Intensity of a spectral line

One effect of saturation, and the dependence of e on /, is to decrease the maximum absorption intensity of a spectral line. The central part of the line is flattened and the intensity of the wings is increased. The result is that the line is broadened, and the effect is known as power, or saturation, broadening. Typically, microwave power of the order of 1 mW cm may produce such broadening. Minimizing the power of the source and reducing the absorption path length t can limit the effects of power broadening. 

Halb-weiss, n. Textiles) half-bleach, -wert-druck, m. half-value pressure, -wertsbreite, /. width at half of maximum intensity (of a spectral line or band), -wertzeit,/. half-life period. -woUe, /. half-wool, union. -woU-farberei, /. union dyeing, -wuste, /, semi-desert. 

The intensity of a spectral line is related to the solution concentration of the analyte in a similar complex manner to that described for arc/spark emission (p. 293) although the degree of ionization a will generally be much less... 

Table 8.7). Thus, intensity and concentration are directly proportional. However, the intensity of a spectral line is very sensitive to changes in flame temperature because such changes can have a pronounced effect on the small proportion of atoms occupying excited levels compared to those in the ground state (p. 274). Quantitative measurements are made by reference to a previously prepared calibration curve or by the method of standard addition. In either case, the conditions for measurement must be carefully optimized with reference to the choice of emission line, flame temperature, concentration range of samples and linearity of response. Relative precision is of the order of 1-4%. Flame emission measurements are susceptible to interferences from numerous sources which may enhance or depress line intensities. 

Investigation of atomic spectra yields atomic energy levels. An important chemical application of atomic spectroscopy is in elemental analysis. Atomic absorption spectroscopy and emission spectroscopy are used for rapid, accurate quantitative analysis of most metals and some nonmetals, and have replaced the older, wet methods of analysis in many applications. One compares the intensity of a spectral line of the element being analyzed with a standard line of known intensity. In atomic absorption spectroscopy, a flame is used to vaporize the sample in emission spectroscopy, one passes a powerful electric discharge through the sample or uses a flame to produce the spectrum. Atomic spectroscopy is used clinically in the determination of Ca, Mg, K, Na, and Pb in blood samples. For details, see Robinson. 

Accordingly, from the photomultiplier signal the number of analyte atoms brought from a given amount of sample into the radiation source can be calculated directly. As all constants in the calculation shown, however, are not known apriori, AES in practice is a relative method and a calibration has to be performed. The determination of the calibration function is an important part of the working procedure. The calibration function relates the intensity of a spectral line (I) to the concentration c of an element in the sample. From the work of Scheibe [336] and Lomakin [337] the following relationship between absolute intensities and elemental concentrations was proposed ... 

The observed intensity of a spectral line is determined by the rate of transition between the initial and final states corresponding to the frequency of that line. The rate of transition is, in turn, governed by the intensity of exciting radiation, the path length of exciting radiation through the sample, the concentration of potential absorbers or emitters in the sample, and the probability that a radiative transition will occur between the initial and final states of the absorber or emitter. In quantitative analysis, it is the concentration of absorbers or emitters in the sample that is of interest. These factors will be discussed further in the experimen-... 

In the absence of any radiation field, /(i/kj) = 0 The population Nk of level k simply decays exponentially with a lifetime A 1 to level j. This provides one way of defining the intensity of a spectral line. 

The oscHllator strength /is an expression of the intensity of a spectral line and represents the probability that an atom will undergo an electronic transition in unit time and absorb or emit a photon. 

The intensity of a spectral line is related to the total number of states in the level from which the transition originates as given by the expression M = 2J + 1. If a population is assigned to each state of a level (a condition... 

From equation (2-31) it is evident that the intensity of a spectral line for a particular transition is proportional to its oscillator strength, and varies exponentially with the absolute temperature and inversely exponentially with the energy of the transition. 

The intensity of a spectral line can be strongly influenced by two major sources of error, namely, selective absorption of the primary beam and absorption and enhancement of the fluorescent radiation. These effects may be further complicated by physical phenomena that are already present, or are introduced as a result of specimen preparation procedures. The dependence of x-ray spectral intensity upon the physical state of the specimen is well known. Effects such as surface roughness, particle shape, particle size, and size distribution can all lead to nonproportional relationships between spectral intensity and elemental composition. This chapter discusses the problems associated with specimen preparation. The basic techniques are covered briefly and special attention is devoted to several methods in common use today. 

The absolute measured intensity of a spectral line depends upon many factors previously discussed in Chaps. 2 and 3. IWo dominant factors controlling the production of fluorescent x-rays are the fluorescent yield and the excitation overvoltage (V—0) - . These two factors may be used to obtain reliable, rapid semiquantitative analyses from a qualitative identification spectrum. This will be discussed subsequently. Figures 8.5 through 8.7 illustrate the atomic number-dependence of the K fluorescent yield [ci>k]> the L fluorescent yield [o>l], and a combined critical excitation overvoltage fluorescent yield factor for K and L spectra. 

Calibration Function. The determination of the calibration function is important it relates the intensity of a spectral line I to the concentration c of an element in the sample. Scheibe [207] and Lomakin [208], propose the following relation between absolute intensities and elemental concentrations ... 

It might be expected that the intensity of a spectral line from a sample would be directly proportional to the amount of the corresponding element in the sample. In practice the intensity can deviate considerably from the expected linear relation due to absorption in the matrix material and multiple scattering processes. However, it is possible to correct for such effects and very reliable quantitative analyses can be performed. X-ray fluorescence measurements on alloys have an elemental sensitivity of about 10 ppm (ppm parts per million, 1 10 ). The typical penetration depth of the radiation in the metal is about 1 /zm and thus, primarily, the surface is analysed. X-ray emission techniques have been discussed in [5.3,4]. 

It is because (11.5.11) involves transition energies and densities for all excited states b that the calculation of second-order quantities such as the polarizability is difficult, since usually the available excited states and their number is very limited. We note in passing, however, a connection with quantities encountered in spectroscopy the intensity of a spectral line for the (electric-dipole-induced) transition a b, under the influence of isotropic radiation, is usually characterized by a dimensionless quantity, the oscillator strength , and this is defined by... 

Masers also serve as a warning that the intensity of a spectral line is not necessarily a direct measure of its abundance. Population inversions enhance the brightness temperatures, leading to overestimates of excitation and abundance in those species in which masing occurs. Because not all molecules undergo maser amphfication, the assumption of thermal equilibrium is usually not bad, but should be employed with caution. 

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