Measurement of line intensity

Scales giving directly the spacing d of the reflecting planes causing each line may also be made for any particular wavelength, such as Cu Koc. 

Many diffraction problems require an accurate measurement of the integrated intensity, or the breadth at half maximum intensity, of a diffraction line on a powder photograph. For this purpose it is necessary to obtain a curve of intensity vs. 20 for the line in question. 

The microphotometer is little used today because the counter of a diffractometer is faster, more accurate, and more sensitive. However, when only a camera is available or when circumstances are such that a camera is required (Sec. 6-1), 

6-3 For a Debye pattern made in a 5.73-cm-diameter camera with Cu Ka radiation, calculate the separation of the components of the Ka doublet in degrees and in centimeters for 0=10, 35, 60, and 85°. 

6-5 A powder pattern of zinc is made in a Debye-Scherrer camera 5.73 cm in diameter with Cu Ka radiation. 

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Quantities concerned with spectral absorption intensity and relations among these quantities are discussed in references [59]—[61], and a list of published measurements of line intensities and band intensities for gas phase infrared spectra may be found in references [60] and [61]. 

With the advent of photoelectric devices for measurement of line intensities, this should be simplified greatly. 

The intensities of spectral lines depend not only on the population density of the molecules in the absorbing or emitting level but also on the transition probabilities of the corresponding molecular transitions. If these probabilities are known, the population density can be obtained from measurements of line intensities. This is very important, for example, in astrophysics, where spectral lines represent the main source of information from the extraterrestrial world. Intensity measurements of absorption and emission lines allow the concentration of the elements in stellar atmospheres or in interstellar space to be determined. Comparing the intensities of different lines of the same element (e.g., on the transitions Ei Ek and Ee -> Ek from different upper levels Ei, Ee to the same lower level Ek) furthermore enables us to derive the temperature of the radiation source from the relative population densities A/, Ne in the levels Ei and Ee at thermal equilibrium according to (2.18). All these experiments, however, demand a knowledge of the corresponding transition probabilities. 

The spectrometer has an in-built preamplifier and A/D converter, its data acquisition is fidly computerpersonal computer or laptop equipment. A typical spectrum recorded in the case of a miniaturized microwave plasma discharge operated with argon is shown in Fig. 29b [65]. The resolution obtained does not allow the avoidance of interferences from multiple lines however, for measurements of line intensities in the case of line-poor spectra or for recording survey spectra the device is very useful. 

In the previous sections we have seen that the intensities of spectral lines depend not only on the population density of molecules in the absorbing or emitting level but also on the transition probabilities of the corresponding molecular transitions. If these probabilities are known, the population density can be obtained from measurements of line intensities. This is very important, for example, in astrophysics, where spectral lines represent the... 

The ubiquitous use of the word Tine to describe an experimentally observed transition goes back to the early days of observations of visible spectra with spectroscopes in which the lines observed in, say, the spectmm of a sodium flame are images, formed at various wavelengths, of the entrance slit. Although, nowadays, observations tend to be in the form of a plot of some measure of the intensity of the transition against wavelength, frequency or wavenumber, we still refer to peaks in such a spectmm as lines. 

In practice the laser can operate only when n, in Equation (9.2), takes values such that the corresponding resonant frequency v lies within the line width of the transition between the two energy levels involved. If the active medium is a gas this line width may be the Doppler line width (see Section 2.3.2). Figure 9.3 shows a case where there are twelve axial modes within the Doppler profile. The number of modes in the actual laser beam depends on how much radiation is allowed to leak out of the cavity. In the example in Figure 9.3 the output level has been adjusted so that the so-called threshold condition allows six axial modes in the beam. The gain, or the degree of amplification, achieved in the laser is a measure of the intensity. 

All the ealeulations for every analytieal line use its own AC-10 virtual unified sample material eontaining 10% of ehemieal element analyzed. In praetiee, instead of AC-10 speeimen, one ean use eertified sample material named Benehmark Referenee Material (BRM). One must know eomplete ehemieal eontent of BRM. Having measured analytieal line intensity of the speeimen, one ean determine the intensity from AC-10 by eorreetion system. Anyone eertified sample material ean be used as BRM for a few elements. Quantitative eomposition of BRM does not depend on the range of varying ehemieal elements eontent in samples analyzed substantially faeilitating a seleetion and ehange of these BRM. 

To summarize Filtering is an effective way of producing intense monochromatic beams, but it is severely limited because it cannot be used at all wavelengths and cannot achieve high spectral purity at any wavelength. The analysis of a spectrum, that is, the selection of a line and the measurement of its intensity, requires Bragg reflection. 

The constancy of the quotient in the last line of Table 7-2 is greatly improved over that in the line above the last, proving that Equation 7-5 holds. So far as we know, this is the first case in which the absorption effects for a series of solutions have been obtained so precisely. Examples of this kind place on a firmer basis the calculation of semiquantitative analytical results from measured intensities when the composition of the matrix (all of S but E, the element sought) in a sample is approximately known. For example, tungsten contents could be estimated from measurements of L7I intensity for sodium tungstate solutions even when other salts are present in the absence of such salts, tungsten contents... 

The absorption derivative amplitude is proportional to T22 whereas the width is proportional to T2 l. In other words, the derivative amplitude is inversely proportional to the square of the line width. Furthermore, the product of the amplitude and the square of the width is independent of T2 and is sometimes taken as a measure of the intensity of the line, i.e., proportional to M0. 

H. N. Russell analyzes solar spectrum with theoretical transition probabilities and eye estimates of line intensities. Notes predominance of hydrogen (also deduced independently by Bengt Stromgren from stellar structure considerations) and otherwise similarity to meteorites rather than Earth s crust. M. Minnaert et al. introduce quantitative measurements of equivalent width, interpreted by the curve of growth developed by M. Minnaert, D. H. Menzel and A. Unsold. 

Qualitative analysis may be made by searching the emission spectrum for characteristic elemental lines. With modem high resolution optics and computer control, the emission spectrum may be readily examined for the characteristic lines of a wide range of elements (Figure 8.13). Quantitative measurements are made on the basis of line intensities which are related to the various factors expressed in equation (8.1). Under constant excitation... 

Arc Spectrum.—Vanadium has been estimated in ores with fair accuracy by comparative measurement of the intensity of the lines in the arc spectrum.9... 

In addition to the different energy positions of the photolines shown in Fig. 2.4, the different heights of these lines are also a pronounced property of such spectra. It seems natural to use this height as a measure of the intensity of a photoline and, hence, for the cross section of a specific n/ orbital at the given photon energy. However, as will be seen in the next section, the appropriate quantity for the intensity is the area under a photoline (more correctly the dispersion corrected... 

As asserted in the previous section, the height of the photolines shown in Fig. 2.4 does not provide the correct measure of the intensity of a photoline. It will now be demonstrated that the appropriate measure for intensities is the area A under the line, recorded within a certain time interval, at a given intensity of the incident light, and corrected for the energy dispersion of the electron spectrometer. This quantity, called the dispersion corrected area AD, then depends in a transparent way on the photoionization cross section er and on other experimental parameters. In order to derive this relation, the photoionization process which occurs in a finite source volume has to be considered, and the convolution procedures described above have to be included. In order to facilitate the formulation, it has to be assumed that certain requirements are met. These concern ... 

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