Chapter 1
Atoms and Nuclei: Their Physics and Origins

1.1 INTRODUCTION

Isotope geochemistry has grown over the last 60 years to become one of the most important fields in the earth sciences. It has two broad subdivisions, namely, radiogenic isotope geochemistry and stable isotope geochemistry. These subdivisions reflect the two primary reasons why the relative abundances of isotopes of elements vary in nature, which are radioactive decay and chemical fractionation; in this context, "fractionation" is any process in which the isotopes of the same element behave differently. One might recognize a third subdivision, i.e., cosmogenic isotope geochemistry, where interactions with high-energy cosmic rays produce nuclear changes.

The growth in the importance of isotope geochemistry reflects its remarkable success in attacking fundamental problems of earth science, as well as problems in astrophysics, physics, and biology (including medicine). Isotope geochemistry has played an important role in transforming geology from a qualitative, observational science into a modern quantitative one. To appreciate the point, consider the Ice Ages, a phenomenon that has fascinated the geologist and the layman alike for more than 150 years. The idea that much of the Northern Hemisphere was once covered by glaciers was first advanced by Swiss zoologist Louis Agassiz in 1837. His theory was based on observations of geomorphology and modern glaciers in the Alps. Over the next 100 years, this theory advanced very little, other than the discovery that there had been more than one ice advance and that it was a global phenomenon. No one knew exactly when these ice advances had occurred, how long they lasted, or why they occurred. Stable and radiogenic isotopic studies in the last 60 years have determined the exact times of these ice ages and the exact extent of temperature change (i.e., about 3°C or so in temperate latitudes, and more at the poles). Knowing the timing of these glaciations has allowed us to conclude that variations in the Earth's orbital parameters (the Milankovitch parameters) and resulting changes in insolation have been the pacemaker of these ice ages. Comparing isotopically determined temperatures with carbon dioxide (CO2) concentrations in bubbles in carefully dated ice cores leads to the conclusion that changes in atmospheric CO2 concentration in response to these changes in insolation were the immediate cause of these climate swings. Careful uranium-thorium (U-Th) dating of corals has also revealed the detailed timing of the melting of the ice sheet and the consequent rise in sea level. Comparing this with stable isotope geothermometry shows that melting lagged warming (not too surprisingly). Other isotopic studies revealed changes in the ocean circulation system as the last ice age ended. In turn, changes in ocean circulation were likely the principal driver of changes in atmospheric CO2. Forty years ago, all this seemed very interesting, but not very "relevant." Today, it provides us with critical insights into how the planet's climate system works. With the current concern over potential global warming and greenhouse gases, this information seems extremely "relevant."

Some isotope geochemistry even seeps into public consciousness through its application to archeology and forensics. For example, a National Geographic television documentary described how carbon-14 dating of 54 beheaded skeletons in a mass grave in Dorset, England revealed these skeletons were from the tenth century and how strontium and oxygen isotope ratios revealed they were those of Vikings executed by Anglo-Saxons and not vice versa, as originally suspected. And the story of how isotopic analysis of the remains of English King Richard III, which were found under a parking lot in Leicester, revealed details of his life was widely reported in newspapers. Forensic isotopic analysis gets occasional mention both in shows, such as CSI: Crime Scene Investigation, and in newspaper reporting of real crime investigations.

Other examples of the impact of isotope geochemistry would include diverse topics, such as ore genesis, mantle dynamics, hydrology and hydrocarbon migration, monitors of the cosmic ray flux, crustal evolution, the origin of life, plate tectonics, volcanology, oceanic circulation, atmospheric evolution, environmental protection and monitoring, and paleontology. Indeed, there are few, if any, areas of geological inquiry where isotopic studies have not had a significant impact.

