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 is generally believed to be both universal in nature and have constant value in time. It is contrasted with a mathematical constant, ...

and the natural unit for expressing the

magnetic moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnets ...

of an

electron The electron (, or in nuclear reactions) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary partic ...

caused by its

orbital Orbital may refer to: Sciences Chemistry and physics * Atomic orbital * Molecular orbital * Hybrid orbital Astronomy and space flight * Orbit ** Earth orbit Medicine and physiology * Orbit (anatomy), also known as the ''orbital bone'' * Orbito ...

or spin angular momentum. The Bohr magneton, in

SI units The International System of Units, known by the international abbreviation SI in all languages and sometimes pleonastically as the SI system, is the modern form of the metric system and the world's most widely used system of measurement. E ...

is defined as

\mu_\mathrm = \frac ,

And in Gaussian CGS units:

\mu_\mathrm = \frac ,

where * is the

elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a funda ...

, * is the

reduced Planck constant The Planck constant, or Planck's constant, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalen ...

, * is the electron rest mass, * is the

speed of light The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...

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 na ...

(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, is a fundamental physical constant of foundational importance in quantum mechanics. The constant gives the relationship between the energy of a photon and its frequency, and by the mass-energy equivalen ...

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

kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its a ...

to orbital

frequency Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from '' angular frequency''. Frequency is measured in hertz (Hz) which is ...

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

e\hbar/(12m_\mathrm)

. Langevin assumed that the attractive force was inversely proportional to distance to the power

n+1,

and specifically

n=1.

The Romanian physicist Ștefan 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 Weiss magneton was experimentally derived in 1911 as a unit of

equal to

joule The joule ( , ; symbol: J) is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applie ...

s per tesla, 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 physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922 ...

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 one of the pioneers of quantum physics. In 1945, after having been nominated by Albert Einstein, Pauli received the Nobel Prize in Physics fo ...

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, a moving electric charge of the electron forms a current, hence 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, presented by Niels Bohr and Ernest Rutherford in 1913, is a system consisting of a small, dense nucleus surrounded by orbiting electrons—similar to the structure of the Solar Sy ...

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, being approximately two.

References

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

History

Theory

See also

References