Angular momentum electronic spectra

Two kinds of environmental interactions are commonly important in the ESR spectrum of a free radical (i) To the extent that the unpaired electron has residual, or unquenched, orbital angular momentum, the total magnetic moment is different from the spin-only moment (either larger or smaller,... 

The first application of quantum theory to a problem in chemistry was to account for the emission spectrum of hydrogen and at the same time explain the stability of the nuclear atom, which seemed to require accelerated electrons in orbital motion. This planetary model is rendered unstable by continuous radiation of energy. The Bohr postulate that electronic angular momentum should be quantized in order to stabilize unique orbits solved both problems in principle. The Bohr condition requires that... 

E are the projections of the electron orbital angular momentum on the molecular axis and the subscript is the projection of the total electron angular momentum on the molecular axis directed from the heavy atom to fluorine. It is convenient to describe the spin-rotational spectrum of the ground electronic state in terms of the effective spin-rotational Hamiltonian following [90, 117] ... 

In this case the planar complex is diamagnetic and possesses the usual narrow line, high-resolution diamagnetic spectrum. The tetrahedral complex in Td symmetry would possess a 3T ground state. In approximately tetrahedral nickel(II) complexes the orbital angular momentum is incompletely quenched the result is a very short electron spin relaxation time and an NMR spectrum with relatively narrow, paramagnetic shifted resonances. 

The angular momentum or an electron moving in an orbit of the type described by Bohr is ail axial vector L = r x p, formed from the radial distance r between electron and nucleus and the linear momentum p of the electron relative lo a fixed nucleus. Figure 2 shows the customary method used to illustrate the axial vector L in terms of the orbital morion of any object, of which the electron of the Bohr atom is only one example. Although Bohr s planetary model needed only circular orbits lo explain the spectral lines observed in the spectrum of a hydrogen atom, subsequent... 

The energy spectrum of atoms and ions with j j coupling can be found using the relativistic Hamiltonian of iV-electron atoms (2.1)-(2.7). Its irreducible tensorial form is presented in Chapter 19. The relativistic one-electron wave functions are four-component spinors (2.15). They are the eigenfunctions of the total angular momentum operator for the electron and are used to determine one-electron and two-electron matrix elements of relativistic interaction operators. These matrix elements, in the representation of occupation numbers, are the parameters that enter into the expansions of the operators corresponding to physical quantities (see general expressions (13.22) and (13.23)). 

In 1913 Bohr amalgamated classical and quantum mechanics in explaining the observation of not only the Balmer series but also the Lyman, Paschen, Brackett, Pfund, etc., series in the hydrogen atom emission spectrum, illustrated in Figure 1.1. Bohr assumed empirically that the electron can move only in specific circular orbits around the nucleus and that the angular momentum pe for an angle of rotation 9 is given by... 

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