Absorption and Scattering of Radiation

Radiotracer techniques have proved to be indispensable with respect to the examination of the individual steps of an analytical procedure, in particular with the aim of revealing the sources of systematic errors. Actually, tracer techniques have contributed essentially to the development of the present state of trace element analysis. 

The most significant sources of error in trace element analysis are contamination or losses by adsorption or volatilization. The key property of radiotracers with respect to the investigation of the accuracy of analytical techniques is the emission of easily detectable radiation in any stage of an analytical procedure with extraordinarily high sensitivity. 

Mechanisms and yields of analytical procedures such as precipitation or coprecipitation that are essential for their apphcation can be elucidated. Furthermore, general analytical data can be obtained by apphcation of tracer techniques, for example distribution coefficients, stability constants and solubilities. 

Backscattering of radiation can be taken as the basis for surface analysis. It is due to electron-electron interaction, which is nearly independent of the atomic number Z of the material, and to scattering by atomic nuclei, which increases with Z. Both effects overlap, and the saturation value of backscattering increases approximately with fZ. Because the backscattered radiation originates from the layers near the surface, surface analysis is possible. An example is the determination of heavy elements in a solid or liquid matrix of light elements by use of the fi radiation of Sr. 

Backscattering of y rays and X rays depends on the mass per unit area and the effective average atomic number Z. The saturation value of backscattering decreases approximately with this number. For example, the composition of ores can be determined by this method. Elastic scattering of y radiation ((y,/) process) can also be applied for analytical purposes. High selectivity is obtained by resonance absorption, i.e. by application of a radionuclide that decays into a stable ground state of the element to be determined. The y rays emitted by the (y,/) process are measured. 

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The absorption and scattering of radiation may be described with Beer s law [Eq. (8-48)], which we repeat here for convenience... 

The optical properties of metal nanoparticles have traditionally relied on Mie theory, a pm-ely classical electromagnetic scattering theory for particles with known dielectrics [172]. For particles whose size is comparable to or larger than the wavelength of the incident radiation, this calculation is rather cumbersome. However, if the scatterers are smaller than 10% of the wavelength, as in nearly all nanocrystals, the lowest-order term of Mie theory is sufficient to describe the absorption and scattering of radiation. In this limit, the absorption is determined solely by the frequency-dependent dielectric function of the metal particles and the dielectric of the baekgrotmd matrix in which they are... 

The usual Lambert-Beer Law that is the basis of solution spectrometry is not valid for densitometry because both absorption and scattering of radiation occur during direct zone measurement on a layer. The Kubelka-Munk equation is usually used to relate signal intensity and zone concentration (weight per zone) for the reflectance (absorption) mode of densitometry ... 

The use of radionuclide techniques in analytical chemistry was first reported in 1913 by G. Hevesy and F. Paneth in a study of the solubility of lead sulfide in water, using the natural lead isotope " Pb as indicator [67], Isotope dilution analysis was introduced by O. Hahn in 1923 [68J, using Pa to determine the yield of Pa. The development of radioreagent methods followed, and further development of radioanalytical chemistry has established a range of analytical methods and techniques ll]-[4], [61], [65], [87], [93], [95], [97]. These include the use of artificial radionuclides and labeled compounds, the principles of nuclear activation [4]-[10], [66] (- Activation Analysis), and absorption and scattering of radiation [11], [12]. The most important procedures are shown in Table 1. 

Transmissivity—The fraction of radiant energy that is transmitted from the radiating object through the atmosphere to a target. The transmissivity is reduced due to absorption and scattering of energy by the atmosphere itself. 

The major contributors to radiation are soot, carbon dioxide, water vapor, inorganic particulates and other intermediate products whose concentrations depend upon the particular fuel. The presence of solid particles such as ash and carbonaceous material affects the radiation heat transport as they are continuous emitters, absorbers, and scatterers of radiation. Carbonaceous particles tend to be large relative to the wavelength of radiation and have surfaces with high absorptivity. 

Analytical applications have been found for all parts of the electromagnetic spectrum ranging from microwaves through visible radiation to gamma (y) rays (Table 1). The emission and absorption of electromagnetic radiation are specific to atomic and molecular processes and provide the basis for sensitive and rapid methods of analysis. There are two general analytical approaches. In one, the sample is the source of the radiation in the other, there is an external source and the absorption or scattering of radiation by the sample is measured. Emission from the sample may be spontaneous, as in radioactive decay, or stimulated by thermal or other means, as in flame photometry and fluorimetry. Both approaches can be used to provide qualitative and quantitative information about the atoms present in, or the molecular structure of, the sample. 

Two effects could, in principle, serve to invalidate this assumption. Highly unlikely in the troposphere is that sufficient heat would be generated by chemical reactions to influence the temperature. Absorption, reflection, and scattering of radiation by trace gases and particles could result in alterations of the fluid behavior. 

A photocatalytic reactor and reactor model that permits the precise evaluation of radiation absorption and scattering. The radiation field is analyzed in terms of a ID one-directional radiative transfer model. With this approach, the LVRPA at every point inside the reactor can be known. The same reactor has been used here. 

Drolen BL, Tien CL Absorption and scattering of a omerated soot particulate, J Quant Spectrosc Radiat Twk 37(5) 433—448, 1987. 

Conventional methods used to measure total activity in liquid samples are seldom adequate for any useful purpose and the data obtained are usually impossible to interpret. Evaporation of the sample in preparation for counting can result in losses of volatile nuclides such as C, Ru, and I. Large uncertainties are usually introduced due to absorption and scattering of the beta particles in the deposited salts on the planchet. Low energy radiation, emitted by such common nuclides as C, Fe, Ca, and Cr, is not normally detected by these methods. 

Choi, M. K., Liebman, L. A., Brock, J. R., Finite Element Solution of the Maxwell Equations for a Absorption and Scattering of Electromagnetic Radiation by a Coated Dielectric Particle, Chem. Eng. Comm., 1996, 151, 5-17. 

Colorimetry, in which a sample absorbs visible light, is one example of a spectroscopic method of analysis. At the end of the nineteenth century, spectroscopy was limited to the absorption, emission, and scattering of visible, ultraviolet, and infrared electromagnetic radiation. During the twentieth century, spectroscopy has been extended to include other forms of electromagnetic radiation (photon spectroscopy), such as X-rays, microwaves, and radio waves, as well as energetic particles (particle spectroscopy), such as electrons and ions. ... 

Attenuation of radiation as it passes through the sample leads to a transmittance of less than 1. As described, equation 10.1 does not distinguish between the different ways in which the attenuation of radiation occurs. Besides absorption by the analyte, several additional phenomena contribute to the net attenuation of radiation, including reflection and absorption by the sample container, absorption by components of the sample matrix other than the analyte, and the scattering of radiation. To compensate for this loss of the electromagnetic radiation s power, we use a method blank (Figure 10.20b). The radiation s power exiting from the method blank is taken to be Pq. 

Chemistry students are familiar with spectrophotometry, the qualitative and quantitative uses of which are widespread in contemporary chemistry. The various features of absorption spectra are due to the absorption of radiation to promote a particle from one quantized energy state to another. The scattering phenomena we discuss in this chapter are of totally different origin classical not quantum physics. However, because of the relatively greater familiarity of absorption spectra, a comparison between absorption and scattering is an appropriate place to begin our discussion. 

Attenuation—A process by which a beam from a source of radiation is reduced in intensity by absorption and scattering when passing through some material. 

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