Line Doppler

This effect is only of real consequence at the higher MMW frequencies. Gordy and Cook (ref 3, p. 47) calculate for example that for the 572.053 GHzNHs line at 300 K the Doppler width lAv = 1.7 MHz, comparable with collisional broadening at 13 Pa. In the 24 GHz region, the ammonia line Doppler widths are 72 kHz, much less than the collisional broadening at typical working pressures. 

Surin used the Orotron oscillator as a tuneable source of coherent MMW radiation to study the spectroscopy of SiH4 and ND3 in the 90-160 GHz range. The gas was introduced into a cell placed in a Fabry-Perot cavity 10. The absorption signals were detected from variation of the Orotron electron beam current. No phase or frequency lock schemes were necessary and resolution achieved was sufficient to resolve the lines Doppler profiles sensitivity was estimated as 3-5 X 10" m . 

In atomic absorption spectrophotometry, a hollow cathode lamp is used which emits the characteristic line spectrum of the cathode metal. The light from the lamp passes through an atomised mist of the gaseous element and a line of the emitted spectrum (die resonance line) is absorbed. A monochromator then allows this line alone to reach the detector and the narrow absorption band is recorded and/or displayed. Because atoms have no rotational or vibrational levels, transitions from one electronic level to another produces narrow absorption or emission lines. Doppler and pressure broadening vary from 0.01-0.00 Inm. 

High-resolution spectroscopy used to observe hyperfme structure in the spectra of atoms or rotational stnicture in electronic spectra of gaseous molecules connnonly must contend with the widths of the spectral lines and how that compares with the separations between lines. Tln-ee contributions to the linewidth will be mentioned here tlie natural line width due to tlie finite lifetime of the excited state, collisional broadening of lines, and the Doppler effect. 

The actual line shape in a spectrum is a convolution of the natural Lorentzian shape with the Doppler shape. It must be calculated for a given case as there is no simple fomuila for it. It is quite typical in electronic... 

Figure B2.5.12 shows the energy-level scheme of the fine structure and hyperfme structure levels of iodine. The corresponding absorption spectrum shows six sharp hyperfme structure transitions. The experimental resolution is sufficient to detennine the Doppler line shape associated with the velocity distribution of the I atoms produced in the reaction. In this way, one can detennine either the temperature in an oven—as shown in Figure B2.5.12 —or the primary translational energy distribution of I atoms produced in photolysis, equation B2.5.35.

Velocity recoils are measured at short times after tire initial ultraviolet excitation pulse by probing tire nascent Doppler profiles for tire different spectral lines probed in tliese last steps. 

Figure C3.3.6. Doppler-line profiles for molecules scattered into the CO COO O J= 72) state by collisions with hot methylpyrazine molecules as depicted by the equations above each half of the figure. The energy of methylpyrazine...

This result, when substituted into the expressions for C(t), yields expressions identieal to those given for the three eases treated above with one modifieation. The translational motion average need no longer be eonsidered in eaeh C(t) instead, the earlier expressions for C(t) must eaeh be multiplied by a faetor exp(- co2t2kT/(2me2)) that embodies the translationally averaged Doppler shift. The speetral line shape funetion I(co) ean then be obtained for eaeh C(t) by simply Fourier transforming ... 

The reaction path shows how Xe and Clj react with electrons initially to form Xe cations. These react with Clj or Cl- to give electronically excited-state molecules XeCl, which emit light to return to ground-state XeCI. The latter are not stable and immediately dissociate to give xenon and chlorine. In such gas lasers, translational motion of the excited-state XeCl gives rise to some Doppler shifting in the laser light, so the emission line is not as sharp as it is in solid-state lasers. 

Of the four types of broadening that have been discussed, that due to the natural line width is, under normal conditions, much the smallest and it is the removal, or the decrease, of the effects of only Doppler, pressure and power broadening that can be achieved. 

Such beams have many uses, including some imporfanf applications in specfroscopy. In particular, pressure broadening of specfral lines is removed in an effusive beam and, if observations are made perpendicular to fhe direction of fhe beam, Doppler broadening is considerably reduced because fhe velocify componenf in fhe direction of observation is very small. 

Figure 9.3 Doppler limited laser line with twelve axial modes within the line width...

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. 

Figure 9.25 (a) A Doppler-limited line, (b) The detection. V, potential psd, phase-sensitive detector... 

Figure 9.26 (a) Doppler line shape with a Lamb dip. (b) As in (a) but with modulation and phase-... 

In a skimmed supersonic jet, the parallel nature of the resulting beam opens up the possibility of observing spectra with sub-Doppler resolution in which the line width due to Doppler broadening (see Section 2.3.4) is reduced. This is achieved by observing the specttum in a direction perpendicular to that of the beam. The molecules in the beam have zero velocity in the direction of observation and the Doppler broadening is reduced substantially. Fluorescence excitation spectra can be obtained with sub-Doppler rotational line widths by directing the laser perpendicular to the beam. The Doppler broadening is not removed completely because both the laser beam and the supersonic beam are not quite parallel. 

A remarkable feature of these spectra is the resolution of individual rotational lines in such large molecules. [Note that the expanded specttum in, for example. Figure 9.47(a) covers only 5000 MFIz (0.17 cm )]. This is due partly to the very low rotational temperature (3.0 K for aniline and 2.2 K for aniline Ar), partly to the reduction of the Doppler broadening and partly to the very high resolution of the ring dye laser used. 

Doppler broadening arises from the random thermal agitation of the active systems, each of which, in its own test frame, sees the appHed light field at a different frequency. When averaged over a Maxwellian velocity distribution, ie, assuming noninteracting species in thermal equilibrium, this yields a line width (fwhm) in cm C... 

Limits of detection become a problem in capillary electrophoresis because the amounts of analyte that can be loaded into a capillary are extremely small. In a 20 p.m capillary, for example, there is 0.03 P-L/cm capillary length. This is 1/100 to 1/1000 of the volume typically loaded onto polyacrylamide or agarose gels. For trace analysis, a very small number of molecules may actually exist in the capillary after loading. To detect these small amounts of components, some on-line detectors have been developed which use conductivity, laser Doppler effects, or narrowly focused lasers (qv) to detect either absorbance or duorescence (47,48). The conductivity detector claims detection limits down to lO molecules. The laser absorbance detector has been used to measure some of the components in a single human cell (see Trace AND RESIDUE ANALYSIS). 

J. Stark (Greifswald) discovery of the Doppler effect on canal rays and of the splitting of spectral lines in electric fields. 

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. 

Natural width of D lines 10 MHz Peak D2 cross section for Doppler linewidth 8.8 10 m2... 

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