Modern Physics

The Quantum Physics of Atoms, Solids, and Nuclei: Third Edition

Robert L. Sproull, W. Andrew Phillips

• Publisher: Dover Publications
• Year: 2015
• ISBN:
  9780486802268
• Topic: Physical Sciences
• Subtopic: Atomic & Molecular Physics

This introduction to the concepts and methods of quantum mechanics employs the analysis of one-dimensional problems to offer students a quantitative understanding of atomic, molecular, solid-state, and nuclear physics. Applications of these concepts and methods help answer the most intriguing questions of modern physics: What holds matter together? Holds it apart? How does the variety of chemical properties of different elements arise? How do electrons move through solids? Why do nuclei that occur in nature possess only certain combinations of protons and neutrons?
The text presents meaningful problems by topic — supplemented by ample illustrations, applications, and exercises — that address the most intriguing questions of modern physics. Answers to selected problems appear in the appendix. Geared toward science and engineering majors, this volume is also appropriate for independent study by those who have completed a general physics course.

1

ATOMS, NUCLEI, AND PARTICLES

1-1 INTRODUCTION

An analytical introduction to much of the basic physics developed in the twentieth century is presented in this book. The new physics has been of great intrinsic interest, almost a new science in itself, and in addition has provided applications in engineering that are already considerable and are expanding rapidly. The study of modern physics has led to new devices and energy sources, to more convenient and accurate instruments, to new materials of construction, and to a clearer understanding of existing materials.

This book is primarily concerned with physical laws and processes, but applications in other sciences and in engineering will be described frequently. Television camera tubes, transistors, nuclear reactors, and other devices will be analyzed as part of the application of the basic physics; but most of the applications will be found in other science and engineering courses and in engineering practice.

The atom can be said to mark the boundary between nineteenth and twentieth century physics. Although the idea that matter is composed of atoms was popular in the nineteenth century, it was only at the end of the century that consistent measurements of atomic size became available, and the atomic theory placed on a sound quantitative footing. Since 1900 physics has been increasingly concerned with the internal structure of atoms, and such studies have provided an important element in the development of twentieth century physics. In this first chapter we parallel the historical development by describing a number of experiments that have been used to investigate atomic structure in more and more detail, and in so doing we introduce many important concepts and theories, useful later in the book. At various places in this chapter, as indeed in the first few chapters, it will frequently be necessary to assert some properties of particles and to assume the existence of sources and detectors. These assertions and assumptions will be justified only much later in the book. However, in the later chapters we attempt a uniformly analytical approach; that is, we make assertions or conclusions only by logical arguments based on experiments or on theories well tested by experiment.

This chapter opens with an account of a modern experiment that effectively allows one to see atoms and gives estimates of atomic sizes and binding energies. The properties of two subatomic particles, the electron and the proton, are described in Sec. 1-3, and this is followed by an account of the first investigation of the structure of the atom. The conclusion of this investigation is that the atom consists of a tiny, positively charged core, the nucleus, surrounded by one or more electrons. Although most of our discussion of the nucleus is left to Chapters 11 and 12, Sec. 1-6 gives some idea of the sizes and binding energies of nuclei. However, to provide a background to nuclear physics, the variation of mass with velocity and the famous Einstein E = Mc² relation are presented in Sec. 1-5. Finally, a section is devoted to particle physics, where we try to give an idea of the properties of highly energetic particles.

As the chapter progresses, we look at the atom (or nucleus) on a finer and finer spatial scale and in general at effects that occur at higher and higher energies. These spatial and energy scales bring us to the most important conclusion of this chapter, that the problem of the interactions among particles can be divided into two separate problems: (1) The binding together of protons and neutrons into the nucleus at the center of the atom; (2) the motions of the electrons around the nucleus. This division can be achieved because (1) the energies of interaction between protons and neutrons in a nucleus are very much greater, by a factor of between 10² and 10⁶, than the energies of interaction between electrons and nuclei; (2) a nucleus is much smaller than an atom. Therefore the size and energy scales of atomic experiments are such that the nuclei remain unchanged; we can consider the nucleus as a heavy particle and can ignore its size and internal structure. Nuclear experiments, on the other hand, involve such large energies and small distances that the presence of electrons surrounding the nucleus are of little consequence. Therefore we can deal separately with atomic physics (Chapters 3 to 6) and nuclear physics (Chapters 11 and 12). Furthermore, we shall see in Sec. 1-7 that the whole field of particle physics can be considered almost independently of the question of the structure of the nucleus.

1-2 THE ATOM

The idea that matter is composed of atoms is so basic to modern physics that it is difficult to realize that it was only at the turn of the century that scientists were finally convinced of the truth of the atomic theory. Philosophically, the idea is of long standing, but scientists were persuaded of the truth of the theory only when consistent measurements of atomic size became available. Perhaps the most important of these measurements was provided by X-ray diffraction experiments; these will be described in Sec. 3-5. A more recent technique, known as field-ion microscopy, is described in this section and comes as close as we can get to an actual picture of an atom.

In the field ion microscope a very fine needle of tungsten, niobium, or some other refractory metal is placed at the center of an evacuated chamber (as shown in Fig. 1-1a). A large potential difference is established between the needle, which is positive, and a negative or ground electrode close to the outer wall. The glass surface of the chamber is coated with a phosphor so that a flash of light is produced when it is struck by energetic particles (just as a television tube produces a flash of light when the screen is struck by electrons). Typically, the radius of curvature of the needle is approximately 100 nm, so that a voltage of 5000 V applied between needle and screen gives an electric field at the tip of the needle of 5 × 10¹⁰ Vm^–1 (Problem 1-1). When a small amount of helium gas is let into the chamber, a pattern of spots appears on the phosphor, as shown in Fig. 1-2.

Even without any detailed explanation, this picture gives strong evidence that matter is not continuous but discrete on a scale of approximately 10^–10 m. This scale can be evaluated by combining a measurement of the s...