Half-width Doppler

Doppler broadening. Collisions broadening becomes less important at the lower pressures found at higher altitudes, so that the Lorentzian half-width and the Doppler half-width become comparable at altitudes of approximately 30-40 km. 

V/c)vo. To this is applied the distribution of velocities. After evaluation of constants, this simplifies to the Doppler half-width ... 

Avd Avn Avp c A AW Doppler half-width in hertz natural half-width l/47cyN pressure-broadened half-width 1 /4nyP variable of integration wavelength of radiant flux triangle function of unit height and half-width % scaled ratio (AvN -1- Avc) /ln 2/AvD... 

Expressing the distance from the line center in terms of Doppler half-widths, we identify... 

The quantity AxD is the Doppler half-width encountered earlier. Newton s method requires knowledge of the first derivative, which is easily provided by multiplying each term in Eq. (59) by n/SX. 

When pressure broadening dominates, the situation is more complicated because the resulting Lorentzian profile contributes significant area far from the line center. A further complication in this case is that the Lorentzian half-width cannot be accurately calculated and must be measured in other experiments. If both Doppler and pressure broadening are present, however, and if the Lorentzian to Doppler half-width ratio is small, the correction necessitated by pressure broadening is small. In this situation an accurate value of the Lorentzian half-width may not be needed. Line strength in the case of combined Doppler and pressure broadening may be obtained from the equivalent width by the use of tables (Jansson and Korb, 1968). 

Cases have been observed where the isotopic line absorption profiles completely overlap, e.g. boron-10 and -11 in a krypton-filled lamp at 249.7 nm [244]. Hannaford and Lowe [245] later showed that this was caused by an unusually large Doppler half-width induced by the fill-gas, and, if neon is used, the 208.9 and 209.0 nm lines can allow the determination of boron-10 and boron-11 isotope ratios. The 208.89/208.96 nm doublet was found to be more useful than the 249.68/249.77 nm doublet. Enriched isotope hollow-cathode lamps were used as sources. A sputtering cell was preferred to a nitrous oxide/acetylene flame as the atom reservoir, as it could be water-cooled to reduce broadening and solid samples could be used, thus avoiding the slow dissolution in nitric acid of samples of boron-10 used as a neutron absorber in reactor technology. 

Create a spreadsheet lo caleulale the Doppler half width AA,) in nanomelers for Ihe nickel and iron lines cited in (b) and (e) from. 3(K)()-10.OtX) K. 

The fluorescence equation is dependent on the nature of the excitation source. If a line-like radiation source is employed, a term which takes into consideration the half-width of the excitation line with respect to the half-width of the absorption line is included. In the case of a continuum source, a term for the product of the Doppler half-width and the continuum incident radiation must be added to the equation. 

Figure 3.10 presents a typical function An uj). It can be seen that the dispersion curve is a superposition of two curves. The relatively wide component curve describes the anomalous refractive-index dispersion within the limits of the Doppler profile. The maximum refractive-index variation due to linear absorption is reached when the field frequency is tuned off resonance by an amount approximately equal to the Doppler half-width ... 

It would appear that measurement of the integrated absorption coefficient should furnish an ideal method of quantitative analysis. In practice, however, the absolute measurement of the absorption coefficients of atomic spectral lines is extremely difficult. The natural line width of an atomic spectral line is about 10 5 nm, but owing to the influence of Doppler and pressure effects, the line is broadened to about 0.002 nm at flame temperatures of2000-3000 K. To measure the absorption coefficient of a line thus broadened would require a spectrometer with a resolving power of 500000. This difficulty was overcome by Walsh,41 who used a source of sharp emission lines with a much smaller half width than the absorption line, and the radiation frequency of which is centred on the absorption frequency. In this way, the absorption coefficient at the centre of the line, Kmax, may be measured. If the profile of the absorption line is assumed to be due only to Doppler broadening, then there is a relationship between Kmax and N0. Thus the only requirement of the spectrometer is that it shall be capable of isolating the required resonance line from all other lines emitted by the source. 

