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 A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that cannot be explained by a theory and therefore must be measured experimentally. It is distinct from a mathematical constant, which has a ...

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 Spin or spinning most often refers to: * Spin (physics) or particle spin, a fundamental property of elementary particles * Spin quantum number, a number which defines the value of a particle's spin * Spinning (textiles), the creation of yarn or thr ...

angular momentum. In

SI units The International System of Units, internationally known by the abbreviation SI (from French ), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official st ...

, 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 In particle physics, the electron mass (symbol: ) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy ...

, * 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 Walther Heinrich Wilhelm Ritz (22 February 1878 – 7 July 1909) was a Swiss theoretical physicist. He is most famous for his work with Johannes Rydberg on the Rydberg–Ritz combination principle. Ritz is also known for the variational method n ...

(1907) and

Pierre Weiss Pierre-Ernest Weiss (25 March 1865, Mulhouse – 24 October 1940, Lyon) was a French physicist who specialized in magnetism. He developed the domain theory of ferromagnetism in 1907. Weiss domains and the Weiss magneton are named after him. W ...

. Already before the

Rutherford model The Rutherford model is a name for the first model of an atom with a compact nucleus. The concept arose from Ernest Rutherford discovery of the nucleus. Rutherford directed the Geiger–Marsden experiment in 1909, which showed much more alpha ...

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 __NOTOC__ Richard Martin Gans (7 March 1880 – 27 June 1954), German of Jewish origin, born in Hamburg, was the physicist who founded the Physics Institute of the National University of La Plata, Argentina. He was its Director in two different ...

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 Paul Langevin (23 January 1872 – 19 December 1946) was a French physicist who developed Langevin dynamics and the Langevin equation. He was one of the founders of the '' Comité de vigilance des intellectuels antifascistes'', an anti-fascist ...

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 Ștefan Procopiu (; January 19, 1890 – August 22, 1972) was a Romanian physicist and a titular member of the Romanian Academy. Biography Procopiu was born in 1890 in Bârlad, Romania. His father, Emanoil Procopiu, was employed at the Bâr ...

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 The Weiss magneton was an experimentally derived unit of magnetic moment equal to joules per tesla, which is about 20% of the Bohr magneton. It was suggested in 1911 by Pierre Weiss. Origin The idea of elementary magnets originated from the ...

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 Wolfgang Ernst Pauli ( ; ; 25 April 1900 – 15 December 1958) was an Austrian theoretical physicist and a pioneer of quantum mechanics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics "for the ...

gave the Bohr magneton its name in an article where he contrasted it with the magneton of the experimentalists which he called the

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 In classical electromagnetism, Ampère's circuital law, often simply called Ampère's law, and sometimes Oersted's law, relates the circulation of a magnetic field around a closed loop to the electric current passing through the loop. James ...

. Second, the inherent rotation, or spin, of the electron has a

spin magnetic moment Spin is an intrinsic form of angular momentum carried by elementary particles, and thus by composite particles such as hadrons, atomic nuclei, and atoms. Spin is quantized, and accurate models for the interaction with spin require relativistic ...

. 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 Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed sy ...

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 In atomic physics, the electron magnetic moment, or more specifically the electron magnetic dipole moment, is the magnetic moment of an electron resulting from its intrinsic properties of spin and electric charge. The value of the electron magne ...

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