Total absorption coefficient

Etherington, 1958 gives the total attenuation coefficient in air p, = 0.0804 cmVgm, and the energy absorption coefficient = 0.0311 cmVgm for tissue. 

The alternating component of the applied voltage causes a continuous variation in the efficiency of the x-ray excitation (Step II) during each cycle of operation. A polychromatic x-ray beam has a different total absorption coefficient and a different ratio of photoelectric to scattering absorption coefficient for each wavelength (Step V). It is very difficult to take account of these factors exactly. Fortunately, reasonable estimates will suffice in the making of the calculations for Table 4-4 and Figure 4-15. The efficiency has been taken as that for the root-mean-... 

Fenton. The maximum performance is usually observed at pH slightly below 3 because of two reasons (i) colloids that begin to precipitate at pH above 3 via the binuclear species (Q 2,2) are suppressed and (ii) the concentration of Fe(OH) ( i) is close to its maximum. Fe(OH ) species possess a high absorption coefficient under irradiation and maximize the oxidation yield. This holds for diluted systems. When the total Fe concentration is increased, the binuclear species become dominant and precipitation is favored. Figure 6.3b clarifies this aspect by showing the Fe2(OH)2 + concentration profiles for increasing Fe concentrations. In those cases, lowering the pH to about 2 is favorable. 

Another problem is that the anthocyanin mixtures may be very complicated and not all absorptivity coefficients may be known. Even when they are known, it is necessary to first evaluate whether the objective is the estimation of total anthocyanin content or the determination of individual pigments, and then to decide which absorption coefficient(s) to use. The absorptivity is dependent on both the chemical structure of the pigment and also on the solvent used, and preferably the coefficient used should be one obtained in the same solvent system as the one used in the experiment. If the identity of the pigment is unknown, it has been suggested that it could be expressed as cyanidin-3-glucoside since that is the most abundant anthocyanin in nature. 

If we express the effective thickness t for the resonant absorption in terms of the total absorber thickness t in g cm, a nuclear absorption coefficient can be defined in cm g such that = t. The signal amplitude is then given by ... 

Absorption Coefficient—Fractional absorption of the energy of an unscattered beam of x- or gamma-radiation per unit thickness (linear absorption coefficient), per unit mass (mass absorption coefficient), or per atom (atomic absorption coefficient) of absorber, due to transfer of energy to the absorber. The total absorption coefficient is the sum of individual energy absorption processes (see Compton Effect, Photoelectric Effect, and Pair Production). 

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 ... 

Here p E) is the total absorption coefficient at energy E and /jl0 is the smooth atomlike absorption coefficient. In order to be able to extract structural information from the EXAFS, we need to go from the energy to the wave vector form using the formulation ... 

If total internal reflection does occur at point C, the amount of absorption could be doubled. Too long a path within the particle, or a very high absorption coefficient, could mean that all the light is absorbed and the colouring power of the particle will thus be lost. This demonstrates one reason why the mean particle size of the coloured pigment must be arranged to minimise this possibility. 

Spin selection rule An electronic transition takes place with no change in the total electron spin - that is, AS = 0 - hence singlet <- triplet transitions are forbidden or very weakly allowed. For example, the S0 —> Ti transition in anthracene has a molar absorption coefficient, emax, some 108 times less than that corresponding to the S0 —> Si transition. 

The molar absorption coefficient of the coloured product can be used in the quantitation of individual amino acids but this value varies from one amino acid to another and must be determined under the conditions of the assay. An accepted value, however, must be used in the quantitation of the total amino acids in a mixture when absorbance readings are normally taken at 570 nm. 

Here, L total is the depth of the etched hole per pulse and is assumed to be the sum of photochemical and photothermal contributions, Tphoto and Thermal, respectively 0Ceff is the effective photon absorption coefficient of the medium and can vary with laser emission characteristics, e g., photon density Fis the incident laser fluence Fth is the medium s threshold fluence A and F are the effective frequency factor with units of pm/pulse and the effective activation energy with units of J/cm2, respectively, for the zeroth-order thermal rate constant F0, comparable in magnitude to Fth, is important only at low fluences.64 Equation (5) is obtained after assuming that the polymer temperature T in the laser-exposed region of mass mp and the thermal rate constant k are given, respectively, as... 

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. 

The total loss, or absorption, caused by both viscosity and thermal conductivity is called the classical absorption coefficient a j, and is given by Eq. 2.15c. 

For the measurement of small absorption coefficients or refractive indices, it is often advantageous to place the probe inside the laser cavity ). The sensitivity is then increased by a factor which depends on the quality of the Q factor of the cavity and which can be very large (about 100 or more), since quite small changes in total absorption may cause large changes in laser intensity, especially if the laser is operated close above threshold. 

X-Ray Absorption Data. The x-ray absorption data shown in Figure 2 were obtained using a computer program based on the mass absorption coefficients, y, total energy, as found in the paper of Storm and Israel (1 ) and using the fundamental absorption equation for x-rays (II). 

To test the applicability of statistical techniques for determination of the species contributions to the scattering coefficient, a one-year study was conducted in 1979 at China Lake, California. Filter samples of aerosol particles smaller than 2 ym aerodynamic diameter were analyzed for total fine mass, major chemical species, and the time average particle absorption coefficient, bg. At the same time and location, bgp was measured with a sensitive nephelometer. A total of 61 samples were analyzed. Multiple regression analysis was applied to the average particle scattering coefficient and mass concentrations for each filter sample to estimate aj and each species contribution to light scattering, bgn-j. Supplementary measurements of the chemical-size distribution were used for theoretical estimates of each b pj as a test of the effectiveness of the statistical approach. 

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