Approximate Abundance Ratios

Approximate ratios of isotope abundance ratios are important in identifying elements. For example, the naturally occurring Cl, Cl isotopes exist in an abundance ratio of about 3 1, and C, exist in a ratio of about 99 1. 

For marble provenance studies, the most successful technique seems to be the measurement, through mass spectrometry, of the abundance ratios of the stable isotopes of carbon and oxygen (116). However, no single technique appears to provide unequivocal results, especially in cases such as the different Mediterranean sources, and a combination is often necessary to arrive at an approximate place of origin (117). 

The radicals are produced during metamorphism by radiation from radioactive materials in the mineral matter. None of the common radioactive elements (U, Th, K40) has much of its radiation energy in neutron emission, and so we need consider only a-particles and electrons. Typical concentrations of potassium in the mineral matter of coal are known, and from the K40/K39 abundance ratio, one can easily estimate probable levels of K40 concentration. Little is known of the concentrations of U and Th, except that they are lower in shaley materials than in any other kind of rock, but one can assume an approximate level of one part in 107 parts of mineral matter. 

It should be emphasized that solar abundance ratios are used here only as a convenient referenoe point. The LMC is known to have a total heavy element abundance that is approximately two to three times less than solar (van Genderen, van Driel, and Greidanus 1986 Dufour 1984). The abundances of Sc, Sr, and Ba in the LMC are not known because of the difficulty in detecting lines of these elements in objects. They are probably not solar however, unless the history of nucleosynthesis in the Large Cloud is completely different from that in our Galaxy, the relative abundances of the s-process elements with respect to each other and to Fe should not differ greatly from those of the sun. 

Once the cosmic abundance ratios are chosen, one can solve the coupled kinetic equations in a variety of approximations to determine the concentrations of the species in the model as functions of the total gas density. Division of the concentrations by the total gas density utilized in the calculation then yields the relative concentrations or abundances. The simplest approximation is the steady-state treatment, in which the time derivatives of all the concentrations are set equal to zero. In this approximation, the coupled differential equations become coupled algebraic equations and are much easier to solve. This was the approach used by Herbst and Klemperer (1973) and by later investigators such as Mitchell, Ginsburg, and Kuntz (1978). In more recent years, however, improvements in computers and computational methods have permitted modelers to solve the differential equations directly as a function of initial abundances (e.g. atoms). Prasad and Huntress (1980 a, b) pioneered this approach and demonstrated that it takes perhaps 107 yrs for a cloud to reach steady state assuming that the physical conditions of a cloud remain constant. Once steady state is reached, the results for specific molecules are not different from those calculated earlier via the steady-state approximation if the same reaction set is utilized. Both of these approaches typically although not invariably yield calculated abundances at steady-state in order-of-magnitude agreement with observation for the smaller interstellar molecules. 

The primary focus of isotopic studies on human bone has revolved around the distinction between consumption of C3 plant material and plant material Some years ago, it was discovered that the C3 (or Calvin) and the (or Hatch-Slack) photosynthetic pathways generated plant tissue with quite different abundances, an approximately 15 parts per thousand (0/00) difference in the isotopic ratio ( ) This isotopic difference between two types of plants is the main basis for most studies of human diets that have used stable isotopes of carbon as an analytical tool Most plants in temperate areas are of the C3 type, but corn (maize) is a plant and is of special interest to archaeologists because of the apparent dependence of many cultures on maize agriculture ... 

In 1979, Saleh et al. studied the metabolism of B7-515 (P-32) and technical toxaphene in six mammals and chicken. Both were metabolized the least in chicken and the most in monkeys [175] B7-515 (P-32) was readily degraded, and three metabolites were formed. Two of them were B6-923 and B6-913, which were excreted with the feces [175]. Also, the octachlorobornanes B8-806/B8-809 (P-42) were metabolized by all test species, and highest degradation rates were found for monkeys [175]. A second feeding study of primates was conducted by Andrews et al. [202], B8-1413 (P-26), B9-1679 (P-50), B8-2229 (P-44), and B9-1025 (P-62) were identified as the most abundant toxaphene congeners in both blood and adipose tissue [202]. In blood an equilibrium level of approximately 40 ppb was reached after 10 weeks and in adipose tissue levels of ca. 4000 ppb after 15-20 weeks [202]. Different abundance ratios were found for GC/ECD and GC/NICI-MS, and GC/NICI-MS was considered as less suitable for this study [202]. 

Isotopic Composition. Stable carbon isotope analysis recently has been shown to have application as an indicator of wood degradation (32). This method is based on the characteristically low abundance of (approximately 1% of all carbon) relative to in lignins versus polysaccharides (33). Preferential removal of polysaccharide carbon leaves a lignin-rich wood with a lowered overall ratio. Stable carbon isotope analyses are... 

The use of approximate matching between the mass bias solutions and the spiked sample solutions removes the necessity for making dead time corrections provided, that the matching includes both the isotopic ion abundances and their ratios. Arranging for just the isotopic ion abundance ratios to be matched in the mass bias and spiked sample solutions is not sufficient. 

Boron B has two stable isotopes, B and B, which account for approximately 19.82% and 80.18% of the amount, respectively. The isotopic composition of boron is defined as the deviation of the B/ B from the standard, i.e., value 6 B%o. The standard is the isotopic composition of boron in boric acid (SRM NBS 951 with abundance ratio 4.04362). In natural waters, the value 6 B%o varies from -16%o to + 60%o (Kharaka et al., 2003). Such a wide range of boron isotopic composition is caused by the fractionation process during mass exchange between water and rock. 

As already mentioned, in general the most useful nuclei for NMR observation are those for which the spin quantum number I is 112. Some of these are listed in Table 4.1, together with their natural abundances, N, magnetogyric ratios, approximate resonance frequencies in a field in which the proton resonance of a calibrant Si(CH3)4 is at exactly 100 MHz, and relative receptivities. This last quantity is a useful guide to the relative signal strengths obtainable from solutions of different elements at equal concentrations and is proportional to y NI/(I- -1). 

Isotopes of an element are formed by the protons in its nucleus combining with various numbers of neutrons. Most natural isotopes are not radioactive, and the approximate pattern of peaks they give in a mass spectrum can be used to identify the presence of many elements. The ratio of abundances of isotopes for any one element, when measured accurately, can be used for a variety of analytical purposes, such as dating geological samples or gaining insights into chemical reaction mechanisms. 

Routine mass spectrometry can be used to identify many elements from their approximate ratios of isotope abundances. For example, mercury-containing compounds give ions having the seven isotopes in an approximate ratio of 0.2 10.1 17.0 23.1 13.2 29.7 6.8. 

Other important areas of mass spectrometric investigation of isotope ratios need accurate, not approximate values. For example, for some investigations in archaeology, pharmaceuticals, and chemistry, very accurate precise ratios of isotope abundances are needed. 

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