}{m_\mathrm{e}}$

In atomic physics, the Bohr magneton (symbol μ_B) is a physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum.

The Bohr magneton is defined in SI units by

$\mu_\mathrm{B} = \frac{e \hbar}{2 m_\mathrm{e}}$

and in Gaussian CGS units by

$\mu_\mathrm{B} = \frac{e \hbar}{2 m_\mathrm{e} c}$

where

e is the elementary charge,

ħ is the reduced Planck constant,

m_e is the electron rest mass and

c is the speed of light.

The electron magnetic moment, which is the electron's intrinsic spin magnetic moment, is approximately one Bohr magneton.

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. 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. At the First Solvay Conference in November that year, Paul Langevin obtained a submultiple. The Romanian physicist Ştefan Procopiu had obtained the expression for the magnetic moment of the electron in 1911. The value is sometimes referred to as the "Bohr–Procopiu magneton" in Romanian scientific literature.

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. In the summer of 1913, this value was naturally obtained by the Danish physicist Niels Bohr as a consequence of his atom model. The result was also independently derived in 1913 by Procopiu using Max Planck's quantum theory. 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.

Although the spin angular momentum of an electron is 1/2 ħ, the intrinsic magnetic moment of the electron caused by its spin is still approximately one Bohr magneton. The electron spin g-factor is approximately two.

See also

• Nuclear magneton
• Electron magnetic moment
• Niels Bohr
• Ștefan Procopiu
• Physical constant
• Anomalous magnetic moment
• Zeeman effect
• Parson magneton