Electrons atomic spectra

Unfortunately, the Schrodinger equation for multi-electron atoms and, for that matter, all molecules cannot be solved exactly and does not lead to an analogous expression to Equation 4.5 for the quantised energy levels. Even for simple atoms such as sodium the number of interactions between the particles increases rapidly. Sodium contains 11 electrons and so the correct quantum mechanical description of the atom has to include 11 nucleus-electron interactions, 55 electron-electron repulsion interactions and the correct description of the kinetic energy of the nucleus and the electrons - a further 12 terms in the Hamiltonian. The analysis of many-electron atomic spectra is complicated and beyond the scope of this book, but it was one such analysis performed by Sir Norman Lockyer that led to the discovery of helium on the Sun before it was discovered on the Earth. 

This represents three integral values because of the three vector components of f, and a transition is allowed if any one is nonzero. It turns out that integration over the radial coordinate gives a nonzero result for any choice of n and n, but the angular coordinate integration requires that / and V differ by 1 for the result to be nonzero. Thus, the selection rule for a one-electron atom spectrum is stated concisely as... 

XPS X-ray photoelectron spectroscopy [131-137] Monoenergetic x-rays eject electrons from various atomic levels the electron energy spectrum is measured Surface composition, oxidation state... 

The hydrogen atom, containing a single electron, has played a major role in the development of models of electronic structure. In 1913 Niels Bohr (1885-1962), a Danish physicist, offered a theoretical explanation of the atomic spectrum of hydrogen. His model was based largely on classical mechanics. In 1922 this model earned him the Nobel Prize in physics. By that time, Bohr had become director of the Institute of Theoretical Physics at Copenhagen. There he helped develop the new discipline of quantum mechanics, used by other scientists to construct a more sophisticated model for the hydrogen atom. 

Hund s rule, like the Pauli exclusion principle, is based on experiment It is possible to determine the number of unpaired electrons in an atom. With solids, this is done by studying their behavior in a magnetic field. If there are unpaired electrons present the solid will be attracted into the field. Such a substance is said to be paramagnetic. If the atoms in the solid contain only paired electrons, it is slightly repelled by the field. Substances of this type are called diamagnetic. With gaseous atoms, the atomic spectrum can also be used to establish the presence and number of unpaired electrons. 

This technique can be applied to samples prepared for study by scanning electron microscopy (SEM). When subject to impact by electrons, atoms emit characteristic X-ray line spectra, which are almost completely independent of the physical or chemical state of the specimen (Reed, 1973). To analyse samples, they are prepared as required for SEM, that is they are mounted on an appropriate holder, sputter coated to provide an electrically conductive surface, generally using gold, and then examined under high vacuum. The electron beam is focussed to impinge upon a selected spot on the surface of the specimen and the resulting X-ray spectrum is analysed. 

Although Dirac s equation does not directly admit of a completely self-consistent single-particle interpretation, such an interpretation is physically acceptable and of practical use, provided the potential varies little over distances of the order of the Compton wavelength (h/mc) of the particle in question. It allows, for instance, first-order relativistic corrections to the spectrum of the hydrogen atom and to the core-level densities of many-electron atoms. The latter aspect is of special chemical importance. The required calculations are invariably numerical in nature and this eliminates the need to investigate central-field solutions in the same detail as for Schrodinger s equation. A brief outline suffices. 

It was fairly straightforward to modify Bohr s model to include the idea of energy sublevels for the hydrogen spectrum and for atoms or ions with only one electron. There was a more fundamental problem, however. The model still could not explain the spectra produced by many-electron atoms. Therefore, a simple modification of Bohr s atomic model was not enough. The many-electron problem called for a new model to explain spectra of all types of atoms. However, this was not possible until another important property of matter was discovered. 

To produce this type of atomic emission in a pyrotechnic system, one must produce sufficient heat to generate atomic vapor in the flame, and then excite the atoms from the ground to various possible excited electronic states. Emission intensity will increase as the flame temperature increases, as more and more atoms are vaporized and excited. Return of the atoms to their ground state produces the light emission. A pattern of wavelengths, known as an atomic spectrum, is produced by each element. This pattern - a series of lines - corresponds to the various electronic... 

Matrix-isolated alkali atoms (or small clusters) also undergo easy photoionization, and the electrons released in this process may attach themselves to nearby substrates to form the corresponding radical anions. However, one drawback of alkah metal atoms or clusters is that they tend to swamp the electronic absorption spectrum of the target reactive intermediate that can only thus be detected by IR. 

Very broadly speaking, two situations have to be considered in explaining devices such as those we have mentioned. In the first, which is relevant to the ruby laser and to phosphors for fluorescent lights, the light is emitted by an impurity ion in a host lattice. We are concerned here with what is essentially an atomic spectrum modified by the lattice. In the second case, which applies to LEDs and the gallium arsenide laser, the optical properties of the delocalised electrons in the bulk solid are important. 

Energy Spectrum of Many-electron Atom. Radiative and Autoionizing Transitions (Initial Formulas)... 

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)). 

The main ideas of the book are described in seven Parts divided into 33 Chapters, which are subdivided into Sections. In Part 1 we present the initial formulas to calculate the energy spectrum of a many-electron atom in non-relativistic and relativistic approximations, accounting for the relativistic effects as corrections and use perturbation theory in order to describe the energy spectra of an atom. Radiative and autoionizing... 

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. 

---