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Electron magnetic dipole moment

 

 
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Electron magnetic dipole moment
 
 
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In atomic physics
Atomic physics

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nuclei. It is primarily concerned with the Electron configuration and...
, the electron magnetic dipole moment is the magnetic moment
Magnetic moment

In physics, astronomy, chemistry, and electrical engineering, the term magnetic moment of a system usually refers to its magnetic dipole moment, and is a measure of the strength of the system's net Magnetism....
 of an electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
 caused by its intrinsic property of spin
Spin (physics)

In quantum mechanics, spin is a fundamental property of atomic nucleus, hadrons, and elementary particles. For particles with non-zero spin, spin direction is an important intrinsic degrees of freedom ....
.

electron is a negatively charged particle with angular momentum
Angular momentum

In physics, the angular momentum of a particle about an origin is a vector quantity related to rotation, equal to the mass of the particle multiplied by the cross product of the position vector of the particle with its velocity vector....
. A rotating electrically charged
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 body in classical electrodynamics causes a magnetic dipole effect creating magnetic poles of equal magnitude but opposite polarity like a bar magnet. For magnetic dipoles, the dipole moment points from the magnetic south to the magnetic north pole.






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In atomic physics
Atomic physics

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nuclei. It is primarily concerned with the Electron configuration and...
, the electron magnetic dipole moment is the magnetic moment
Magnetic moment

In physics, astronomy, chemistry, and electrical engineering, the term magnetic moment of a system usually refers to its magnetic dipole moment, and is a measure of the strength of the system's net Magnetism....
 of an electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
 caused by its intrinsic property of spin
Spin (physics)

In quantum mechanics, spin is a fundamental property of atomic nucleus, hadrons, and elementary particles. For particles with non-zero spin, spin direction is an important intrinsic degrees of freedom ....
.

Explanation of magnetic moment

The electron is a negatively charged particle with angular momentum
Angular momentum

In physics, the angular momentum of a particle about an origin is a vector quantity related to rotation, equal to the mass of the particle multiplied by the cross product of the position vector of the particle with its velocity vector....
. A rotating electrically charged
Electric charge

Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. Electrically charged matter is influenced by, and produces, electromagnetic fields....
 body in classical electrodynamics causes a magnetic dipole effect creating magnetic poles of equal magnitude but opposite polarity like a bar magnet. For magnetic dipoles, the dipole moment points from the magnetic south to the magnetic north pole. The electron exists in a magnetic field which exerts a torque
Torque

Torque is the tendency of a force to rotate an object about an axis . Just as a force is a push or a pull, a torque can be thought of as a twist....
 opposing its alignment creating a potential energy that depends on its orientation with respect to the field. The magnetic energy of an electron is approximately twice what it should be in classical mechanics. The factor of two multiplying the electron spin angular momentum comes from the fact that it is twice as effective in producing magnetic moment. This factor is called the electronic spin g-factor
G-factor

A g-factor is a dimensionless quantity which characterizes the magnetic moment and gyromagnetic ratio of a particle or atomic nucleus. It is essentially a proportionality constant that relates the observed magnetic moment ? of a particle to the appropriate angular momentum quantum number and the appropriate fundamental quantum unit of ma...
. The persistent early spectroscopists, such as Alfred Lande
Alfred Landé

Alfred Land? was a German-American physicist known for his contributions to Quantum mechanics. He is responsible for the Land? g-factor and an explanation of the Zeeman Effect....
, worked out a way to calculate the effect of the various directions of angular momenta. The resulting geometric factor is called the Lande g-factor
Landé g-factor

In physics, the Land? g-factor is a particular example of a g-factor, namely for an electron with both Spin and orbital angular momentum. It is named after Alfred Land?, who first described it in 1921....
.

The intrinsic magnetic moment μ of a particle with charge q, mass m, and spin s, is

where the dimensionless quantity
Dimensionless quantity

In dimensional analysis, a dimensionless quantity is a quantity without any physical units and thus a pure number. Such a number is typically defined as a product or ratio of quantity which do have units, in such a way that all the units cancel out....
 g is called the g-factor
G-factor

A g-factor is a dimensionless quantity which characterizes the magnetic moment and gyromagnetic ratio of a particle or atomic nucleus. It is essentially a proportionality constant that relates the observed magnetic moment ? of a particle to the appropriate angular momentum quantum number and the appropriate fundamental quantum unit of ma...
.

