Absorption coefficient Quantity used

The more obvious and direct approach would be to develop methods for direct absorption studies of clusters in molecular beams. This would eliminate the need for an action to take place, for example, should the cluster fail to dissociate on the time scale of the experiment. It would also allow for the measurement of the absorption coefficient, a useful quantity for comparison with theory. The challenge here was to overcome the inherent low density of clusters in order to obtain an absorption with reasonable signal to noise. As in the case of conventional absorption spectroscopy, multipassing the laser through the molecular beam was the obvious first step to take. However, two additional technical innovations were necessary before direction absorption studies could be accomplished fast differential optical detection and slit nozzles. The combination of these three methods allowed for direct absorption studies in the mid infrared of van der Waals and hydrogen-bonded... 

The physical meaning of the quantities a(A) and K X) can be stated thus the reciprocal of the Napierian coefficient of absorption a(A) corresponds to the thickness of the medium for which the incident intensity is divided by the base of the Napierian logarithm (i.e., e = 2.718281828...), while the reciprocal of the Bunsen-Roscoe coefficient of absorption K X) corresponds to the thickness of the medium for which the incident intensity is divided by ten. In most practical applications the decadic absorption coefficient is used, but the Napierian absorption coefficient is introduced more naturally in theoretical equations. 

In his treatment, Sherman makes use of emission coefficients t that perform the function of the empirical k in Equation 6-4. Both quantities are proportional to. the product of absorption coefficient, of fluorescence yield and of (1 — 1/r), where r is the absorption-jump ratio involved (4.4). 

For determination of the number of protonic sites and Lewis acid sites on the surface, the integrated absorbances of the bands at 1450 cm-i (due to pyridine chemisorbed on Lewis acid sites, L-Py) and 1490 cm i (due to both the L-Py and pyridine chemisorbed on protonic acid sites, B-Py) were used with the tangent background for all samples. The values obtained were normalized to the weight of the sample wafer. To obtain the apparent absorption coefficients of the bands, a known amount of pyridine was adsorbed on the sample, and the absorbance of each band was measured. Then, a small quantity of water which is sufficient to convert all Lewis acid sites into protonic acid sites was introduced into the IR-... 

When a polymer absorbs very strongly in the visible region, near IR incident radiation is used. In a very coloured solution the scattered intensity is reduced by a factor exp(—e)2) where e is the absorption coefficient of the solvent. Hence i0 must be multiplied by exp(+e ) in order to obtain the true scattered intensity undiminished by absorption effects. For small values of efi, the quantity exp(efi) approximates well to (1 + e2) so that Eq. (42) becomes38. ... 

The International Union of Pure and Applied Chemistry recommends that the definition should now be based on the ratio of the radiant power of incident radiation (Pq) to the radiant power of transmitted radiation (P). Thus, A = log(Po/P) = log T. In solution, Pq would refer to the radiant power of light transmitted through the reference sample. T is referred to as the transmittance. If natural logarithms are used, the quantity, symbolized by P, is referred to as the Napierian absorbance. Thus, B = ln(Po/P). The definition assumes that light reflection and light scattering are negligible. If not, the appropriate term for log(Po/P) is attenuance. See Beer-Lambert Law Absorption Coefficient Absorption Spectroscopy... 

Useful for quantification of anthocyanins, the molar absorption coefficients of several anthocyanins have been reviewed." " However, these compilations reveal lack of uniformity between the reported values, most probably due to the unavailability of pure anthocyanins in sufficient quantities to allow reliable weighing under optimal conditions, and the lack of standardization of anthocyanin solvent used for measurements. 

ABSORPTION COEFFICIENT 1. For the absorption of one substance or phase in another, as in the absorption of a gas in a liquid, the absorption coefficient is the volume of gas dissolved by a specified volume of solvent thus a widely used coefficient is the quantity a in the expression a = Vo/Vp, where Vo is the volume of gas reduced to standard conditions. V is the volume of liquid, and p is the partial pressure of the gas. 

Toraya s WPPD approach is quite similar to the Rietveld method it requires knowledge of the chemical composition of the individual phases (mass absorption coefficients of phases of the sample), and their unit cell parameters from indexing. The benefit of this method is that it does not require the structural model required by the Rietveld method. Furthermore, if the quality of the crystallographic structure is poor and contains disordered pharmaceutical or poorly refined solvent molecules, quantification by the WPPD approach will be unbiased by an inadequate structural model, in contrast to the Rietveld method. If an appropriate internal standard of known quantity is introduced to the sample, the method can be applied to determine the amorphous phase composition as well as the crystalline components.9 The Rietveld method uses structural-based parameters such as atomic coordinates and atomic site occupancies are required for the calculation of the structure factor, in addition to the parameters refined by the WPPD method of Toraya. The additional complexity of the Rietveld method affords a greater amount of information to be extracted from the data set, due to the increased number of refinable parameters. Furthermore, the method is commonly referred to as a standardless method, since the structural model serves the role of a standard crystalline phase. It is generally best to minimize the effect of preferred orientation through sample preparation. In certain instances models of its influence on the powder pattern can be used to improve the refinement.12... 

