atomic physics Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...

, the Bohr magneton (symbol ) is a physical constant and the natural unit for expressing the

magnetic moment In electromagnetism, the magnetic moment or magnetic dipole moment is the combination of strength and orientation of a magnet or other object or system that exerts a magnetic field. The magnetic dipole moment of an object determines the magnitude ...

of an

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary charge, elementary electric charge. It is a fundamental particle that comprises the ordinary matter that makes up the universe, along with up qua ...

caused by its orbital or spin angular momentum. In SI units, the Bohr magneton is defined as

\mu_\mathrm = \frac

and in the Gaussian CGS units as

\mu_\mathrm = \frac ,

where * is the

elementary charge The elementary charge, usually denoted by , is a fundamental physical constant, defined as the electric charge carried by a single proton (+1 ''e'') or, equivalently, the magnitude of the negative electric charge carried by a single electron, ...

, * is the

reduced Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

, * is the electron mass, * is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant exactly equal to ). It is exact because, by international agreement, a metre is defined as the length of the path travelled by light in vacuum during a time i ...

History

The idea of elementary magnets is due to Walther Ritz (1907) and Pierre Weiss. Already before the Rutherford model of atomic structure, several theorists commented that the magneton should involve the

Planck constant The Planck constant, or Planck's constant, denoted by h, is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and the wavelength of a ...

''h''. By postulating that the ratio of electron

kinetic energy In physics, the kinetic energy of an object is the form of energy that it possesses due to its motion. In classical mechanics, the kinetic energy of a non-rotating object of mass ''m'' traveling at a speed ''v'' is \fracmv^2.Resnick, Rober ...

to orbital

frequency Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

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 value of ''eħ''/(2''m''_e). Langevin assumed that the attractive force was inversely proportional to distance to the power , and specifically . The Romanian physicist Ștefan Procopiu had obtained the expression for the magnetic moment of the electron in 1913. The value is sometimes referred to as the "Bohr–Procopiu magneton" in Romanian scientific literature. The Weiss magneton was experimentally derived in 1911 as a unit of

equal to which is about 20% of the Bohr magneton. In the summer of 1913, the values for the natural units of atomic angular momentum and magnetic moment were obtained by the Danish physicist

Niels Bohr Niels Henrik David Bohr (, ; ; 7 October 1885 – 18 November 1962) was a Danish theoretical physicist who made foundational contributions to understanding atomic structure and old quantum theory, quantum theory, for which he received the No ...

as a consequence of his atom model. 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.

Theory

A magnetic moment of an electron in an atom is composed of two components. First, the orbital motion of an electron around a nucleus generates a magnetic moment by Ampère's circuital law. Second, the inherent rotation, or spin, of the electron has a spin magnetic moment. In the

Bohr model In atomic physics, the Bohr model or Rutherford–Bohr model was a model of the atom that incorporated some early quantum concepts. Developed from 1911 to 1918 by Niels Bohr and building on Ernest Rutherford's nuclear Rutherford model, model, i ...

of the atom, for an electron that is in the orbit of lowest energy, its orbital angular momentum has magnitude equal to the

, denoted ''ħ''. The Bohr magneton is the magnitude of the magnetic dipole moment of an electron orbiting an atom with this angular momentum. The spin angular momentum of an electron is ''ħ'', but the intrinsic electron magnetic moment caused by its spin is also approximately one Bohr magneton, which results in the electron spin ''g''-factor, a factor relating spin angular momentum to corresponding magnetic moment of a particle, having a value of approximately 2.

References

{{reflist Atomic physics Niels Bohr Physical constants Quantum magnetism Magnetic moment

History

Theory

See also

References