The g-factor is an essential value related to the magnetic moment of the subatomic particles and corrects for the precession of the angular momentum. One of the triumphs of the theory of quantum electrodynamics
Quantum electrodynamics

Quantum electrodynamics is a relativity theory quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s....
 is its accurate prediction of the electron g-factor, which has been experimentally determined to have the value 2.002319... The value of 2 arises from the Dirac equation
Dirac equation

In physics, the Dirac equation is a theory of relativity quantum mechanics wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary particle spin-? particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity....
, a fundamental equation connecting the electron's spin with its electromagnetic properties, and the correction of 0.002319..., called the anomalous magnetic dipole moment
Anomalous magnetic dipole moment

In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle....
 of the electron, arises from the electron's interaction with virtual photons in quantum electrodynamics
Quantum electrodynamics

Quantum electrodynamics is a relativity theory quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s....
. Reduction of the Dirac equation for an electron in a magnetic field to its non-relativistic limit yields the Schrödinger equation with a correction term which takes account of the interaction of the electron's intrinsic magnetic moment with the magnetic field giving the correct energy.

The total spin magnetic moment
Magnetic moment

In physics, astronomy, chemistry, and electrical engineering, the term magnetic moment of a system usually refers to its magnetic dipole moment, and is a measure of the strength of the system's net Magnetism....
 of the electron is

where in Dirac mechanics, but is slightly larger due to Quantum Electrodynamic
Quantum electrodynamics

Quantum electrodynamics is a relativity theory quantum field theory of electrodynamics. QED was developed by a number of physicists, beginning in the late 1920s....
 effects, is the Bohr magneton
Bohr magneton

In atomic physics, the Bohr magneton is a physical constant of magnetic moment of electrons. It was discovered in 1913 by Romanian physicist Stefan Procopiu and rediscovered independently two years later by Denmark physicist Niels Bohr....
, s is the electron spin, and is the reduced Planck constant. An electron has an intrinsic magnetic dipole moment of approximately one Bohr magneton.

The z component of the electron magnetic moment is

where ms is the spin quantum number.

It is important to notice that is a negative constant multiplied by the spin
Spin (physics)

In quantum mechanics, spin is a fundamental property of atomic nucleus, hadrons, and elementary particles. For particles with non-zero spin, spin direction is an important intrinsic degrees of freedom ....
, so the magnetic moment is antiparallel to the spin angular momentum.

Orbital magnetic dipole moment

Generally, for a hydrogen
Hydrogen

Hydrogen is the chemical element with atomic number 1. It is represented by the chemical symbol H. At standard temperature and pressure, hydrogen is a colorless, odorless, nonmetallic, tasteless, highly combustion and explosive Diatomic molecule gas with the molecular formula H2....
 atomic electron
Electron

The electron is a subatomic particle that carries a negative electric charge. It has elementary particle and is believed to be a point particle....
 in state where and are the principal, azimuthal and magnetic quantum numbers respectively, the total magnetic dipole moment
Dipole moment

Dipole moment refers to the quality of a system to behave like a dipole. Dipole moment is the measured polarity of a polar covalent bond. It is defined as the product magnitude of charge on the atoms and the distance between the two bonded atoms....
 due to orbital angular momentum
Angular momentum

In physics, the angular momentum of a particle about an origin is a vector quantity related to rotation, equal to the mass of the particle multiplied by the cross product of the position vector of the particle with its velocity vector....
 is given by

where is the Bohr magneton
Bohr magneton

In atomic physics, the Bohr magneton is a physical constant of magnetic moment of electrons. It was discovered in 1913 by Romanian physicist Stefan Procopiu and rediscovered independently two years later by Denmark physicist Niels Bohr....
.

The z-component of the orbital magnetic dipole moment for an electron with a magnetic quantum number
Magnetic quantum number

In atomic physics, the magnetic quantum number is the third of a set of quantum numbers which describe the unique quantum state of an electron and is designated by the letter m....
 ml is given by

See also

  • Anomalous magnetic dipole moment
    Anomalous magnetic dipole moment

    In quantum electrodynamics, the anomalous magnetic moment of a particle is a contribution of effects of quantum mechanics, expressed by Feynman diagrams with loops, to the magnetic moment of that particle....
  • Nuclear magnetic moment
    Nuclear magnetic moment

    The nuclear magnetic moment is the magnetic moment of an atomic nucleus and arises from the spin of the protons and neutrons. It is mainly a magnetic dipole moment; the quadrupole moment does cause some small shifts in the hyperfine structure as well....
  • Fine structure
    Fine structure

    In atomic physics, the fine structure describes the splitting of the spectral lines of atoms due to first order relativistic corrections.The gross structure of line spectra is the line spectra predicted by non-relativistic electrons with no spin....
  • Hyperfine structure
    Hyperfine structure

    The term hyperfine structure refers to a collection of different effects leading to small shifts and splittings in the energy levels of atoms, molecules and ions....
  • g-factor
    G-factor

    A g-factor is a dimensionless quantity which characterizes the magnetic moment and gyromagnetic ratio of a particle or atomic nucleus. It is essentially a proportionality constant that relates the observed magnetic moment ? of a particle to the appropriate angular momentum quantum number and the appropriate fundamental quantum unit of ma...


Footnotes