In 1971, Walcher [326] succeeded in observing a resonance effect of about 0.6% in as a function of the Doppler velocity using a TI2O3 source and an enriched (81% ° Hg) HgO absorber at 4.2 K. The half-width turned out to be Fexp = 76 (10) mm s corresponding to a lower limit of the half-life of fi/2 > 0.1 ns. It is clear that the properties of the ° Hg Mossbauer isotope do not render it an interesting isotope from a chemical point of view. 

The major requirement of the light source for atomic absorption is that it should emit the characteristic radiation (the spectrum) of the element to be determined at a half-width less than that of the absorption line. The natural absorption line width is about 10 4 (A), but due to broadening factors such as Doppler and collisional broadening, the real or total width for most elements at temperatures between 2000 ° and 3000 °K is typically 0.02 — 0.1 A. Hence, a high resolution monochromator is not required. 

Ideally, the emission line used should have a half-width less than that of the corresponding absorption line otherwise equation (8.4) will be invalidated. The most suitable and widely used source which fulfils this requirement is the hollow-cathode lamp, although interest has also been shown in microwave-excited electrodeless discharge tubes. Both sources produce emission lines whose halfwidths are considerably less than absorption lines observed in flames because Doppler broadening in the former is less and there is negligible collisional broadening. 

FIGURE 14-8 (a) Meaning of equivalent width, W (b) Doppler and Lorentzian line-shapes for equivalent half-widths (c) transmission curves for an absorption line for a weak and strong absorber, respectively (adapted from Lenoble, 1993). 

AxN, Axp, AxD, Axv line-profile half-widths in cm-1 for natural, pressure-broadened, Doppler-broadened, and combined Doppler-and pressure-broadened cases, respectively generally Ax = Av/c, where c is velocity of light... 

It is of interest to compare the half-widths at half-intensity of the spectral functions of the three systems shown in Fig. 3.2. These amount to roughly 140, 80 and 50 cm-1 for He-Ar, Ne-Ar and Ar-Kr, respectively, which are enormous widths if compared to the widths of common Doppler profiles, etc. The observed widths reflect the short lifetimes of collisional complexes. From the theory of Fourier transforms we know that the product of lifetime, At, and bandwidth, A/, is of the order of unity, Eq. 1.5. The duration of the fly-by interaction is given roughly by the range of the induced dipole function, Eq. 4.30 (1/a = 0.73 a.u. for He-Ar), divided by the mean relative speed, Eq. 2.12. We obtain readily ... 

Example Gas Temperature Calculation from Doppler Broadening Effect. The half-widths of the 4302.19 A. and 4844.02 A. lines for iron were measured on the axes of an iron electrode arc and found to be 0.032 and 0.037 A., respectively. What is the translational temperature of the gas Equation (22) simplifies to ... 

Table 1.3 Comparative list of approximate half-widths of selected elements for Doppler and Lorentzian broadening...

For the most part, it is Doppler broadening and, to a lesser extent, Holtz-mark broadening that have the greatest influence on the half-widths of the spectral lines of interest in analytical atomic spectroscopy. 

Line sources are capable of producing the best linear relationship between instrument response and concentration. For optimum linear response, the halfwidth of the source line used for excitation should be less than the half-width of the absorption line of the sample. This requirement is met by most line sources, since at temperatures of the flame, absorption lines of the sample undergo substantial Doppler and collisional broadening whereas the corresponding source lines remain narrow. 

Figure J. 23. Lorentzian, Doppler, and Voigt spectral line profiles for approximately equal half widths and intensities. (From Andrews et al.., 1987).

To treat predissociation quantitatively, precise measurements of the width (full width at half maximum, FWHM, or T, often misleadingly referred to as the half-width) of each rotational level are necessary. In the absence of Doppler broadening, the lineshape ora(E) is usually Lorentzian,... 

In a study of line broadening mechanisms in low-pressure laser-induced plasmas, Oornushkina et al. present the following expression for the half width for Doppler broadening AAd of an atomic line. 

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