Integral absorption coefficient

In this expression the only variable is N0 and it is this which governs the extent of absorption. Thus it follows that the integrated absorption coefficient is directly proportional to the concentration of the absorbing species. 

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. 

Fig. 21. Integrated intensity OH and OD bands versus time for adsorbed labeled propylene. CH3- CH=CD2 O, OH , OD. CD3—CH=CH2 A, OH A, OD. The integrated intensity for OD was multiplied by 1.35, the isotopic shift, in an attempt to correct for expected differences in the integrated absorption coefficient.

Table 3.1. Binary integrated absorption coefficients of rare gas mixtures.

Table 3.2. Ternary integrated absorption coefficients of the translational band. Measurement from [95] calculation [296],...

In the framework of the impact approximation of pressure broadening, the shape of an ordinary, allowed line is a Lorentzian. At low gas densities the profile would be sharp. With increasing pressure, the peak decreases linearly with density and the Lorentzian broadens in such a way that the area under the curve remains constant. This is more or less what we see in Fig. 3.36 at low enough density. Above a certain density, the l i(0) line shows an anomalous dispersion shape and finally turns upside down. The asymmetry of the profile increases with increasing density [258, 264, 345]. Besides the Ri(j) lines, we see of course also a purely collision-induced background, which arises from the other induced dipole components which do not interfere with the allowed lines its intensity varies as density squared in the low-density limit. In the Qi(j) lines, the intercollisional dip of absorption is clearly seen at low densities, it may be thought to arise from three-body collisional processes. The spectral moments and the integrated absorption coefficient thus show terms of a linear, quadratic and cubic density dependence,... 

In the vacuum ultraviolet absorption bands in the region 1280 to 1600 A correspond to the fourth positive system A1 n-X L+. The absorption cross sections of this system are given in Fig. V-7. Since the widths of the CO rotational lines are much smaller than the instrumental resolution ( 10 cm" 1), it is not possible to obtain the absorption cross section of each rotational line [see Section 1-8 for details]. Thus, the cross sections shown in Fig. V-7 are much less than the true cross sections. An estimate of the integrated absorption coefficient of the (0,0) band is 1.7 x 104cm-latm-1 (899). Various electronic states and transitions are given in Fig. V-8. 

I 8 1 The Ifccr-Lambcrl Law in the Molecular System, 41 I 8.2 Deviation from the Beer-Lamberl Law, 42 I 8.3 Measurement of the Integrated Absorption Coefficient, 44... 

The ionization of NO by the Lyman-a line is the main source of ions in the D region. The photodissociation of NO in the upper atmosphere occurs from the /t2Z + (F > 4), B2n (c > 7), and C2n (F > 0). The dissociation rate of NO by the solar radiation is proportional to the integrated absorption coefficient of various bands (that is, the oscillator strength). From Table V 4 it can be seen that absorption by the /if (12,0) and 6 bands is most important in leading to photodissociation. 

The Schumann-Runge bands converge to the limit at 1750 A corresponding to the production of Of3/3) + Of1/)). The integrated absorption coefficients of the Schumann-Runge system from (0,0) to (20,0) have been... 

As with N02, the observed radiative lifetime of the A 1Bl state of S02 (4 x 10"5 sec) is much longer than the value calculated from the integrated absorption coefficient (2 x 10" 7 sec)229. This is again presumably due to strong interaction with the electronic ground state203. 

Fluorescence from ketene upon absorption of light in the near ultraviolet has not been observed. The quantum yield of fluorescence is less than 10 Since the radiative lifetime calculated from the integrated absorption coefficient is 40//see, the lifetime of the excited state must be less than 0.4 nsec. Since the lifetime of the initially formed excited state is much shorter than the dissociative lifetimes, an excited state responsible for dissociation must be different from the one initially formed at 3340 and 3660 A. 

For transitions between individual states any of the more fundamental quantities Gjh B ji9 Ajh or Mji may be used the relations are as given above, and are exact. Note, however, that the integrated absorption coefficient A should not be confused with the Einstein coefficient Ajt (nor with absorbance, for which the symbol A is also used). Where such confusion might arise, we recommend writing A for the band intensity expressed as an integrated absorption coefficient over wavenumber. 

Details of the derivation of the harmonic o.scillator dielectric function and of the Kramers-Kronig transformation are described in standard textbooks, such as (Kuzmany, 1990b Kittel, 1976). Eq. 4.8-1 is also well known as the Kramers-Heisenberg dielectric function. The integrated absorption coefficient in Eq. 4.8-5 is very often used in conventional vibronic IR spectroscopy to characterize the concentration of the absorbing species. 

It is common to use the peak absoiption coefficient instead of the integral absorption coefficient. In most cases only small errors are introduced by this simplification. It is evident that the detection limit decreases with the membrane method as I//At/.s - For gases extracted by the membrane the usual rotational vibrational bands vanish if the compound is dissolved in a polymer, since the molecule is no longer able to rotate freely. As a result, one relatively sharp absorption band is observed which has the same integral absorption coefficient as the rotational vibrational absorption band. So, for gases the detection limit is decreased by an additional factor h,> (see Table 6.5-3). For the ATR-method the thickness of the sample is the effective thickness multiplied by the number of reflections N. So we get as detection limit for the membrane method... 

B) Spectroscopic Analyses. (i) Infrared spectra were recorded from KBr discs in absorption mode using the techniques and equipment outlined in reference (7). Integrated absorption coefficients... 

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