Lambert-Beer type law

Based on the Lambert-Beer-type law of exponenhal attenuation of peak intensity (I) with excitation depth (z),... 

When X-rays pass through matter, they inevitably lose intensity via interactions with the material. The loss in intensity is proportional to the original intensity and to the thickness d of the material inserted into the beam path. Thus, a Lambert-Beer-type law results ... 

The attenuation of a beam of high-energy photons traversing matter can be described by a Lambert-Beer-type law according to Equation 4.1 ... 

Transparent materials interact with light only by absorption. This interaction is formulated quantitatively in the Bouguer-Lambert and Beer s Laws (c.f. i). In paper, however, surface reflection is the dominating type of interaction. This results in very desirable properties like high brightness and opacity, but complicates the interpretation of optical tests with regard to absorption data. The Kubelka-Munk theory attempts to separate the two types of... 

As with other types of absorption spectroscopy e.g., UV-visible spectroscopy), the basis of quantitative analysis in infrared spectroscopy is the Bouguer-Beer-Lambert law or Beer s law (equation (13)) ... 

When a beam of infrared light of intensity I0 is passed through a sample, it can either be absorbed or transmitted, depending upon its frequency and the structure of the molecules. The final intensity I of the infrared light that passes through the sample can be calculated by the Lambert-Beer law (2.4) which is applicable to all types of electromagnetic radiation. 

Other types of optode have been designed, often using fluorescent dyes for detecting different analytes. A pH optode was described by Peterson et al [16, 17], who coupled a bifurcated fiber optic cable to a small cavity containing a pH-sensitive dye. Using the Lambert-Beer law, the pH can be related to the concentration of the dye Cjye) and its buffering capacity (pX) by... 

Unfortunately, many problems arise applying Lambert-Beer to practical analysis, if the conditions of the derivation are ignored [12,13,18]. First, at certain conditions deviations from the linear behavior are obtained, which either can be related to instrumental problems or deviation from Lambert-Beer law. Second, in general broad absorption bands in the UV/Vis reduce the selectivity [15,17] of this type of spectroscopy. In consequence, in multicomponent samples a so-called multicomponent analysis has to be pursued, which increases expenditure of evaluation (see Sec. 5.5.)... 

The equation used in photosedimentation theory to link the opacity of a suspension to the properties of the suspension is the Lambert-Beer law. The Lambert-Beer law is an energy exponential decay law of the type that occurs in many physical situations. [Note that in some optical textbooks the law is called the Lambert law and in others, the Beer law, since different historians of science variously attribute the law to either the German scientist Johan Heinrich Lambert (1728-1777) or to the German astronomer Wilhelm Beer (1797-1850). The Lambert-Beer law states that... 

In beam-type analyzers, the collision event leading to ion activation can be considered in terms of the Lambert-Beer law, because the precursor ion beam flux [Mp]o is exponentially reduced when passing through a collision chamber of length I containing gas at target number density n... 

In the study of reactions of the types ether than exchange mentioned previously, the usual technique involves the spectrophotometric examination of reaction mixtures. The absorbance changes that occur, at a suitable wavelength where only one species (either reactant or product) absorbs, as the reaction proceeds are measured (manually or recorded). Treatment of the data via the Beer-Lambert law enables rate coefficients and laws to be found in the usual manner. Stopped flow and temperature jump techniques have been used for very rapid reactions. 

T-O-T stretch measured by framework IR, as discussed in Section 4.5.3.2. The comparison of areas as described above does provide quantitative information about the relative changes in acidity between the samples since the area is direction proportional to the concentration (Beer-Lambert law, discussed in Section 4.5.2.) It most cases, this relative, but quantitative comparison between samples is sufficient to provide information about how various treatments or modifications have altered acid site distributions. Since extinction coefficients can change with zeolite type (Table 4.5), these comparisons are best for samples of the same zeolite type. Therefore, caution should be used when comparing data from samples with different zeolite structures. 

In analytical spectrometry there are many types of calibration curves which are set up by measuring spectrometric reference solutions. The measurements yield a curve of absorbance versus concentration, and the points between the data of the reference solutions are interpolated by fitting a suitable curve, which normally follows the Beer-Lambert law and which gives rise to a straight line through the origin of the coordinate system. The measurement conditions and the results of the calibration curve evaluations in the case of chromium and lead measurements by electrothermal atomic absorption spectrometry are presented in Table 1. 

---