Isotopes fractional abundance

Element Isotope Fractional abundance 1 %o change International standard... 

Equation 1.21 can be rearranged for this special case, by replacing m /squared matrix element of that transition, being the dipole moment of the molecule. Equation 1.22 can be made more general by adding /v, the fraction of molecules in that vibrational state, and for completeness taking into account the isotopic fractional abundance i of the molecular species. The resulting formula becomes for all practical purposes (ref. 3, p. 117)... 

The mass contributed by each isotope is proportional to its fractional abundance, as given by Equation ... 

Elemental molar mass = (Fractional abundance) (Isotopic molar mass)... 

The molar mass of a naturally occurring mixture of isotopes is the weighted average of the isotopic molar masses. Each isotope contributes to the total in proportion to its percentage (fractional) abundance, and the average is calculated using Equation. ... 

First, the percentages must be converted to fractions by dividing by 100%. Then we multiply these fractional abundances by the Isotopic masses and add the results. A table helps in organizing these manipulations ... 

If no KIE is present, the contribution of the derivative atom to the measured 8 value of the derivatised compound can be calculated using a simple mass balance equation (14.2), where n is number of moles of the isotope of interest, F is the fractional abundance of the isotope of interest, c refers to the compound of interest, d refers to the derivative group and... 

Each of the isotopic masses is multiplied by its fractional abundance. The resulting products are summed to obtain the average atomic mass. 

Huang L, Sturchio NC, Abrajano T, Heraty LJ, Holt BD (1999) Carbon and chlorine isotope fractionation of chlorinated aliphatic hydrocarbons by evaporation. Org Geochem 30(8A) 777-785 Jambon A, Deruelle B, Dreibus G, Pineau F (1995) Chlorine and bromine abundance in MORB the contrasting behavior of the Mid-Atlantic Ridge and East Pacific Rise and implications for chlorine geodynamic cycle. Chem Geol 126 101-117... 

Newton R, Aranovich L (1996) Simple granulite melting in concentrated NaCl-KCl solutions at deep crustal conditions. Geol Soc Am Annu Meet Abstracts with Programs 158 Numata M, Nakamura N, Koshikawa H, Terashima Y (2002) Chlorine isotope fractionation during reductive dechlorination of chlorinated ethenes by anaerobic bacteria. Env Sci Tech 36(20) 4389-4394 Numata M, Nakamura N, Gamo T (2001) Precise measurement of chlorine stable isotopic ratios by thermal ionization mass spectrometry. Geochem J 35(2) 89-100 Owen HR, Schaeffer OA (1995) The isotope abundances of chlorine from various sources. J Am Chem Soc 77 898-899... 

Figure 1. Schematic representation of the calcium mass spectrum in (a) natural materials, (b) a Ca- Ca tracer solution used for separating natural mass dependent isotopic fractionation from mass discrimination caused by thermal ionization, and (c) a typical mixture of natiwal calcium and tocer calcium used for analysis. The tracer solution has roughly equal amounts of Ca and Ca. In (c) the relative isotopic abundances are shown with an expanded scale. Note that in the mixed sample, masses 42 and 48 are predominantly from the tracer solution, and masses 40 and 44 are almost entirely from natural calcium. This situation enables the instrumental fractionation to be gauged from the Ca/ Ca ratio, and the natural fractionation to be gauged from the sample Ca/ Ca ratio.

Skulan J, DePaolo DJ, Owens TL (1997) Biological control of calcium isotopic abundances in the global calcium cycle. Geochim Cosmochim Acta 61 2505-2510 Skulan J, DePaolo DJ (1999) Calcium isotope fractionation between soft and mineralized tissues as a monitor of calcium use in vertebrates. Proc Nat Acad Sci 96 13,709-13,713... 

Ca = 0.000031, and Ca = 0.001824. The high relative abundance of °Ca (a result of its mass number A, which is a multiple of 4 and thus exceptionally stable cf section 11.3) is one of the two main problems encountered in this sort of dating (in Ca-rich samples, the relative enrichment in °Ca resulting from °K decay is low with respect to bulk abundance). The other problem is isotopic fractionation of calcium during petrogenesis (and also during analysis see for this purpose Russell et al., 1978). These two problems prevent extensive application of the K-Ca method, which requires extreme analytical precision. The isochron equation involves normalization to the Ca abundance... 

Radioactive decay is one process that produces variations in isotope abundance. The second cause for differences in isotope abundance is isotope fractionation, caused by small chemical and physical differences between the isotopes of an element. It is exclusively this important process that will be discussed in the following chapters. 

Brand W (2002) Mass spectrometer hardware for analyzing stable isotope ratios. In P de Groot (ed.) Handbook of stable isotope analytical techniques. Elsevier, Amsterdam Brandriss ME, O Neil JR, Edlund MB, Stoermer EF (1998) Oxygen isotope fractionation between diatomaceous silica and water. Geochim Cosmochim Acta 62 1119-1125 Bremner JM, Keeney DR (1966) Determination and isotope ratio analysis of different forms of nitrogen in soils. III. Soil Sci Soc Am Proc 30 577-582 Brenninkmeijer CAM (1993) Measurement of the abundance of CO in the atmosphere and the and 0/ 0 ratio of atmospheric CO with applications in New Zealand and Australia. J Geophys Res 98 10595-10614... 

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