Atomic spectra theory

As we saw in Chapter 1, the importance of numbers in chemistry derives from the fact that experimental measurement of a particular chemical or physical property will always yield a numerical value to which we attach some significance. This might involve direct measurement of an intrinsic property of an atom or molecule, such as ionization energy or conductivity, but, more frequently, we find it necessary to use theory to relate the measured property to other properties of the system. For example, the rotational constant, B, for the diatomic molecule CO can be obtained directly from a measurement of the separation of adjacent rotational lines in the infrared spectrum. Theory provides the link between the measured rotational constant and the moment of inertia, I, of the molecule by the formula ... 

The viewing region of the plasma can achieve a temperature of 5000-6000°C and is reasonably stable. The sample solution is aspirated into the core area between the two arms of the Y where it is atomised, excited and viewed. This technique keeps with the atomic spectroscopy theory in that the measurements are obtained by emission from the valence electrons of the atoms that are excited, and the emitted radiation consists of short well-defined lines. All these lines fall in the UV or VIS region of the spectrum and identification of these lines permits qualitative/quantitative detection of elements. 

The most interesting case is photoemission of 4/ electrons in the rare earths as noted in the previous section, because of the collapsed nature of the 4/ orbitals, the photoemission spectrum can be interpreted completely even in the solid by atomic multiplet theory, and this applies also to magnetic circular dichroism. Thole and van der Laan [642] have derived sum rules for magnetic dichroism in rare-earth 4/ photoemission. They have shown that the integrated intensity is simply the sum over each sublevel of its occupation number times the total transition probability from that sublevel to the continuum shell. Polarisation effects in the 4/ photoemission spectra of rare earths are very large, and this tool based on quasiatomic analysis is of considerable significance it provides a new... 

Some important successes of classical quantum theory Bohr s theory of the atomic spectrum of hydrogen... 

The quantum theory, however, is essentially a physical theory, developed to explain observations like the atomic spectrum of hydrogen. Chemical ideas do not emerge from it easily. The theory is also very mathematical. Most chemists have to accept the results of quantum-mechanical calculations on trust. My approach avoids these problems. While I bring in the quantum theory where it is helpful, my treatment is essentially chemical. This makes for an easier introduction to the subject, and leads, I believe, to a better understanding of the key ideas, and the chemical thinking behind them. 

This is the Rydberg constant, R, from the hydrogen atom spectrum. Quantum mechanics therefore predicts the experimentally determined hydrogen atom spectrum. At this point, quantum mechanics predicts everything that Bohr s theory did and more, and so supersedes the Bohr theory of the hydrogen atom. 

Harold Urey discovered deuterium in 1931 by very carefully evaporating four liters of liquid hydrogen down to a single milliliter and measuring the electronic spectrum. New lines in the atomic spectrum confirmed the presence of heavy hydrogen" right where quantum theory predicted. Calculate the expected positions of the four visible lines of the Balmer series for deuterium atoms. (See Chapter 9 for the details on the Balmer series for H atoms.)... 

A complete quantum mechanical treatment of the interaction of molecules and fields would require quantum electrodynamics, which is probably the most successful theory, that was ever derived. Using it, one can reproduce very accurately the Lamb shift in the hydrogen atom spectrum and the g-factor of the free electron ge 2.002. Nevertheless it is not yet regularly employed in the calculation of electromagnetic properties of molecules and the effects are expected to be very small. 

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