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In atomic physics, the spin quantum number is a quantum number that parametrizes the intrinsic angular momentum (or spin angular momentum, or simply spin) of a given particle. The spin quantum number is the fourth of a set of quantum numbers which describe the unique quantum state of an electron and is designated by the letter s. Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ...
A quantum number describes the energies of electrons in atoms. ...
Gyroscope. ...
In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is generated by the motion of its center of mass about an external point. ...
In particle physics, an elementary particle or fundamental particle is a particle not known to have substructure; that is, it is not made up of smaller particles. ...
A quantum number describes the energies of electrons in atoms. ...
A quantum state is any possible state in which a quantum mechanical system can be. ...
Derivation As a quantized angular momentum, (see angular momentum quantum number) it holds that The Principal quantum number (usually written n) is the first quantum number of an atomic orbital. ...
 where  is the quantized spin vector, is the norm of the spin vector,- s is the spin quantum number associated with the spin angular momentum,
 is Planck's reduced constant (Dirac's constant). Given an arbitrary direction z (usually determined by an external magnetic field) the spin z-projection is given by In linear algebra, functional analysis and related areas of mathematics, a norm is a function which assigns a positive length or size to all vectors in a vector space, other than the zero vector. ...
A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...
Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ...
 where ms is the secondary spin quantum number, ranging from −s to +s in steps of one. This generates 2s+1 different values of ms.
The allowed values for s are non-negative integers or half-integers. Fermions (such as the electron, proton or neutron) have half-integer values, whereas bosons (e.g. photon, mesons) have integer spin values. The integers consist of the positive natural numbers (1, 2, 3, …), their negatives (−1, −2, −3, ...) and the number zero. ...
In mathematics, a half-integer is a number of the form , where is an integer. ...
In particle physics, fermions, (named after Enrico Fermi), are particles with semi-integer spin. ...
Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ...
Properties In physics, the proton (Greek proton = first) is a subatomic particle with an electric charge of one positive fundamental unit (1. ...
Properties In physics, the neutron is a subatomic particle with no net electric charge and a mass of 939. ...
In physics, bosons, named after Satyendra Nath Bose, are particles with integer spin. ...
In quantum physics, the photon (from Greek φως, phÅs, meaning light) is the quantum of the electromagnetic field (light). ...
In particle physics, a meson is a strongly interacting boson, that is, it is a hadron with integral spin. ...
Algebra The algebraic theory of spin is a carbon copy of the Angular momentum in quantum mechanics theory. First of all, spin satisfies the fundamental conmutation relation: Gyroscope. ...
![[S_i, S_j ] = i hbar epsilon_{ijk} S_k](http://upload.wikimedia.org/math/8/d/9/8d9f476ea94ffcbbb6a468e7fe075d6e.png) , ![left[S_i, S^2 right] = 0](http://upload.wikimedia.org/math/1/d/9/1d9fdcb6b99e9ca6504fdec0f7f08a03.png) This means that is imposible to know two coordinates of the spin at the same time because of the restriction of the Uncertainty_principle. The Heisenberg uncertainty principle or just uncertainty principle (sometimes also the Heisenberg indeterminacy principle - a name given to it by N. Bohr) is one of the cornerstones of quantum mechanics. ...
Next, the eigenvectors S2 and Sz satisfy: In linear algebra, the eigenvectors (from the German eigen meaning inherent, characteristic) of a linear operator are non-zero vectors which, when operated on by the operator, result in a scalar multiple of themselves. ...
-
   where  are the up and down operators.
Electron spin There are a set of quantum numbers associated with the energy states of the atom. The four quantum numbers n, l, m, and s specify the complete and unique quantum state of a single electron in an atom called its wavefunction or orbital. The wavefunction of the Schrödinger wave equation reduces to the three equations that when solved lead to the first three quantum numbers. However, line emission spectra of some atoms when measured in an external magnetic field turned out to be more complicated than predicted by the first three quantum numbers. There needed to be a fourth quantum number that could properly predict spectra that matched the complexity found in nature so that this new quantum number had to behave as if it were also derived from the algebra of angular momentum vectors. A solution to this problem was suggested in early 1925 by George Uhlenbeck and Samuel Goudsmit, students of Paul Ehrenfest (who rejected the idea), and independently by Ralph Kronig, one of Landé's assistants, by introducing the idea of the self-rotation of the electron which would naturally be an angular momentum vector. A quantum state is any possible state in which a quantum mechanical system can be. ...
This article discusses the concept of a wavefunction as it relates to quantum mechanics. ...
Electron atomic and molecular orbitals Atomic orbitals are the quantum states of the individual electrons in the electron cloud around a single atom. ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, is the definition of energy of a quantum system. ...
Extremely high resolution spectrum of the Sun showing thousands of elemental absorption lines (fraunhofer lines) Spectroscopy is the study of spectra, that is, the dependence of physical quantities on frequency. ...
George Eugene Uhlenbeck (1900 - 1988) was a U.S. (Indonesian-born) physicist. ...
Samuel Goudsmit (1902–1978) was a Dutch-American physicist famous for jointly proposing the concept of electron spin with George Eugene Uhlenbeck. ...
Paul Ehrenfest Paul Ehrenfest (Vienna, January 18, 1880 – Amsterdam, September 25, 1933) was an Austrian physicist and mathematician, who obtained Dutch citizenship on March 24, 1922. ...
