Absorption coefficient monochromatic

Radiative transfer with respect to the confined gas is either monochromatic or gray. The gray gas absorption coefficient is denoted here by fC(m-1). In subsequent sections the monochromatic absorption coefficient is denoted by KfX). 

The total monochromatic absorption coefficient is given by the sum of the contributions from all four processes ... 

Equation 1-5 was written for a sample containing a single element upon which monochromatic x-rays are incident. In so far as x-ray absorption is an atomic property, the mass absorption coefficients for other samples are additive functions of the weight-fractions of the elements, free or combined, that are present that is,... 

Equation (3.19) gives a first approximation to the temperature structure of an atmosphere in radiative equilibrium, and departures from greyness can also be treated approximately by defining a suitable mean absorption coefficient (see Chapter 5). The emergent monochromatic intensity at an angle 9 to the normal (relevant to some point on the solar disk) is also found by integrating the equation of transfer (3.11) ... 

A variety of alternating copolymers based on H-allyl- and N-(3-ethynylphenyl)maleimides, with substituted styrenes and vinyl ethers, have been prepared and their response to x-ray irradiation studied. Broadband and monochromatic x-ray exposures were conducted at the Stanford Synchrotron Radiation Laboratory. Sensitivities were observed to correlate with mass absorption coefficients of the copolymers and were found to be as high as 5-10 mJ/cm2. Preliminary fine line lithographic studies indicate 0.5 ion resolution capabilities. 

The effect of increased x-ray absorption on sensitivity was explored by conducting monochromatic exposures of a bromine-containing resist, poly(N-allyl maleimide-vinyl benzyl bromide), at photon energies which bracket the bromine absorption edges between 1.6 and 1.8 keV contrast curves obtained for these monochromatic exposures are shown in Figure 7. The results are also plotted as l/D "5 vs absorption coefficient in Figure 8 the data accurately follow the predicted inverse relationship defined by Equation 1. 

Each o-vni is a strong function of monochromatic light energy hv as a threshold hv = Et is approached. This phenomenon will be discussed in the next section. However, for completeness we should relate Eq. (34a) to a common expression involving the absorption coefficient a and electron lifetime x... 

Monochromatic detection. A schematic of a monochromatic absorbance detector is given in Fig. 3.12. It is composed of a mercury or deuterium light source, a monochromator used to isolate a narrow bandwidth (10 nm) or spectral line (i.e. 254 nm for Hg), a flow cell with a volume of a few pi (optical path 0.1 to 1 cm) and a means of optical detection. This system is an example of a selective detector the intensity of absorption depends on the analyte molar absorption coefficient (see Fig. 3.13). It is thus possible to calculate the concentration of the analytes by measuring directly the peak areas without taking into account the specific absorption coefficients. For compounds that do not possess a significant absorption spectrum, it is possible to perform derivatisation of the analytes prior to detection. 

This formula is based on Lambert s hypothesis that the intensity 7 of monochromatic radiation is decreased by d/ (i.e. negative) as it passes through a thickness dx of a material with an absorption coefficient k at the chosen wavelength (Fig. 11.17). Thus,... 

Absorption spectra. The absorption coefficient, a, also called the absorption spectrum if known as a function of frequency v, is obtained from a measurement of transmitted and incident intensities, /(v) and /o(v), of monochromatic light, according to... 

L. M. Trafton. The pressure induced monochromatic translational absorption coefficients for homopolar and nonpolar gases and gas mixtures with particular application to H2. Astrophys. J., 146 558, 1966. 

Apparently monochromatic resonance radiation of mercury which passes through mercury vapor at the saturated pressure at 25 °C is about half absorbed in four millimeters distance. Beer s law is not obeyed at all because the incident radiation cannot be considered to be actually monochromatic, and absorption coefficients of mercury vapor vary many times between zero and very high values in the very short space of one or two hundredths of an Angstrom unit. Moreover, absorption of mercury resonance radiation by mercury vapor is sufficiently great even at room temperature to make radiation imprisonment a very important phenomenon. If the reaction vessel has any dimension greater than a few millimeters the apparent mean life of Hg(63P ) may be several fold the true radiative life of 1.1 x 10"7 sec, reaction (27), because of multiple absorption and re-emission. 

In the simplest case, this system can be solved using the method of multilinear regression [30,31,40], In some cases, it is necessary to experimentally determine p the mass absorption coefficient of the mixture [39,40], To carry out this procedure, a monochromatic CuKa radiation was used, and with the help of the following equation [39,40]... 

Note that Eq. (5-136b) is identical to the expression for the gas emissivity for a column of path length ft. In Eqs. (5-136) the gas absorption coefficient is a function of gas temperature, composition, and wavelength, that is, Kb = Kb(T,X). The net monochromatic radiant flux density at dAi due to irradiation from the gas volume is then given by... 

Condition 4. For most polyatomic molecules monochromatic light is impossible to obtain. Monochromatic light for experiments of this type would be defined as one for which the absorption coefficient is constant. To say the least, the incident radiation will cover much unresolved rotational structure within a single band. The more common case found with high-pressure arcs and color filters will be that two or more vibration transitions within a given electronic transition will be involved. Since the absorption coefficient will never be a true constant, the strongly absorbing parts of the spectrum will be important at low pressures and will decrease in relative importance as the pressure increases. 

Monochromatic line absorption coefficient, (atm-m)" Gas absorption coefficient, m" ... 

To obtain monochromatic Ka, a filter system is necessary to filter out the continuous X-rays and other characteristic X-rays, which are not generated with Ka from the X-ray tube. X-ray filters can be made from material that strongly absorbs X-rays other than Ka. Generally, materials exhibit various abilities to absorb X-rays. X-ray absorption by materials is a function of the linear absorption coefficient (fi) and mass density (p). The X-ray intensity (/) passing through an absorption layer with thickness x is expressed by the following equation. 

The fluorescent radiation emitted by the sample should be as intense as possible, so that it will be accurately measurable in a short counting time. The intensity of this emitted radiation depends on both the wavelength and the intensity of the incident primary radiation from the x-ray tube. Suppose that monochromatic radiation of constant intensity and of wavelength k is incident on an element which has a K absorption edge at k, and that we can continuously vary k. As we decrease k from a value larger than no K fluorescence occurs until k is just shorter than Ajf, The fluorescent intensity is then a maximum. Further decrease in k causes the fluorescent intensity to decrease, in much the same manner as the absorption coefficient. This is natural since, as mentioned in Sec. 1 -5, fluorescence and true absorption are but two aspects of the same phenomenon. At any one value of A, the fluorescent intensity is directly proportional to the incident intensity. 

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