Photoelectric coefficient

The probability of this interaction occurring is called the photoelectric cross section or photoelectric coefficient. Its calculation is beyond the scope of this book, but it is important to discuss the dependence of this coefficient on parameters such as E., Z, and A. The equation giving the photoelectric coefficient may be written as... 

The second term in brackets indicates correction terms of the first order in Z. Figure 4.17 shows how the photoelectric coefficient changes as a function of E and Z. Fig. 4.17 and Eq. 4.46 show that the photoelectric effect is more important for high-Z material, i.e., more probable in lead (Z = 82) than in A1 (Z = 13). It is also more important for = 10 keV than = 500 keV (for the same material). Using Eq. 4.46, one can obtain an estimate of the photoelectric coefficient of one element in terms of that of another. If one takes the ratio of t for two elements, the result for photons of the same energy is... 

Table 2.1 Scattering and Photoelectric Coefficients for Carbon When Eo = 8046 eV (Cu Kai)...

Uses. Tballium compounds have limited use in industrial appHcations. The use of thaHous sulfate in rodenticides and insecticides has been replaced by other compounds less harmful to animals (see Insect control technology Pesticides). Tb allium sulfide has been used in photoelectric cells (see Photovoltaic cells). A thallium bromide—thallium iodide mixture is used to transmit infrared radiation for signal systems. ThaHous oxide is used in the manufacture of glass (qv) that has a high coefficient of refraction. Tb allium formate—malonate aqueous solutions (Cletici s solution) have been used in mineral separations. Many thallium compounds have been used as reagents in organic synthesis in researchlaboratoti.es. 

Cobalt, sepn. of from nickel, (cm) 532 Codeine and morphine, D. of 740 Coefficient of variation 135 Colloidal state 418 See also Lyophilic, Lyophobic Colorimeters light filters for, 661 photoelectric, 645, 666 Colorimetric analysis 645 criteria for, 672 general remarks on, 645, 672 procedure, 675 solvent selection, 674 titration, 652... 

The values of r and a in Table 4-2 show that photoelectric absorption generally makes the greater contribution to the mass absorption coefficient. Absorption leading to scattering, which will be discussed in the next section, gains in relative importance as atomic number Z and wavelength X decrease. 

Between absorption edges, the photoelectric (true) mass absorption coefficient r can be expressed as the following approximate empirical function of Z and X ... 

Wavelength of Primary Beam, A Exciting Potential, V Scattering Coefficient, a Photoelectric Absorption Coefficient, T cr/r... 

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-... 

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). 

The photoelectric mass absorption coefficients of these polymegs and of poly(methyl methacrylate) PMMA at 8.3 X and 13.3 + A are shown in Table II. These coefficients were calculated using relation (8) and the data listed in Table I. 

Table I. Photoelectric Mass Absorption Coefficients of Halogen Atoms and of Carbon, Oxygen, Hydrogen at 8.34 A (A1 Kali2 emission line) and 13.34 A (Cu Lai. o emission line) (6)...

Table II. Photoelectric Mass Absorption Coefficients of the Halogenated Polymethacrylates and of PMMA...

Far from the Laue condition the absorption shows the normal photoelectric absorption, as would be measured (with allowance for density) in a liquid or gas of the same atomic species. Close to the Laue condition, the absorption is quantified by the imaginary parts of the susceptibilities, leading to imaginary components of the wavevectors. These imaginary components are always normal to the crystal surface and hence the planes of constant attenuation are parallel to the surface. The attenuation coefficient (n) normal to the surface is given by (n)=-4 lm(K o) (4.28)... 

Figure 5 X-ray mass attenuation coefficients for aluminum as a function of photon energy. At low energies, photoelectric absorption predominates. At higher energy, incoherent (Compton) scatter becomes almost the exclusive contributing mode. Eventually, pair production dominates at very high energies (above 10 MeV).

Figure 7 The atomic number dependence of attenuation in different energy domains. This is illustrated by how the mass attenuation coefficient of the predominating mode (photoelectric (PE) at 50 keV, incoherent (Inc) at 500 keVand pair production (PP) at 5 MeV) varies with Z.

Fig. 2-2, Room-temperature absorption coefficients and cross sections of NO by photoelectric detection A = 590-960 A absorption coefficients to base e for 1 atm of gas at 273°K (from Metzger and Cook309 with permission).

The sedimentation equilibrium experiment requires much smaller volumes of solution, about 0.15 ml. With six-hole rotors and multichannel centerpieces (41) it is potentially possible to do fifteen experiments at the same time. For situations where the photoelectric scanner can be used one might (depending on the extinct coefficients) be able to go to much lower concentrations. Dust is no problem since the centrifugal field causes it to go to the cell bottom. For conventional sedimentation equilibrium experiments, the analysis of mixed associations under nonideal conditions may be virtually impossible. Also, sedimentation equilibrium experiments take time, although methods are available to reduce this somewhat (42, 43). For certain situations the combination of optical systems available to the ultracentrifuge may allow for the most precise analysis of a mixed association. The Archibald experiment may suffer some loss in precision since one must extrapolate the data to the cell extremes (rm and r6) to obtain MW(M, which must then be extrapolated to zero time. Nevertheless, all three methods indicate that it is quite possible to study mixed associations. We have indicated some approaches that could be used to overcome problems of nonideality, unequal refractive index increments, and unequal partial specific volumes. 

We should note that the photoelectric effect often leaves an inner shell vacancy in the atom that previously contained the ejected electron. This vacancy will be filled by an atomic transition, called fluorescence, and generally produces an X-ray photon. In an interesting twist of fate, the X-ray photon will have an energy that is just below the sharp rise in the attenuation coefficient due to conservation of momentum and can often escape from the absorber. Recall that the direction of the fluorescence photon will be uncorrelated with the direction of the incident photon and a fraction will be emitted backwards from the absorber. The absorber will thus emit its own characteristic X-rays when it is irradiated with high-energy photons. 

Fio. 3. Sedimentation coefficient and molecular weight as functions of pH. (A) Sedimentation coefficients as a function of pH. (O) s°0 w values were determined for samples adjusted from neutral pH to each pH value. The concentrations were 72 mg/ml, except at pH 5 and pH 4, where they were 4j0 mg/ml in 0.01 Af tris-0.01 Af sodium acetate. (0) s°0 w values were determined for samples adjusted from neutral pH to the given pH. Concentrations were 0.62 mg/ml in 0.1 Af NaCl-0.01 Af tris-0.01 M sodium acetate. ( ) s° w values were determined for samples prepared at pH 2, then dialyzed at the appropriate pH. Concentrations were 0.62 mg/ml in 0.1 M NaCl-0.01 Af tris-0.01 M sodium acetate. (O) Determinations with Schlieren optics all other determinations were made with the use of ultraviolet optics with the photoelectric scanner. (B) Weight average molecular weight as a function of pH. (0) M values were determined for samples adjusted from neutral pH to each pH indicated, by dialysis, 0.62 mg/ml, in 0.1 M NaCl-0.01 M tris-0.01 M sodium acetate. (O) Mw values were determined for samples prepared at pH 2, then dialyzed at the appropriate pH, 0.62 mg/ml in 0.1 M NaCl-0.01 Af tris-0.01 Af sodium acetate. 

According to Evans (1995), differentiation of features within the materials is possible because p at each point directly depends on the electron density of the material in that point (pe), the atomic number (Z) of the chemical components of the materials in that point, and the energy of the incoming X-ray beam (/0). In particular, the linear attenuation coefficient can be approximately considered as the sum of the Compton scatter and photoelectric contributions ... 

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