Doppler broadening emission line

Fig. 5 Component probability pc q) for a single Doppler-broadened emission line. The ordinate scale depends on the q domain chosen for normalization.

This situation corresponds to the well-known saturation effect in the emission of most gas laser transitions, where, for the same reason, fewer upper-state molecules can contribute to the gain of the laser transition at the center of the doppler-broadened fluorescence line than nearby. When tuning the laser frequency across the doppler-line profile, the laser intensity therefore shows a dip at the centerfrequen-cy, called the Bennet hole or Lamb dip after W.R. Bennet who discovered and explained this phenomen, and W.E. Lamb 2) who predicted it in his general theory of a laser. 

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. 

D3) absorption and emission lines (from n = 3 states) in H2 (D2) plasmas were strongly Doppler-broadened which seems to indicate high, nonthermal energies (about 0.3 eV) of the absorbing or emitting H3 molecules. The energy is close to that expected if the excited (n = 3) H3 molecules were formed by recombination of Hj, but in Amano s work no Hj ions should have been present. Perhaps, the fast H3 molecules are produced from H + H2 collisions, and the spectroscopic observations provide indirect evidence for the existence of H3 molecules. The conjecture needs to be examined by more detailed work. 

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. 

For simplicity, suppose that we have an emission spectrum consisting of a single, predominantly Doppler-broadened line. This spectrum may be taken as an approximation to the case of widely separated and nonoverlapping lines of equal intensity. Again for simplicity, now consider the typical emission spectrum to be continuous, not sampled. Thus q(x) is given by q(x) = q0 exp( —x2) for a typical line, where q0 is the peak height. We have chosen the abscissa to be measured in either wavelength or wave number relative to a typical line center. For illustrative purposes only, the x interval for the observation is taken to be 2 Ax. If the line is centered in this interval at x = 0, we can never have q(x) < exp ( — Ax2). 

Linewidth is also affected by pressure broadening from collisions between atoms. Collisions shorten the lifetime of the excited state. The uncertainty in the frequency of atomic absorption and emission lines is roughly numerically equal to the collision frequency between atoms and is proportional to pressure. The Doppler effect and pressure broadening are similar in magnitude and yield linewidths of 10-3 to I0-2 nm in atomic spectroscopy. 

The relatively weak dependence on the ratio Ktat/ i abs suggests that the modification to our calculated results will not be great except at very early times. The effective temperature calculated for Model 10H, for example, is, without modification, within 15% of the values inferred from the spectrum (Suntzeff, private communication) on days 1.14 (13,600 K), 1.51 (12,700 K), and 1.85 (11,690 K). Figure 5 illustrates the effect for K<0 0.3, and 0.1. The latter corresponds to a color temperature one third greater than the effective emission temperature. Karp et a1. (1977) have considered the effect of Doppler broadened lines on the bound-bound opacity. For typical photospheric densities (1012 g cm-3) and temperatures (5000 K to 50,000 K) the line opacity is approximately 20% to 200% that of electron scattering (see their Table 3). This should keep the color temperature within about 20% of the effective emission temperature. 

It has been found, however, in practice that a perfectly straight analytical working curve (— log T plotted against concentration) is seldom obtained in atomic absorption spectroscopy. The reasons for this are usually a combination of instrumental problems broadening of the emission line of the light source due to self-reversal, Doppler and pressure broadening of the absorption lines of the atoms in the flame, failure to exclude flame emission entirely, use of a focused instead of a parallel... 

Dalby and Bennett " which has given accurate probabilities for a series of transitions. The technique is described briefly onpp. 291-2. Accurate determination of concentrations may still be hindered by self-absorption of the radiation, particularly in the case of the hydroxyl radical. Penner and co-workers have overcome the difficulty by the use of a double path technique, and are able to determine the rotational temperature and concentration of hydroxyl radicals in both flame and shock-tube studies. The single and double path emissivities are compared simultaneously, the double path beam being chopped to give modulation at about 5 sec intervals. The method of correction for line widths and Doppler broadening is discussed . 

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