Mean characteristics of atomic spectra

Here p( ,) stands for the probability of finding this level with energy , in the spectrum and it equals the statistical weight of the level qi = 2J,- + 1, divided by the total statistical weight of the spectrum, i.e. 

For the spectrum corresponding to transitions between energy levels (transition array), the probability of the ith line can be expressed in terms 

The first-order initial moment represents the average energy of the spectrum E 

It is convenient to use the centred moments pk defined with respect to the average energy, i.e. 

The first-order centred moment is equal to zero. The second one describes the variance of spectrum 

The fcth-order initial moment a for a set of levels or spectral line energies E, Ei.Eq is 

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R. Karazija. Sums of Atomic Quantities and Mean Characteristics of Spectra, Mokslas, Vilnius, 1991. 

The thiazolium ring, as most heterocycloammoniums, is a Lewis acid conferring to the carbon atom in the 2-position the carbocationic property of adding the free pair of a base either organic or mineral that may be the molecule of solvent as ROH (Scheme 11). For many nuclei of suitable acidity, these equilibria can be observed in dilute solution by means of absorption spectra when species A and C possess different characteristics (24). For example, benzothiazolium and benzoxazolium in methanol and ethanol give at 10 mole liter 8 and 54% of the alkoxy derivatives for the former and 29 and 90% for the latter respectively. 

Having explicit formulas for a number of first moments we can approximately restore the envelope line of the radiation spectrum without its detailed calculations. If lines in the spectrum have one symmetric maximum, then its envelope line is approximated by a normal function whose reconstruction requires only the mean energy and variance of the spectrum. Such an approach is useful for the case of complex spectra consisting of many lines, which, due to low resolutions as well as Doppler and collisional broadening or large natural width, form continuous or quasi-continuous bands. Studies of variation of these statistical characteristics along isoelectronic sequences give a wealth of information on intra-atomic interactions. 

Atomic spectroscopy is the oldest instrumental elemental analysis principle, the origins of which go back to the work of Bunsen and Kirchhoff in the mid-19th century [1], Their work showed how the optical radiation emitted from flames is characteristic of the elements present in the flame gases or introduced into the burning flame by various means. It had also already been observed that the intensities of the element-specific features in the spectra, namely the atomic spectral lines, changed with the amount of elemental species present. Thus the basis for both qualitative and quantitative analysis with atomic emission spectrometry was discovered. These discoveries were made possible by the availability of dispersing media such as prisms, which allowed the radiation to be spectrally resolved and the line spectra of the elements to be produced. 

Just as the emission spectrum of hydrogen has four characteristic lines that identify it, so the emission spectrum for each element has a characteristic set of spectral lines. This means that the energy levels within the atom must also be characteristic of each element. But when scientists investigated multi-electron atoms, they found that their spectra were far more complex than would be anticipated by the simple set of energy levels predicted for hydrogen. Figure 7.4 shows spectra for three elements. 

Flame atomic absorption spectrometry requires a means by which an aqueous solution containing metal ions can be aspirated into a reducing flame environment by which atomic Mg or Ca vapor is formed. Photons from the characteristic Mg emission of a hollow-cathode lamp (HCL) are absorbed by ground-state Mg atoms present in the approximately 2300°C air-acetylene flame. The amount of radiant energy absorbed as a function of concentration of an element in the flame is the basis of AA and follows Beer s law. In contrast to molecular absorption in solution, atomic spectra consist of lines and originate either from atomic absorption or atomic emission processes, which are depicted schematically below (1, Chap. 9) ... 

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