The whole realm of phenomena at the atomic or subatomic level is the special province of quantum theory. When isolated from radiation and other atoms, most atoms remain stable indefinitely: they neither collapse nor explode. When atoms are excited electrically or by collisions or otherwise, they emit radiation of discrete wavelengths characteristic of the kind of atoms excited. The simplest model of the atom is a hard, tiny, electrically neutral sphere—just the smallest possible fragment of the bulk material that possesses the identity of a given chemical element. Neils Bohr's theory was built primarily on the photon concept of radiation, which was understood as an hypothesis but was not yet unambiguously verified when Bohr did his early work. Bohr's first solution of the hydrogen-atom problem in his historic 1913 paper depended on a rather arbitrary combination of classical and quantum ideas.
The whole realm of phenomena at the atomic or subatomic level is the special province of quantum theory. When isolated from radiation and other atoms, most atoms remain stable indefinitely: they neither collapse nor explode. When atoms are excited electrically or by collisions or otherwise, they emit radiation of discrete wavelengths characteristic of the kind of atoms excited. The simplest model of the atom is a hard, tiny, electrically neutral sphere—just the smallest possible fragment of the bulk material that possesses the identity of a given chemical element. Neils Bohr's theory was built primarily on the photon concept of radiation, which was understood as an hypothesis but was not yet unambiguously verified when Bohr did his early work. Bohr's first solution of the hydrogen-atom problem in his historic 1913 paper depended on a rather arbitrary combination of classical and quantum ideas.
The atom is the reference point for the whole of the science of materials, whatever we choose to call the particular discipline: physics, chemistry, geology, biochemistry, and so on. The atomic model as formulated by Dalton proposes that the chemical elements are composed of indivisible atoms, all the atoms of a given element possessing identical properties. The Bohr atom is important historically, but in the quantum mechanical model of the atom all the details proposed in the Bohr atom, including quantisation, arise without the need for any assumptions. Highly excited or energetic atoms, called ‘Rydberg atoms’ after a Swedish spectroscopist, provide a link between classical and quantum physics. The periodic orbits characteristic of classical systems still form useful components of quantum chaos models for helium and larger atoms. The situation as unstable periodic orbits embedded in a sea of more common nonperiodic orbits.
In 1913, Niels Bohr developed an accurate model for the hydrogen atom. The mathematics involved and the simplicity of this model is easily understood. The intention of the paper is not to replace Bohr's model, but to find a similar model for all atoms. The model discussed, which was developed on the same basis as Bohr's model for the hydrogen atom, calculates the radii and the energies of the orbits. The wavelength of an emitted photon when an electron makes a ‘jump’ from a higher state to a lower state can also be calculated from the model. Finally, the paper demonstrates that the model obeys the de Broglie's hypothesis that the moving electron exhibits both wave and particle properties.
To solve the problems of the classical model of the atom of both the atom's instability and the fact that it does not emit a line at a well-defined wavelength, we introduce the necessary quantum-mechanical ideas of angular momentum and energy quantization and provide a simple description of the hydrogen atoms. We go on to consider how to build up the structure of more complicated atoms. We also consider what quantum mechanics has to say about the exchange of energy between atoms in collisions and in interaction with light. This description includes collisional excitation and deexcitation and radiative processes (spontaneous and stimulated emission, absorption).
The interaction between matter and radiation has fascinated physicists for a long time. On the material side, the most detailed investigations of these processes concentrate on atoms, the basic constituents of matter. The radiation that is involved in these processes is primarily light, i.e., radiation whose wavelength is in the range of a few tenths of a micron to a few microns. Under today's laboratory conditions, this radiation is generally produced by a laser. This introduction outlines our picture of these constituents and presents some of the concepts and models that we will use throughout this book. Atoms Historical Early models: atoms as building blocks The term “atom” was coined by the Greek philosopher Democritus of Abdera (460–370 B.C.), who tried to reconcile change with eternal existence. His solution to this dilemma was that matter was not indefinitely divisible, but consisted of structureless building blocks that he called atoms. According to Democritus and other proponents of this idea, the diverse aspects of matter, as we know it, are a result of different arrangements of the same building blocks in empty space (Melsen 1957; Simonyi 1990). The most important opponent of this theory was Aristotle (384–322 B.C.), and his great influence is probably the main reason that the atomic hypothesis was not widely accepted, but lay dormant for two thousand years. It reappeared only in the eighteenth century, when the emerging experimental science found convincing evidence that matter does indeed consist of elementary building blocks.
Abstract The attempt to explain atomic structure was one of the main motives for the genesis of quantum mechanics (Bohr’s atomic model, spectral lines, etc.); at the same time it represented the first true testing ground for the new theory. The explanation of the existence of discrete atomic levels, their quantitative prediction, understanding of the periodic structure of the elements, the correct interpretation of chemical bonds, etc., can be regarded without exaggeration as one of the greatest achievements of the scientific thought of our time. A door to an entirely new world— that of the atomic and subatomic phenomena—opened, triggering an impressive advance in basic scientific knowledge and modern technology, unprecedented in human history. The very concepts and many of the mathematical tools of quantum mechanics have, in many cases, sprung from the efforts to solve these problems. In this chapter, we study atomic structure, and try to illustrate some of these features.
The first objective of this chapter is to briefly review some of the basic ideas about the structure of matter, in particular the concepts of microscopic physics, in order to recall the knowledge gained in previous physics (and chemistry) courses and make it more precise. Our review will be very concise, and most statements will be made without any proof or detailed discussion. A second objective is to give a brief description of some of the crucial stages in the early development of quantum physics. We shall not follow the strict historical order of this development or present the arguments used at the beginning of the last century by the founding fathers of quantum mechanics; rather, we shall stress the concepts which we shall find useful later on. Our last objective is to give an elementary introduction to some of the basic ideas, like those of a quantum particle or energy level, that will reappear throughout this text. We shall base our review on the Bohr theory, which provides a simple, though far from convincing, explanation of how energy levels are quantized and how the spectrum of the hydrogen atom arises. This chapter should be reread later on, once the basic ideas of quantum mechanics have been made explicit and illustrated by examples. From the practical point of view, it is possible to skip the general considerations of Sections 1.1 and 1.2 at the first reading and begin with Section 1.3, returning to those two sections later on as needed.