Ralph Kronig Ralph Kronig was a German-American physicist (1904-1995). ...
Alfred Landé was a German physicist (1888-1976) known for his contributions to Quantum Theory. ...
An electron spin s = 1/2 is an intrinsic property of electrons. Electrons have intrinsic angular momentum characterized by quantum number 1/2. In the pattern of other quantized angular momenta, this gives total angular momentum:
 where - is Planck's reduced constant (Dirac's constant).
The energy of any wave is the frequency multiplied by Planck's constant. This causes the wave to display particle-like packets of energy called quanta. To show each of the quantum numbers in the quantum state, the formulae for each quantum number include Planck's reduced constant which only allows particular or discrete or quantized energy levels. The reduced Planck's constant is used because in a wave, a cycle is defined by the return from a certain position to the same position such as from the top of one crest to the next crest. This actually is equivalent to a circle both having 360 degrees. There are 2 pi radians per cycle in a wave. Therefore, dividing h by 2π describes a constant that when multiplied by the frequency of a wave gives the energy of one cycle. When the subatomic particle the electron was being described by wavefunctions in Dirac's equation, it was found that the property of spin of all particles is a multiple of h-bar denoted by , that is, h (Planck's constant) divided by 2π. H-bar or has an even multiple for bosons and an odd multiple for fermions. A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ...
Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ...
Lower-case π (the lower case letter is usually used for the constant) The mathematical constant π is an irrational number, approximately equal to 3. ...
Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ...
This article discusses the concept of a wavefunction as it relates to quantum mechanics. ...
In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...
Lower-case π (the lower case letter is usually used for the constant) The mathematical constant π is an irrational number, approximately equal to 3. ...
The hydrogen spectra fine structure is observed as a doublet corresponding to two possibilities for the z-component of the angular momentum, where for any given direction z:
 which solution has only two possible z components for the electron. In the electron, the two different spin orientations are sometimes called "spin-up" or "spin-down".
The spin property of an electron would classically give rise to magnetic moment which was a requisite for the fourth quantum number. The electron spin magnetic moment is given by the formula: In physics, the magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. ...
 where - e is the charge of the electron
- g is the Lande g-factor
and by the equation: The Landé g-factor, , is a multiplicative term in the lifting of the energy degeneracy in for an atom in a weak uniform external magnetic field. ...
 where - g is the Lande g-factor
- μB is the Bohr magneton
When atoms have even numbers of electrons the spin of each electron in each orbital has opposing orientation in different directions. However, many atoms have an odd number of electrons or an arrangement of electrons in which the number of "spin-up" and "spin-down" orientations are not the same. These atoms or electrons are said to have unpaired spins which are detected in electron spin resonance. In atomic physics, the Bohr magneton (symbol ) is named after the physicist Niels Bohr. ...
Electron Paramagnetic Resonance (EPR) or Electron Spin Resonance (ESR) is a spectroscopic technique which detects species that have unpaired electrons, generally meaning that it must be a free radical, if it is an organic molecule, or that it has transition metal ions if it is an inorganic complex. ...
Detection of spin When the spectral lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely-spaced doublets. This splitting is called fine structure and was one of the first experimental evidences for electron spin. The direct observation of the electron's intrinsic angular momentum was achieved in the Stern-Gerlach experiment. In quantum mechanics, the Stern-Gerlach experiment, named after Otto Stern and Walther Gerlach, is a celebrated experiment in 1920 on deflection of particles, often used to illustrate basic principles of quantum mechanics. ...
Dirac equation solves spin When the idea of electron spin was first introduced in 1925, even Wolfgang Pauli had trouble accepting Ralph Kronigs model. The problem was not that a rotating charged particle would have given rise to a magnetic field, but that the electron was so small that the equatorial speed of the electron would have to be greater than the speed of light for the magnetic moment to be of the observed strength. Ralph Kronig Ralph Kronig was a German-American physicist (1904-1995). ...
In 1930, Paul Dirac developed a new version of the Schrödinger Wave Equation which was relativistically invariant, and predicted the magnetic moment correctly, and at the same time treated the electron as a point particle. In the Dirac equation all four quantum numbers including the additional quantum number s arose naturally during its solution. Paul Adrien Maurice Dirac Paul Adrien Maurice Dirac, OM FRS (IPA: [dɪræk]) (August 8, 1902 – October 20, 1984) was a British theoretical physicist and a founder of the field of quantum physics. ...
In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...
See also A quantum number describes the energies of electrons in atoms. ...
The Azimuthal quantum number (or orbital angular momentum quantum number) symbolized as l is a quantum number for an atomic orbital which determines its orbital angular momentum. ...
By virtue of its charge and spin motion, an electron develops a magnetic field. ...
In atomic physics, the principal quantum number symbolized as n is the first quantum number of an atomic orbital. ...
The total angular quantum momentum numbers parameterize the total angular momentum of a given electron, by combining its orbital angular momentum and its intrinsic angular momentum (i. ...
Quantum mechanics is a physical science dealing with the behaviour of matter and electromagnetic waves on the scale of atoms and subatomic particles. ...
In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ...
Ralph Kronig Ralph Kronig was a German-American physicist (1904-1995). ...
In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ...
In physics, spin refers to the angular momentum intrinsic to a body, as opposed to orbital angular momentum, which is generated by the motion of its center of mass about an external point. ...
A quantum state is any possible state in which a quantum mechanical system can be. ...
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