Spin, angular momentum quantum number

The fourth quantum number is called the spin angular momentum quantum number for historical reasons. In relativistic (four-dimensional) quantum mechanics this quantum number is associated with the property of symmetry of the wave function and it can take on one of two values designated as -t-i and — j, or simply a and All electrons in atoms can be described by means of these four quantum numbers and, as first enumerated by W. Pauli in his Exclusion Principle (1926), each electron in an atom must have a unique set of the four quantum numbers. 

Now the total spin-angular momentum quantum number S is given by the number, n, of unpaired electrons times the spin angular momentum quantum number s for the electron, that is, S = nil. Substitution of this relationship into Eq. (5.11) yields an alternative form of the spin-only formula. 

The spin (angular momentum) quantum number ms. In their interpretation of many features of atomic spectra Uhlenbeck and Goudsmit (1925) proposed for the electron a new property called spin angular momentum (or simply spin) and assumed that only two states of spin were possible. In relativistic (four-dimensional) quantum mechanics this quantum number is related to the symmetry properties of the wave function and may have one of the two values designated as A. 

We now consider many-electron atoms. We will assume Russell-Saunders coupling, so that an atomic state can be characterized by total electronic orbital and spin angular-momentum quantum numbers L and S, and total electronic angular-momentum quantum numbers J and Mj. (See Section 1.17.) The electric-dipole selection rules for L, J, and Mj can be shown to be (Bethe and Jackiw, p. 224)... 

Similarly, a nucleus of nuclear spin angular momentum quantum number I and vector I has spin angular momentum L ... 

For many-electron light atoms, the Russell-Saunders coupling rules prevail One combines the orbital angular momenta lt of each electron, treated as a vector, to form the total orbital angular momentum quantum number (and vector) L = h one similarly couples the spin angular momentum quantum numbers s, into a total spin angular momentum quantum number S = s > then one adds L and S to get the total angular momentum vector... 

There is also a fourth quantum number, the spin angular momentum quantum number, m5,... 

The value of J depends on the totai orbitai angular momentum quantum number, L, and the tola spin angular momentum quantum number. S (Appendix C). Some calculated and experimental magnetic moments for lanthanide complexes are shown In Table 11.23... 

L = total orbital angular momentum quantum number S = total spin angular momentum quantum number J = total angular momentum quantum number... 

There is also a fourth quantum number, the spin angular momentum quantum number, ttig, which can take values of + 1 or -1. The spin is not a property of orbitals but of the electrons that we put in the orbitals... 

When there are two electrons in a molecule, their total spin angular momentum quantum number S is given by Equation 1.9. 

The product mn = 2SA + 1X25 + 1) is the number of possible total spin angular momentum quantum numbers S of the encounter complex that are allowed by combination of the quantum numbers SA and SB of the reaction partners as defined by Equation 2.30. 

Nuclei can also possess spin. Whereas every electron has a spin of half, nuclei can have nuclear spin angular momentum quantum number, I, equal to zero or other integer factors of1/2. 

The spin of the nuclei gives rise to nuclear magnetic resonance spectroscopy and there is a corresponding technique, electron spin resonance spectroscopy, arising from electron spin. Photons have a spin angular momentum quantum number of 1. This is the origin of many spectroscopic selection rules. If a photon had no spin, there would be no optical activity... 

Spin state. Syn. spin angular momentum quantum number.The projection of the magnetic moment of a spin onto the z-axis. The orientation of a component of the magnetic moment of a spin relative to the applied field axis (for a spin-V2 nucleus, this can be -cy2 or -1/2). 

S = total spin angular momentum quantum number... 

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