Broadening Doppler

The Doppler effect plays a major role in spectroscopic resolution, in both beam and nonbeam experiments. The sonic form of the Doppler shift, when a moving vehicle emits a sound heard by the stationary observer, is familiar to everyone. The electromagnetic radiation equivalent can be expressed in a very simple form. If a molecular source is moving with a velocity v relative to a receiver, and is emitting radiation of frequency v, the observed frequency / is given by 

The observed frequency / may be smaller or larger than the emitted frequency, depending upon the direction of the moving source relative to the observer. The fractional Doppler shift in wavelength, z, is given by 

We note the important result that the Doppler shift is directly proportional to the frequency. 

In studies of bulk gas samples, as in conventional microwave absorption experiments, one must take account of the fact that one is studying an assembly of molecules moving in different directions at different velocities, and suffering frequent collisions which change both the velocity and direction. It may be shown that for a gas at thermal equilibrium, the Doppler full line width Av at half-height is given by 

the so-called Doppler line width, is the FWHM which is given by  

If the mass m of the atom is expressed by the molar mass M given in g/mol, the width can be written as  

The Doppler broadening effect is caused by the thermal motion of the emitting or absorbing atoms. Under typical conditions the speeds of atoms are about 1000 ms . Although this is considerably smaller than the speed of light (r = 3 X 10 ms ), it is fast enough for the Doppler effect to become noticeable. 

the Doppler broadening is directly proportional to frequency of the line (v) and to the square root of the absolute temperature (T), and inversely proportional to the square root of the atomic mass (M). The Doppler effect accounts for most of the line width. 

Whether radiation is being absorbed or emitted the frequency at which it takes place depends on the velocity of the atom or molecule relative to the detector. This is for the same reason that an observer hears the whistle of a train travelling towards him or her as having a frequency apparently higher than it really is, and lower when it is travelling away from him or her. The effect is known as the Doppler effect. 

If an atom or molecule is travelling towards the detector with a velocity va, then the frequency va at which a transition is observed to occur is related to the actual transition frequency v in a stationary atom or molecule by 

36 2 ELECTROMAGNETIC RADIATION AND ITS INTERACTION WITH ATOMS AND MOLECULES 

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In the limit of very small Doppler broadening, the (co2t2kT/(2me2)) faetor ean be ignored (i.e., exp(-co2t2kT/(2me2)) set equal to unity), and... 

When the Doppler broadening ean not be negleeted relative to the eollisional broadening, the above integral... 

The full width at half height of these Lorentzian peaks is 4Drot- In this ease, one says that the individual peaks have been broadened via rotational diffusion. When the Doppler broadening ean not be negleeted relative to the eollisional broadening, the above integral... 

Except at very low frequencies, pressure broadening may be removed simply by working at a sufficiently low pressure. Doppler broadening may be reduced or removed by two general methods, which will be discussed briefly below. 

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. 

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. 

Natural linewidths are broadened by several mechanisms. Those effective in the gas phase include collisional and Doppler broadening. Collisional broadening results when an optically active system experiences perturbations by other species. Collisions effectively reduce the natural lifetime, so the broadening depends on a characteristic impact time, that is typically 1 ps at atmospheric pressure ... 

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... 

Beam Spectroscopy. Both specificity and sensitivity can be gready enhanced by suppressing coUisional and Doppler broadening. This is accompHshed in supersonic atomic and molecular beams (296) by probing the beam transversely to its direction of dow in a near-coUisionless regime. 

Doppler broadening because of vibrations of the target atoms [3.182-3.184]. Doppler broadening is usually a small contribution, which becomes important only... 

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. 

The arguments seen in section 2.3 suggest that resonant y-absorption should decrease at very low temperatures because the Doppler broadening of the y-lines decreases and may even drop below the value of the recoil energy. In his experiments with solid sources and absorbers, however, R.L. Mossbauer ([1] in Chap. 1) observed on the... 

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. 

Many recombination and spectroscopic studies have been carried out in decaying rare-gas plasmas. Invariably, the buffer gas was the parent gas of the ion under study. In addition to recording the emitted spectra, Frommhold and Biondi60 examined the line shapes of many afterglow lines in neon and in argon. The intent was to find spectroscopic evidence for Doppler broadening of the lines which would prove that... 

Doppler broadening allows for observation that some molecules in a gas cloud may be moving towards the observer and some away from the observer in a line of sight. 

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