Ratios of Isotopic Abundances

The previous discussion demonstrates that measurement of precise isotope ratios requires a substantial amount of operator experience, particularly with samples that have not been examined previously. A choice of filament metal must be made, the preparation of the sample on the filament surface is important (particularly when activators are used), and the rate of evaporation (and therefore temperature control) may be crucial. Despite these challenges, this method of surface ionization is a useful technique for measuring precise isotope ratios for multiple isotopes. Other chapters in this book discuss practical details and applications. 

Precise measurement of isotope ratios can be obtained by comparing the yields of isotopic ions desorbing from a sample placed on a strongly heated filament that is generally made from platinum, tantalum, rhenium, or tungsten. 

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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. 

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. 

If the ratio of isotopic abundance ratios for the product and initial reactant, a quantity that is usually measured in the laboratory, is designated... 

The ratio factors R in O Eq. (30.35) are ideally unity, but small deviations and their uncertainties must be considered. Rg is the ratio of isotopic abundances for the unknown and standard, R, is the ratio of neutron fluences (including fluence drop off, self-shielding, and scattering), is the ratio of effective cross sections if the shape of neutron spectrum differs from the unknown sample to standard, Re is the ratio of counting efficiencies (differences due to geometry, y-ray self-shielding, and dead-time effects). 

Figure 7.9 shows a schematic representation of this effect, in which the ratio of the two isotopes changes with time. To obtain an accurate estimate of the ratio of ion abundances, it is better if the relative ion yields decrease linearly (Figure 7.9) which can be achieved by adjusting the filament temperature continuously to obtain the desired linear response. An almost constant response for the isotope ratio can be obtained by slow evaporation of the sample, viz., by keeping the filament temperature as low as is consistent with sufficient sensitivity of detection (Figure 7.9). 

Before measurement it must be decided exactly which isotopes are to be compared. For oxygen, it is usually the ratio of 0 to 0, and for hydrogen it is H to H. Such isotope ratios are measured by the mass spectrometer. For example, examination of a sample of a carbonaceous compound provides abundances of ions at two m/z values, one related to C and one to C (it could be at m/z 45 and COj at m/z 44). By convention, the heavier isotope is always compared with the lighter isotope. The ratio of isotopes is given the symbol R (Figure 48.1). 

Many artificial (likely radioactive) isotopes can be created through nuclear reactions. Radioactive isotopes of iodine are used in medicine, while isotopes of plutonium are used in making atomic bombs. In many analytical applications, the ratio of occurrence of the isotopes is important. For example, it may be important to know the exact ratio of the abundances (relative amounts) of the isotopes 1, 2, and 3 in hydrogen. Such knowledge can be obtained through a mass spectrometric measurement of the isotope abundance ratio. 

Atoms of elements are composed of isotopes. The ratio of natural abundance of the isotopes is characteristic of an element and is important in analysis. A mass spectrometer is normally the best general instrument for measuring isotope ratios. 

These isotope masses and their ratio of abundances are characteristic of carbon. Similarly, the isotopes of other elements that occur naturally have fixed ratios of isotopes, as given in Tables 47.1 and 47.2 at the end of the accompanying full text. 

Once again, the ratio of the abundance in a crystal of the two isotopes, wAr/wK, provides a clue to the age of the crystal. Mica is a mineral that has been much studied in this type of min-... 

In radiocarbon dating, the quantity to be measured is the ratio of the abundances of the rare isotope (14C) to that of the stable isotopes (12C, 13C). These abundance ratios are not measured on an absolute basis, but are compared to that of an internationally-accepted standard. (It is likely that a similar standard will be adopted for 10Be dating.) These measurement requirements have several consequences ... 

Also, since ratios of isotopic ratios are commonly used to report isotope effect data (see Equations 7.17 and 7.18 for example), the actual numerical value of the abundance ratio of the standard is not important since it drops out from the final equation expressing the isotope effect ... 

The masses of isotopes can be measured with accuracies better than parts per billion (ppb), e.g., m40Ar = 39.9623831235 0.000000005 u. Unfortunately, determinations of abundance ratios are less accurate, causing errors of several parts per million (ppm) in relative atomic mass. The real limiting factor, however, comes from the variation of isotopic abundances from natural samples, e.g., in case of lead which is the final product of radioactive decay of uranium, the atomic weight varies by 500 ppm depending on the Pb/U ratios in the lead ore. [8]... 

Limiting ourselves to the observation of isotopic abundances determined by the 4n + 2 and 4n + 3 decay series, we can construct a concordia diagram (Wetherill, 1956) relating (206p /238 j 207pj /235 j ratios developing at... 

Figure 5. Intensity ratios of isotopically substituted O4 ions as a function of ionizing electron energy. 1(64) corresponds to O4 ions containing four O atoms and, because the experiments were performed under natural abundance conditions, 1(65) and 1(66) correspond to ions where one O atom is replaced with an O and 0, respectively. The dotted lines indicated the expected ratios based on natural abundance.

Single spiking method is essentially a problem of two-component mixing. The ratio of the abundances of two isotopes A and B of an element in the mixture is (Faure, 1986)... 

The other is the ratio of the abundance of the reference isotope of the parent element to the abundance of the reference isotope of the daughter element ... 

From the measured 63Cu/65Cu isotope ratio the isotope abundances of 63Cu and 65Cu are then calculated in a natural sample as roughly 69.2% and 30.8%, respectively. Small deviations from the IUPAC table value10 could be evidence of fine isotope variation in nature. 

For measurements of isotope ratios or isotope abundances, any of the mass spectrometers discussed in the previous chapters, such as SSMS, LIMS, GDMS56 and LA-ICP-MS,6 are of benefit for the direct isotope analysis of solid samples. SSMS and LIMS are rarely applied in isotope analysis due to their relatively low precision. Several applications of the isotope dilution technique as a calibration strategy in SSMS, mostly on geological samples, are known.57-59 GDMS has been mostly applied in multi-element trace analysis and depth profiling and plays only a minor role... 

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