Energy levels atomic spectroscopy

At a surface, not only can the atomic structure differ from the bulk, but electronic energy levels are present that do not exist in the bulk band structure. These are referred to as surface states . If the states are occupied, they can easily be measured with photoelectron spectroscopy (described in section A 1.7.5.1 and section Bl.25.2). If the states are unoccupied, a teclmique such as inverse photoemission or x-ray absorption is required [22, 23]. Also, note that STM has been used to measure surface states by monitoring the tunnelling current as a fiinction of the bias voltage [24] (see section BT20). This is sometimes called scamiing tuimelling spectroscopy (STS). 

Note that in core-level photoelectron spectroscopy, it is often found that the surface atoms have a different binding energy than the bulk atoms. These are called surface core-level shifts (SCLS), and should not be confiised with intrinsic surface states. Au SCLS is observed because the atom is in a chemically different enviromuent than the bulk atoms, but the core-level state that is being monitored is one that is present in all of the atoms in the material. A surface state, on the other hand, exists only at the particular surface. 

The spectroscopy of ion lasers is generally less well understood than that of neutral atom lasers because of the lack of detailed knowledge of ion energy-level schemes. Indeed, ion lasers were first produced accidentally and attempts to assign the transitions came later. 

Analysis of Surface Elemental Composition. A very important class of surface analysis methods derives from the desire to understand what elements reside at the surface or in the near-surface region of a material. The most common techniques used for deterrnination of elemental composition are the electron spectroscopies in which electrons or x-rays are used to stimulate either electron or x-ray emission from the atoms in the surface (or near-surface region) of the sample. These electrons or x-rays are emitted with energies characteristic of the energy levels of the atoms from which they came, and therefore, contain elemental information about the surface. Only the most important electron spectroscopies will be discussed here, although an array of techniques based on either the excitation of surfaces with or the collection of electrons from the surface have been developed for the elucidation of specific information about surfaces and interfaces. 

Absorption spectroscopy records depletion by the sample of radiant energy from a continuous or frequency-tunable source, at resonance frequencies that are characteristic of various energy levels ia atoms or molecules. The basic law of absorption, credited to Bouguer-Lambert-Beer, states that ia terms of the iacident, Jq, and transmitted, light iatensities, the absorbance, M (or transmittance, T), is given by equation 1 ... 

Atomic and Molecular Energy Levels. Absorption and emission of electromagnetic radiation can occur by any of several mechanisms. Those important in spectroscopy are resonant interactions in which the photon energy matches the energy difference between discrete stationary energy states (eigenstates) of an atomic or molecular system = hv. This is known as the Bohr frequency condition. Transitions between... 

In X-ray photoelectron spectroscopy (XPS), a beam of soft X-rays with energy hv s. focused onto the surface of a solid that is held under an ultra-high vacuum, resulting in the ejection of photoelectrons from core levels of the atoms in the solid [20]. Fig. 15 shows an energy level diagram for an atom and illustrates the processes involved in X-ray-induced photoelectron emission from a solid. 

We are now ready to build a quantum mechanical model of a hydrogen atom. Our task is to combine our knowledge that an electron has wavelike properties and is described by a wavefunction with the nuclear model of the atom, and explain the ladder of energy levels suggested by spectroscopy. 

An electron in an atom is like a particle in a box, in the sense that it is confined within the atom by the pull of the nucleus. We can therefore expect the electron s wavefunctions to obey certain boundary conditions, like the constraints we encountered when fitting a wave between the walls of a container. As we saw for a particle in a box, these constraints result in the quantization of energy and the existence of discrete energy levels. Even at this early stage, we can expect the electron to be confined to certain energies, just as spectroscopy requires. 

The real power of ESR spectroscopy for identification of radical structure is based on the interaction of the unpaired electron spin with nuclear spins. This interaction splits the energy levels and often allows determination of the atomic or molecular structure of species containing unpaired electrons. The more complete Hamiltonian is given in Equation (6) for a species containing one unpaired electron, where the summations are over all the nuclei, n, interacting with the electron spin. 

Spectroscopy The absorption of radiation between two energy levels within an atom or molecule... 

Microwave spectroscopy The study of the interaction of microwave radiation with the rotational motion of a molecule. Microwave transitions are not restricted to molecules and can occur in atoms whenever the separation between the energy levels is in the microwave region of the spectrum. 

NMR spectroscopy (a commercial unit shown in Fig. 1.49) uses the fact that some atomic nuclei have a magnetic moment, e. g. very distinct in a proton, the nucleus of hydrogen, but also inl3C, 3IP, 14N, and 33S. In an external magnetic field the energy levels split, as described in quantum mechanics. The size and extend of the split is given by Eq. (9)... 

Useful books from the Oxford University Press primer series include Foundations of Spectroscopy, by Simon Duckett and Bruce Gilbert, OUP, Oxford, 2000 Introduction to Organic Spectroscopy, by Laurence M. Harwood and Timothy D. W. Claridge, OUP, Oxford, 1997 and Energy Levels in Atoms and Molecules, by W. G. Richards OUP, Oxford, 1996. Each, particularly the last, represents a clear and lucid introduction. 

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