Absorption coefficient wavelength dependence

The absorption coefficient k depends in general on wavelength (A). For large nl, e approaches 1 - a perfect emitter. This limit generally occurs at turbulent flames of about 1 m in thickness. 

Values for the mass-absorption coefficient, which is equal to m/p, are listed in standard reference tables. As a first approximation, is proportional to Z A up to the K or L absorption edge thus, the absorption coefficient is dependent on both the element composition and the wavelength of the x-ray (see Fig. 14.14). As mentioned before, there can be one K-absorption edge, three L edges, and five M edges. 

The short circuit current is the product of the photon flux (A.) of the incident solar spectrum and the wavelength-dependent spectral response or collection efficiency Q( k) integrated over all wavelengths 7sc = / k)Q k)dX (see Fig. 61b). The collection efficiency is about 80% between 450 and 600 nm, demonstrating that there is little loss due to recombination (the i-layer is of device quality). The decreasing collection efficiency at the red side is due to the decreasing absorption coefficient of a-Si H. In the blue, the decreasing collection efficiency is due to absorption in the /7-layer and/or buffer layer. 

Both WDXRF and EDXRF lend themselves admirably to quantitative analysis, since there is a relationship between the wavelength or energy of a characteristic X-ray photon and the atomic number of the element from which the characteristic emission line occurs. The fluorescence intensity of a given element is proportional to the weight fraction. Emitted fluorescence radiation is partly absorbed by the matrix, depending on the total mass absorption coefficient ... 

This ratio is called the photostationary state composition. In the photostationary state, the rate of formation of each isomer from the nonvertical excited state is equal to its rate of removal by absorption of light. There is a roughly equal probability of the relaxation of the nonvertical excited state forming either the cis or the trans isomer and so the main factor influencing the photostationary state composition is the competition for absorbing light. This will, of course, depend on the relative values of the molar absorption coefficients of the two isomers at the particular wavelength chosen. 

This reaction can occur either thermally or photochemically, with the equilibrium position (thermal reaction) depending on the thermodynamic stability of the reactant and product, and the photostationary-state composition depending on the relative values of the absorption coefficients at the wavelengths used. 

Tab. 2.1. Examples of molar absorption coefficients, (at the wavelength corresponding to the maximum of the absorption band of lower energy). Only approximate values are given, because the value of slightly depends on the solvent...

Concentrations in the region of 0.1 mol 1 1 are often convenient but it obviously depends upon such factors as the amount of substance available, the cost, the solubility, etc. From this stock solution, a series of accurate dilutions are prepared using volumetric glassware and the absorbance of each dilution measured in a 1-cm cuvette at the wavelength of maximum absorbance for the compound. A plot of absorbance against concentration will give an indication of the validity of the Beer-Lambert relationship for the compound and a value for the molar absorption coefficient may be calculated from these individual measurements or from the slope of the linear portion of the graph ... 

The number of charge carriers generated in the SCR depends on the absorbed flux of incident photons per unit area P, the width W of the SCR and the wave-length-dependent absorption coefficient a of bulk Si. The latter parameter is shown in Fig. 7.6, while the resulting penetration depth for light of different wavelengths is shown in Fig. 10.4a. 

In multicomponent systems A"0 can be written as a sum of the individual absorption coefficients A ot = 2TA , where each AT,(A ) depends in a different way on the wavelength. If one or more of the components are fluorescent, their excitation spectra are mutually attenuated by absorption filters of the other compounds. This effect is included in Eqs. (8.27) and (8.28) so that examples like that of Figure 8.4 can be quantified. The two fluorescent components are monomeric an aggregated pyrene, Mi and Mn. The fluorescence spectra of these species are clearly different from each other but the absorption spectra overlap strongly. Thus the excitation spectrum of the minority component M is totally distorted by the Mi filter (absorption maxima of Mi appear as a minima in the excitation spectrum ofM see Figure 8.4, top). In transparent samples this effect can be reduced by dilution. However, this method is not very efficient in scattering media as can be seen by solving Eqs. (8.27 and 8.28) for bSd — 0. Only the limit d 0 will produce the desired relation where fluorescence intensity and absorption coefficient of the fluorophore are linearly proportional to each other in a multicomponent system. 

EXAMPLE 4.3 Figure 4.9(a) shows the dependence of the absorption coefficient versus the photon energy for indium arsenide, (a) Determine whether or not InAs is a direct-gap semiconductor, (b) Estimate the band-gap energy, (c) If an InAs sample of 1 mm thickness is illuminated by a laser of 1 W at a wavelength of 2 jam, determine the laser power for the beam after it passes through the sample. Only consider the loss of light by optical absorption. 

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