Beer-Lambert equations

Optical methods are especially useful for the selective detection of CO and C02 concentrations. In low-priced sensors, a simple miniature light bulb is used as IR-source. The radiation emitted enters an absorption chamber, through which the flue gas is pumped. An added interference filter lets only the absorption spectra of the target gas pass. The IR detector determines the reduction of the light intensity, which is then transformed into an electrical signal. The correlation between the source intensity and the received intensity is given in the Lambert-Beer equation. 

Lambert-Beer equation (equation 14). With the provision of a reference HO absorption spectrum, and with care to avoid local instrumental artifacts that affect the two beams differently, this design allows the removal of extraneous atmospheric absorption features without requiring assignment to known absorbing species. 

Fig. 6. (a) Influence of IR absorption by gas-phase CO on the SFG signal of a GaAs reference crystal located at the sample position. The data points (open circles) were fitted by using the Lambert-Beer equation to obtain compensation curves (solid lines), (b) The experimental (raw) SFG spectrum of Pt(l 11) in the presence of 200 mbar of CO at 300 K (open circles) is plotted together with the corrected spectrum (black dots) and the corresponding gas-phase compensation curve (solid line) adapted from (151) with permission. Copyright (2001) American Chemical Society. 

The Lambert-Beer equation is useful for choosing conditions for the separation and detection of ions. The eluent ions should have a low absorptivity and the sample ions should have reasonably high absorptivity. In a special case of indirect detection (discussed later), this should be reversed. In this case, the eluent has an absorption signal and the sample is detected by a decrease of the background signal. 

The quantitative analysis of aerosol extinction spectra is based on the Lambert Beer equation (1). The measured optical depth at a specific wavenumber Vj may be expressed as... 

The Lambert Beer equation is always considered to be obeyed exactly. However, apparent deviations are sometimes observed, and it is then necessary to find an explanation in terms of extraneous effects such as dissociation and complex formation. Thus, when certain substances are present in solution, there are shifts in equilibria, and consequent changes in the relative proportions of the various molecular components. If the absorption of light by one of these components is being observed, there will be an apparent deviation from Beer s law, equation (2,16). Also, solutions that scatter light will not obey the law, and it is therefore important to exclude dust particles and large aggregated molecules in photometric experiments. 

Perhaps one of the most important conclusions that can be drawn from this equation is that in heterogeneous reacting systems classical forms of analyzing the light distribution inside the photochemical cell (i.e. the Lambert-Beer equation) are incorrect and, very likely, useless. To integrate the radiative transfer equation (RTF) we need a boundary condition the incoming radiation to the reaction space. It is provided by an emission model for the lamp. 

The effectiveness of these UVAs can be gauged with the Lambert-Beer equation, A = ebc, in which absorbance (A) is the product of the molecule s absorptivity (e), the light s path length (b), and the UVA s concenuation (c) [4-7,4-21]. 

Infrared spectra were measured on a JASCO FT-IR660 Plus over the standard wavenumber range of 400 - 4000 cm. The film thickness was calibrated by the Lambert-Beer equation as follows. 

Flere d is the film thickness, and c and co denote the concentration at time t and the equilibrium state, respectively. The concentration can be replaced by the absorbance using the Lambert-Beer equation (1)... 

Photoexcitation does not occur for all molecules with the same probability. This is because photoabsorption depends on the chemical structure of the chromophore group. As the Lambert-Beer equation describes... 

Lambert-Beer equation, 212 Laplace transformation, 152 Laser light, 153... 

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