The ratio /spectrophotometric measurement, and the value of a is then calculated from eq. (3.5) to yield the desired absorption constant. The numerous absorption constants found in the literature arise from the choice of quantities incorporated in the constant b. Some of the terms most commonly used to express absorption in minerals are summarized in table 3.2. Note that optical densities (O.D.), representing the direct output from many spectrophotometers, lack specificity about sample thickness and element concentrations. Absorption coefficients (a) indicate that sample thicknesses have been measured or estimated. Molar extinction coefficients (e) require chemical analytical data as well as knowledge of sample thicknesses. 

Equation (4.41) contains all selection rules for optical transitions and it contains all transitions between pairs of states involving the same photon energy fko. It thereby models a system with broad bands as being made up of a multitude of 2-level systems. The absorption coefficient can in principle be calculated from theoretical models. Here we will use it as an experimentally determined quantity. 

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. 

Although these values are extremely important quantities, there is no established, general method for measuring them on an absolute basis. Experimental difficulty arises because the species of interest is often a transient, and hence the precise values of its desired physical properties, such as (1) the T-T absorption coefficient and (2) the phosphorescence quantum yield for the specified excitation energy and the specified eigenstate, are not available for the desired spectroscopic analysis. However, some limited methods may be used with adequate caution. These methods involve either luminescence measurement or product analysis ... 

A related, useful quantify for characterizing the absorption of light by semiconductors is the optical penetration depth (Figme 5). This quantity is defined as the inverse of the absorption coefficient that is, penetration depth s. From equation (4), it can be seen that the penetration depth is the distance into the semiconductor at which the transmitted light intensity reaches 1/e of the incident light intensity at the smface of the solid. In general, when compared to direct... 

We calculated the specific surfaces shown in Table 1 by an improvement of the procedure described in Reference 7. In our more recent studies of coals, rather than using the mass absorption coefficient of carbon, we have computed the mass absorption coefficient of each coal from the elemental composition given by the ultimate analysis. These mass absorption coefficients, which depend quite strongly on the composition and concentration of minerals in the coals, varied from about 7 to 12 cm /gm. We also have taken the values of the coal densities from Fig. 2 of Reference (17). This plot shows the coal density as a function of fixed carbon content and thus provides more reliable densities than the approximation we used in Reference (7). The quantity I A was calculated from the scattering data for colloidal silica samples by the procedure outlined in Reference 7. The proximate and ultimate analyses of... 

To leant more about Beer s law, use Google to find the lUPAC Glossary of Terms Used in Photochemistry. Find how the molar absorptivity of a compound (e) is related to the absorption cross section (a). Multiply the absorption cross section by Avogadro s number and note the result. How would the result change if absorbance were expressed as A = —In (P/Pq) rather than the usual definition in terms of base-10 logarithms What are the units of a Which of the quantities e or cr is a macroscopic quantity Which is a microscopic quantity Notice that the lUPAC term for molar absorptivity is molar absorption coefficient. Which of these terms is most descriptive Explain and justify your answer. 

The quantities a, c, f, F, r, and p are the thermal diffusivity, sound speed, heat capacity ratio, bulk viscosity coefficient, shear viscosity coefficient, and density of the sample, respectively and Eo, a, P and Cp are the energy fluence of the laser beam, the optical absorption coefficient, the volume expansion coefficient, and the isobaric heat capacity, respectively, of the fluid. Tlie first and second terms in Eq. 2 describe the time dependences of the thermal and acoustic modes of wave motion, respectively. Since the decays of the acoustic and thermal mode densities back to their ambient values take place on such different time scales (microsecond time scale for acoustic mode and millisecond time scale for thermal mode), they were recorded on the oscilloscope using different time bases. 

All these quantities are equivalent since they all depend on the same transition matrix element, although their units are not the same. The / value has the advantage of being a dimensionless quantity. With broad band illumination, the appropriate quantities are those which are integrated over the spectral feature, such as the / value or the Einstein coefficient. With narrow band illumination (i.e. a monochromatic source narrower than the spectral feature), it is appropriate to use a quantity which is defined point by point within the line profile, such as the absorption coefficient, the cross section, or the differential oscillator strength df/dE. 

For calculating the reduced absorption coefficients directly observed in the spectra, the quasi-static approximation [85] was used. From this approximation, the collision-induced absorption spectra are determined by the following three quantities, (1) excitation energies, (2) Boltzmann distribution of the ground state and (3) induced transition moments as the functions of the internuclear distance. 

The relationships between measurable quantities related to absolute transition probability (e.g. absorption cross section, molar absorption or extinction coefficient, radiative lifetime) and the fundamental quantities used to describe and inter-relate the observable quantities axe fraught with difficulties of unit conversions and internally consistent treatments of initial- and final-state degeneracies. Several excellent papers on this subject exist (Hilborn, 1982 and 2002, Larsson, 1983, Tatum, 1967, Schadee, 1978, and Whiting, et al., 1980). Much of Section 6.1.1 is based on or checked against Hilborn (1982 and 2002), although slightly different notation and definitions are used. 

The quantity Bf23Q3 can be written as A and is known as the decadic absorbance, or simply as the absorbance. This is the term recommended in the SI (see Appendix A). However the terms decadic extinction and optical density are still commonly used, and the student should be familiar with them. The quantity h/2.303 (i.e., the absorbance divided by the light path) is called the linear decadic absorption coefficient and usually is given the symbol a. Thus equation (2.9) can be written as... 

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