One of the first applications of isotope geochemistry remains one of the most important, namely geochronology, the determination of the timing of events in the history of the Earth and the Solar System. The first "date" was obtained in 1907 by Bertram Boltwood, a Yale University chemist, who determined the age of uranium ore samples by measuring the amount of the radiogenic daughter of U, namely, lead (Pb), present. Other early applications include determining the natural abundance of isotopes carried out by Alfred Nier in the first half of the twentieth century, providing key constraints on models of the nucleus and the origin of the elements (nucleosynthesis). Work on the latter problem still proceeds. The origins of stable isotope geochemistry date to the work of Harold Urey and his colleagues in the late 1940s. Paleothermometry was one of the first applications of stable isotope geochemistry as it was Urey who recognized the potential of stable isotope geochemistry to solving the riddle of the Ice Ages.

This book touches on many, though not all, of these applications. Chapter 1 begins with a brief consideration of the physics of the nucleus and then that of the process that created the elements, called nucleosynthesis. Chapters 2 through 4 explore geochronology, and the myriad ways in which isotopes can be used as clocks. We will then introduce the fundamental principles underlying stable isotope geochemistry. With a basic understanding of both stable geochemistry and radiogenic geochemistry, we can then explore how they are used to understand the origin of the Solar System and the Earth. The following three chapters (i.e., Chapters 7-9) explore the isotope geochemistry of the mantle and crust, with radiogenic isotope geochemistry in Chapters 7 and 8 and stable isotope geochemistry in Chapter 9. Chapters 10 and 11 focus on the stable isotope geochemistry of the interactions occurring in the oceans, atmosphere, and land surface, called the "exogene." Chapter 13 elaborates the use of isotopes in the history of the life and archeology. Finally, Chapter 14 explores the isotope geochemistry of those elements at the first right of the periodic table, the noble gases, whose isotopic variations are due to both nuclear and chemical processes and provide special insights into the origins and behavior of the Earth.

1.2 PHYSICS OF THE NUCLEUS

1.2.1 Early development of atomic and nuclear theory

John Dalton, an English schoolteacher, first proposed in 1806 that all matter consists of atoms. In 1815, William Prout found that atomic weights were integral multiples of the mass of hydrogen (H). This observation was strong support for the atomic theory, though it was subsequently shown to be only approximate. Joseph John Thomson of the Cavendish Laboratory in Cambridge developed the first mass spectrograph and in 1912, his analysis of neon1 showed why: those elements not having integer weights had several isotopes, each of which had mass that was an integral multiple of the mass of H. In the meantime, Ernest Rutherford, who was also from the Cavendish Laboratory, had made another important observation: that atoms consisted mostly of empty space. This led to Niels Bohr's model of the atom proposed in 1910; the model held that the atoms consisted of a nucleus, which contained most of the mass, and electrons in orbit about it.

In 1913, Frederick Soddy, then at the University of Glasgow, formulated the concept of isotopes: that certain elements exist in two or more forms, which have different atomic weights but are indistinguishable chemically. It was nevertheless unclear why some atoms had different atomic weights than other atoms of the same element. The answer to this question finally provided in 1932 by James Chadwick, who had been a student of Rutherford, was "the neutron". Chadwick won the 1935 Nobel Prize in physics for his discovery, although Walther Bothe and Herbert Becker from Germany had earlier discovered the particle but mistook it for gamma radiation. Various other experiments showed the neutron could be emitted and absorbed by nuclei; hence, it became clear that differing numbers of neutrons caused some atoms of an element to be heavier than others. This bit of history leads to our first basic observation about the nucleus that it consists of protons and neutrons.

1.2.2 Some definitions and units

Before we consider the nucleus in more detail, let us set out some definitions - N: the number of neutrons; Z: the number of protons (same as atomic number since the number of protons dictates the chemical properties of the atom); A: mass number (N + Z); M: atomic mass; and I: neutron excess number (I = N - Z). Isotopes have the same number of protons but different number of neutrons; isobars have the same mass number (N + Z); and isotones have the same number of neutrons...