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This chapter explores applications drawn from Dirac theory of the electron. In the treatment of electrons, it uses the following: an electron has spin 1/2; its magnetic dipole moment is very nearly twice that of the orbital model in which charge and mass move together; and the spin-orbit interaction is a factor of two off the value arrived at by the heuristic argument in the Chapter 7. The factor of two in the last effect is recovered if one does the Lorentz transformations in a more careful (and correct) way, but it is easier to get it from the relativistic Dirac equation. This equation applied to an electron also says the particle has spin 1/2, as observed, and it says the gyromagnetic ratio in equation (23.11) is g = 2. The small difference from the observed value is accounted for by the quantum treatment of the electromagnetic field.

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful experimental methods available for atomic and molecular level structure elucidation. It is a powerful technique in that it is a noninvasive probe that can be used to identify individual compounds, aid in determining structures of large macromolecules, such as proteins, and examine the kinetics of certain reactions. NMR spectroscopy takes advantage of the magnetic properties of the observed nucleus that are influenced not only by its chemical environment, but also by physical interactions with its environment. Both can be examined by measuring specific NMR parameters such as coupling constants, relaxation times, or changes in chemical shifts. As NMR techniques and instrumentation advance, NMR spectroscopy is becoming more important in the environmental sciences, tackling problems and questions that previously were difficult to answer. For example, sensitivity enhancement techniques increase the ability to examine a sample without chemical or physical pretreatment. A sample examined in this manner is in its original state and is unaffected by chemical or physical reactions caused by the pretreatment procedure. Despite its increasing popularity and numerous advantages, NMR spectroscopy can be a mysterious, and at times daunting, technique. The purpose of this chapter is to provide an overview of basic NMR theory and background for the uninitiated. It is hoped that it will provide enough information to those unfamiliar with NMR and its terminology for them to find the remaining chapters understandable and interesting. Those who desire a greater understanding are referred to the many textbooks on solution-state NMR, solid-state NMR, and the application of NMR to geochemistry, soil chemistry, oils and coals, and carbonaceous solids. The advance that led to NMR spectroscopy came in 1939 with resonance experiments by Rabi and coworkers, who demonstrated the property of nuclear spin. In 1945, the research groups of Bloch and Purcell independently obtained the first nuclear resonance signals. For this they won the 1952 Nobel prize. The first application of NMR spectroscopy in the field of humic substance research was 1H NMR of liquids. González-Vila et al. were the first to apply 13C solution-state NMR to natural humic acids.

Advances in NMR instrumentation and availability have led to increased application to mineral systems and to environmental problems. The sensitivity of high-field NMR systems is nearly sufficient to work at real environmental concentrations. Even with limited sensitivity, the amount of chemical information obtained through NMR spectroscopy makes it a very valuable technique in many model systems. The application of NMR spectroscopy in mineral systems has been primarily limited to studies of the structural metals aluminum and silicon. However, in recent years there have been several publications on mobile cations in minerals, including work on the exchangeable cations in clays. Our interests lie in understanding the sorption of cations in clays, the structural sites available for that sorption, and the role of water in cation–clay interactions. Our goal is to eventually understand the molecular interactions that determine the adsorption and diffusion of cations in clays and, thus, the role of clays in determining cation transport through the geosphere. This fundamental understanding has applications in the fate of heavy metals, radionuclides, and even the mobility of nutrients for plants. It is well known that there are very strong interactions between metals and humic materials and these are also strong contributors to cation mobility. However, for simplicity, we have chosen to focus on the interactions of mobile metal ions with well-characterized clays. An NMR-based approach to this problem can take two complementary directions: first, studies of the structural components of clays such as 29Si and 27Al NMR as a function of cation or hydration; second, NMR studies of probe molecules—which in this case are the cations themselves. High magnetic field, multinuclear NMR spectrometers make it quite possible to study various “uncommon” nuclei with relative ease. It is our experience that using the cations as probe nuclei for studying sorption phenomena yields more information than studies of structural nuclei. This chapter is basically a report of work in progress on several systems that are starting to yield interesting results, which it is hoped will lead to a general understanding of these complex systems.

This chapter explains in simple terms the background physics of imaging using standard X-rays, computed axial tomography (CT), nuclear medicine (including positron emission tomography-PET), and magnetic resonance imaging (MRI). It covers the basics of ionising radiation, and also discusses lasers, which are a form of non-ionising radiation (imaging using ultrasound is covered in Chapter 10). X-rays, CT, aspects of nuclear medicine, and lasers are covered briefly. MRI is examined in more detail as this is a newer modality that is often difficult to comprehend, and in any case often involves the presence of the anaesthetist. Some isotopes are naturally occurring but many of the radioactive nuclides used in medicine are produced artificially by a nuclear reactor or cyclotron. Each of these will provide isotopes that are useful for different purposes. Unstable radioactive nuclides achieve stability by radioactive decay, during which they can lose energy. This occurs in a number of ways. For example, atoms can lose energy by ejection of an alpha particle (an extremely tightly bound basic atomic structure of 2 protons and 2 neutrons, which is equivalent to a helium nucleus). This occurs if they have too many nucleons (protons or neutrons) and results in the atomic number being reduced by two and the atomic mass by 4. Other ways that unstable radionuclides decay include: emission of an electron (β−) from the nucleus if the atoms have an excess of neutrons, or by, either emitting a positron (β+) or capturing an electron if they are neutron deficient. Normally isotopes produced by a reactor will be neutron rich and decay by emitting an electron and the cyclotron will tend to produce isotopes that are proton rich and the decay will then be by emitting a positron. This is illustrated in Table 29.1. The new nuclide formed by the decay process (the daughter nuclide) may be left in an excited nuclear state and can release this excess energy by emission of gamma (γ) radiation as shown in Figure 29.1. This example is where the electron (β−) has been emitted. The situation is more complex when a positron has been emitted.