Electrons from inner shells

Photon beams incident on surfaces induce vibrational excitation of adsorbed molecules at low energies fin the meV ( 10 J) range). Photoemission of electrons from the valence band [the 5-30 eV (8-48 x 10 J) range] yields the surface density of electronic states. Photoemission of electrons from inner shells (30-104... 

Figure 1.5 is a schematic diagram of some of the important interactions between a solid specimen and an incident beam of electrons. The incident beam, if sufficiently energetic, can knock electrons from inner shells in the atoms in the solid giving rise to characteristic X-rays from each of the elements present as higher-energy... 

The availability of photons of the X-ray region at electron storage rings allows the excitation of electrons from inner shells of suitable solute molecules. First reports on the photoconductivity of organometallics in hydrocarbon solution are attributed to Sham (1988). 

In high-energy PES, characteristic x-irradiation with energies between 100 and 2000 eV and half-widths of about 1 eV is used for excitation. Because of the higher excitation energy, valence electrons as well as electrons from inner shells (core electrons) can be photoionized. The core electrons yield direct information on elemental composition and on the chemical state of a given element. Changes... 

When the hole in the /th shell is filled by an electron from theyth shell, there is a hole in the latter shell that will in turn be filled by an electron from a higher kth shell. This may result in the emission of a second x-ray, such that one hole in an inner electron shell can result in a cascade of several x-rays having ever-decreasing energies. 

Exposure of elements to a broad spectrum of X-rays results in the ejection of electrons from their inner shells. Electrons from outer shells falling into these vacancies emit radiation of specific wavelengths (see Figure 14.13). Analysis of this radiation, referred to as X-ray fluorescence (XRF), allows for the identification of the element from which the photon is emitted. Instruments for carrying out this analysis can be either laboratory sized or can be handheld... 

Calculations show that cross-sections obtained in the Hartree-Fock approximation utilizing length and velocity forms of the appropriate operator, may essentially differ from each other for transitions between neighbouring outer shells, particularly with the same n. However, they are usually close to each other in the case of photoionization or excitation from an inner shell whose wave function is almost orthogonal with the relevant function of the outer open shell. In dipole approximation an electron from a shell lN may be excited to V = l + 1, but the channel /— / + prevails. For configurations ni/f1 n2l 2 an important role is... 

The repulsion of outer-shell electrons by inner-shell electrons is particularly important because the outer-shell electrons are pushed farther away from the nucleus and are thus held less tightly. Part of the attraction of the nucleus for an outer electron is thereby canceled, an effect we describe by saying that the outer... 

As a second example of the use of the orbital idea in many-electron atoms, we consider briefly the spectra from inner-shell electrons. One very direct way of measuring the energies of these is by photoelectron spectra, as discussed in Section 1.3 (see Fig. 1.11). Table 5.1 shows the binding (ionization) energies of electrons in the occupied orbitals of Na+ and Cl-, which can be obtained from the photoelectron spectrum of solid NaCl. These data illustrate the fact that the 10 electrons in Na+ occupy the If, 2j, and 2p orbitals, and the 18 in Cl- occupy If, 2s, 2p, 3s, and 3p. Remembering that there am three different p orbitals for each n, we can see that these ions have five and nine occupied orbitals, respectively. Observations such as this provide strong evidence for the shell structure of atoms, and the principle that no more than two electrons can occupy each individual orbital. 

It is not clear whether an increase in the effective nuclear charge is reasonable. In principle, such an increase could be explained by an increased covalency between the inner shell electrons and the ligands, leading to a charge transfer from inner shells to the ligands and thus to an increase of the effective nuclear charge Z for the f-electrons. This effect could be called anti-screening . 

Abstract Electron impact inner-shell ionization cross-section (EIICS) calculations of neutral atoms with atomic numbers Z = 6-92 for /6-shell, Z = 18-92 for E-shell, and Z = 79-92 for M-shell have been reviewed. In this work, the evaluations of the EIICS are discussed using our recently propounded easy-to-use models that are found adequately successful in describing the experimental cross sections. The selection of the range of atomic number Z for different inner-shells was guided by the availability of the EIICS data either from experiments or from rigorous quantal calculations. Details of the models have been... 

The properties of the elements stem from their electronic configurations, and the properties place them in their locations in the periodic table. In each group, the elements have a characteristic outermost electronic configuration. The existence of the transition and inner transition elements stems from adding electrons to inner shells after outer shells have been started. Because the periodic table reflects the electronic structures of the atoms, it can be used as a memory device when writing electronic configurations. The ability to write and understand such configurations is a very important skill. (Section 4.8)... 

The primary electron beam may also be inelastically scattered through interaction with electrons from surface atoms. In this case, the collision displaces core electrons from filled shells e.g, ns (K) or np (L)) the resulting atom is left as an energetic excited state, with a missing inner shell electron. Since the energies of these secondary electrons are sufficiently low, they must be released from atoms near the surface in order to be detected. Electrons ejected from further within the sample are reabsorbed by the material before they reach the surface. As we will see in the next section (re SEM), as the intensity of the electron beam increases, or the density of the sample decreases, information from underlying portions of the sample may be obtained. 

Thus, electrons in inner shells (small n) are tightly bound to the nucleus, and their average position is quite near the nucleus because they are only slightly shielded from the full nuclear charge Z. Electrons in outer shells are only weakly attracted to the nucleus, and their average position is far from the nucleus because they are almost fully shielded from the nuclear charge Z. 

Under equal circumstances, the X-ray diffraction pattern shows an intensity proportional to ZtZ2 and by far the larger part of the intensity is due to the electrons in inner shells. It is very difficult to obtain reliable values for the density of the valence electrons 51) and even in the very favorable case of diamond (where only a-third of the electrons are in inner shells) the electron density around each C+4 core is almost exactly spherical, and certainly not four sausages connecting the closest neighbor atoms. For group-theoretical reasons, the first deviation from spherical symmetry allowed 16 > has octupole symmetry (proportional to xyz) but the strength of this deformation is only a few percent of the spherically symmetric density. 

The effective nuclear charge, Zg , experienced by an electron in an outer shell is less than the actual nuclear charge, Z. This is because the attraction of outer-shell electrons by the nucleus is partly counterbalanced by the repulsion of these outer-shell electrons by electrons in inner shells. We say that the electrons in inner shells screen, or shield, electrons in outer shells from the full effect of the nuclear charge. This concept of a screening, or shielding, effect helps us understand many periodic trends in atomic properties. 

The anomalous dispersion effect is associated with the ejection of photoelectrons from inner shell electrons in an atom. The normal scattering describes the interaction of all the electrons in the atom with the X-ray beam. The radial distribution of the electrons in an atom can be calculated using quantum mechanics, originally by Hartree s self-consistent field method (Hartree 1933). In figure 9.12 this distribution is given for rubidium, which has a K edge at 0.8155 A the mean radius for... 

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