# Bohr magneton

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The value of Bohr magneton
system of units value unit
SI[1] 9.27400968(20)×10−24 J·T−1
CGS[2] 9.27400968(20)×10−21 Erg·G−1
eV[3] 5.7883818066(38)×10−5 eV·T−1
atomic units 12 $\frac{e \hbar}{m_\mathrm{e}}$

In atomic physics, the Bohr magneton (symbol μB) 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.[4][5]

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,
me 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.[6]

## 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.[7] 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.[8] At the First Solvay Conference in November that year, Paul Langevin obtained a submultiple.[9] The Romanian physicist Ştefan 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 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.[13] In the summer of 1913, this value was naturally obtained by the Danish physicist Niels Bohr as a consequence of his atom model.[8][14] The result was also independently derived in 1913 by Procopiu using Max Planck's quantum theory.[11] 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.[7]

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.

## References

1. ^ "CODATA value: Bohr magneton". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved 2012-07-09.
2. ^ Robert C. O'Handley (2000). Modern magnetic materials: principles and applications. John Wiley & Sons. p. 83. ISBN 0-471-15566-7. (value was slightly modified to reflect 2010 CODATA change)
3. ^ "CODATA value: Bohr magneton in eV/T". The NIST Reference on Constants, Units, and Uncertainty. NIST. Retrieved 2012-07-09.
4. ^ L. I. Schiff (1968). Quantum Mechanics. McGraw-Hill. p. 440.
5. ^ R. Shankar (1980). Principles of Quantum Mechanics. Plenum Press. pp. 398–400. ISBN 0306403978.
6. ^ Anant S. Mahajan, Abbas A. Rangwala (1989). Electricity and Magnetism. McGraw-Hill. p. 419. ISBN 978-0-07-460225-6.
7. ^ a b Stephen T. Keith and Pierre Quédec (1992). "Magnetism and Magnetic Materials: The Magneton". Out of the Crystal Maze. pp. 384–394. ISBN 978-0-19-505329-6.
8. ^ a b John Heilbron; Thomas Kuhn (1969). "The genesis of the Bohr atom". Historical Studies in the Physical Sciences 1: 232.
9. ^ Paul Langevin (1911). La théorie cinétique du magnétisme et les magnétons. La théorie du rayonnement et les quanta: Rapports et discussions de la réunion tenue à Bruxelles, du 30 octobre au 3 novembre 1911, sous les auspices de M. E. Solvay. p. 403.
10. ^ Ştefan Procopiu (1911–1913). "Sur les éléments d’énergie". Annales scientifiques de l'Université de Jassy 7: 280.
11. ^ a b Ştefan Procopiu (1913). "Determining the Molecular Magnetic Moment by M. Planck's Quantum Theory". Bulletin scientifique de l’Académie roumaine de sciences 1: 151.
12. ^ "Stefan Procopiu (1890-1972)". Stefan Procopiu Science and Technique Museum. Retrieved 2010-11-03.
13. ^ Marcelo Alonso, Edward Finn (1992). Physics. Addison-Wesley. ISBN 978-0-201-56518-8.
14. ^ Abraham Pais (1991). Niels Bohr's Times, in physics, philosophy, and politics. Clarendon Press. ISBN 0-19-852048-4.