Abundancy of isotopes

The previous discussion has centered on how to obtain as much molecular mass and chemical structure information as possible from a given sample. However, there are many uses of mass spectrometry where precise isotope ratios are needed and total molecular mass information is unimportant. For accurate measurement of isotope ratio, the sample can be vaporized and then directed into a plasma torch. The sample can be a gas or a solution that is vaporized to form an aerosol, or it can be a solid that is vaporized to an aerosol by laser ablation. Whatever method is used to vaporize the sample, it is then swept into the flame of a plasma torch. Operating at temperatures of about 5000 K and containing large numbers of gas ions and electrons, the plasma completely fragments all substances into ionized atoms within a few milliseconds. The ionized atoms are then passed into a mass analyzer for measurement of their atomic mass and abundance of isotopes. Even intractable substances such as glass, ceramics, rock, and bone can be examined directly by this technique. 

This accurate measurement of the ratio of abundances of isotopes is used for geological dating, estimation of the ages of antiquities, testing athletes for the use of banned steroids, examining fine details of chemical reaction pathways, and so on. These uses are discussed in this book under various headings concerned with isotope ratio mass spectrometry (see Chapters 7, 14, 15, 16, 17, 47, and 48). 

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. 

The greater the mass of an individual atom, the greater the molar mass of the substance. However, most elements exist in nature as a mixture of isotopes. We saw in Section B, for instance, that neon exists as three isotopes, each with a different mass. In chemistry, we almost always deal with natural samples of elements, which have the natural abundance of isotopes. So, we need the average molar mass, the molar mass calculated by taking into account the masses of the isotopes and their relative abundances in typical samples ... 

Different isotopes differ in their atomic masses. The intensities of the signals from different isotopic ions allow isotopic abundances to be determined with high accuracy. Mass spectrometry reveals that the isotopic abundances in elemental samples from different sources have slightly different values. Isotopic ratios vary because isotopes with different masses have slightly different properties for example, they move at slightly different speeds. These differences have tiny effects at the level of parts per ten thousand (0.0001). The effects are too small to appear as variations In the elemental molar masses. Nevertheless, high-precision mass spectrometry can measure relative abundances of isotopes to around 1 part in 100,000. 

TABLE 5.6. Calculation of the Abundance of Isotopic Peaks in the Mass Spectrum of Deuterated Acetophenone... 

Table 4.8. Atomic abundance of isotopes of mass m in natural and spike Nd.

A.O. Neir analysed a great number of elements such as Ar, Kr, Xe, K, Rb, Zn, Cd and Hg and determined the relative abundances of isotopes with high degree of accuracy. 

Chemists use an instrument called a mass spectrometer to measure the relative abundance of isotopes. There are different kinds of mass spectrometers, but the basic idea is to measure the mass of a substance by applying a force. The response to this force depends on the object s mass—think of Newton s second law, where acceleration equals force divided by mass. In the case of mass spectroscopy, the substances to be measured are first ionized—they are made into charged particles called ions by stripping electrons. A magnetic field deflects the motion of an ion, and the deflection depends on the ion s mass, most of which is due to the protons and neutrons in the nucleus. The technique separates different isotopes and measures their abundance in a given sample. 

This fundamental equation explains that the velocity of heavier ions (iq of ions with mass m,) is lower than of lighter ions (v2 of ions with mass m2, with m, > m2). Equation (10) is used directly in time resolved measurements, for example in time-of-flight mass spectrometers (ToF-MS). The charged ions of the extracted and accelerated ion beam are separated by their mass-to-charge ratio, m/z, in the mass analyzer. Mass-separated ion beams are subsequently recorded by an ion detection system either as a function of time or simultaneously. Mass spectrometers are utilized for the determination of absolute masses of isotopes, atomic weights, relative abundance of isotopes and for quite different applications in survey, trace, ultratrace and surface analysis as discussed in Chapters 8 and 9. 

In addition, one of the main features of mass spectrometry is, and this is the major advantage in comparison to other atomic and molecular non-mass spectrometric techniques, that it offers the possibility of determining isotope ratios and abundances of isotopes with high precision and accuracy in all types of samples (in solid, liquid and gaseous materials as well). Isotope ratio measurements have applied increasingly for stable isotopes in nature, especially for investigating... 

Measurement of the isotope abundances of a chemical element is based on the fact that the sum of all abundances of isotopes with the same Z is 100 %. For example, copper possesses two stable isotopes with m/z = 63 and 65. If the isotope ratio 63Cu/65Cu has been determined, e.g., by mass spectrometry, then the isotope abundance of 65Cu ( ) can be obtained by ... 

Furthermore, isotope analysis is relevant for determining the atomic weight (Ar(E)) of elements. The Ar(E) is the average of all masses of all naturally occurring stable isotopes (taking into account the abundances of isotopes) of a chemical element (see Appendix I10). By consideration of the masses of isotopes (/ ,) and the known relative abundances of all stable isotopes (Xi) with i = 1 to n of a selected chemical element, the average atomic weight (Ar(E)) of this element can be calculated ... 

Fig. 35. C MAS NMR spectra of methylated zeolite Y ( (Ils-Y) recorded after loading with toluene (natural abundance of ( -isotopes) and thermal treatments at temperatures from 298 (a) to 493 K (e). Asterisks denote spinning sidebands. Reproduced with permission from (263). Copyright 2003 American Chemical Society.

An ion containing a less abundant combination of isotopes, also included under P.I.D., is not classified separately because identification is usually more simple from the more abundant isotopic combination. The mass number and relative abundance of isotopic ions can be calculated from the accompanying table. It might be argued that classification of these could be useful where the more abundant isotopic combination is obscured by another ion of nominally identical mass. This, however, will be an unusual circumstance and can be overcome by careful use of the table or by the use of exact empirical structure determination through high resolution techniques. 

W. Harkins, The constitution and stability of atom nuclei, Philosophical Magazine 42 (1921) 305-339, on 310. See also W. Harkins, Isotopes Their number and classification," Nature 107 (1921) 202-203, which includes what is probably the first diagram of the abundance of isotopes as a function of the atomic number. Like all other physicists at the time, Harkins believed that atomic nuclei consisted of protons and electrons. The number of electrons corresponds to the quantity A-Z, later identified with the neutron number. 

The average relative abundances of isotopes in the Earth s crust, oceans, and atmosphere, commonly expressed as stable isotope ratios, are shown in table 7.5. Small differences in the ratios of a particular element in natural samples can be detected using mass spectrometry, however, it cannot be achieved with high precision and accuracy (Nier, 1947). The solution to this problem, as explained earlier for 14C measurements, is measuring isotope ratios in a sample concurrently with the standard this does allow for adequate precision and accuracy. The equation used to describe this relative difference or del (<5) value is as follows ... 

Table 15.3 Natural Abundances of Isotopes of Some Common Elements...

Table 3.2 Abundance of isotopes for carbon, chlorine, and bromine...

Naturally occurring fluorine consists of 100% of the isotope 19, chlorine consists of about 75% of isotope 35 and about 25% of isotope 37, bromine consists of about equal abundances of isotopes 79 and 81, and iodine consists of 100% of isotope 127. Chemically,... 

The relative abundances of isotopes in a molecule or in a fragment result from their statistical distribution. Let us consider an example in order to explain the calculation of isotopic clusters. What are the relative intensities of the isotopic peaks accompanying the molecular peak of CS2 Sulfur shows up as a mixture of three main isotopes with nominal masses 32, 33 and 34. These three isotopes occupy two possible positions in the CS2 molecule. The total number of possible combinations is 32, that is 9 ... 

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