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American Journal of Physics

On Presenting the Bohr Theory

John I. Shonle

Published Jul 1, 1971• 0 citations
Publisher

Abstract

In this paper we review some of the well-known objections to the standard presentation of the Bohr theory of the hydrogen atom. A proper use of the correspondence principle avoids these objections. We present a clear set of hypotheses which can all be retained in later developments of quantum mechanics. The energy levels are derived and the limitations of the correspondence principle are discussed.

DOI
10.1119/1.1986282

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In this paper we review some of the well-known objections to the standard presentation of the Bohr theory of the hydrogen atom. A proper use of the correspondence principle avoids these objections. We present a clear set of hypotheses which can all be retained in later developments of quantum mechanics. The energy levels are derived and the limitations of the correspondence principle are discussed.
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.
Niels Bohr's studies on the quantum theory of the atom over the years 1912–1923 are discussed. The sources of his work on these questions are analyzed. The beginning of his quantum studies in 1912 is described. His famous paper on the theory of the hydrogen atom and on the origin of spectra is analyzed in detail. The subsequent development of his ideas regarding atomic structure is discussed, with an emphasis on his postulates regarding stationary states and radiative transitions and on the development of the correspondence principle. How well he understood the difficulties of the model theory and how he strived for a profound understanding of quantum phenomena are shown.
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The world should have waited until 1913, when a Danish physicist N. Bohr proposed an entirely new theory for a description and partial explanation of the spectral properties of the hydrogen atom. His theory was based on two postulates, the so-called Bohr postulates, and both of them were impossible to be understood from the point of view of classical physics. Being based on these postulates and employing classical physics, N. Bohr was able to derive explicit expressions for the energy levels of the hydrogen atom and the wavelengths of possible transitions. The hydrogen-like atom has only one electron, and all others have been removed by various ways of ionization. An essential feature of these systems is the presence of one electron only. The Coulomb interaction between this electron and the nucleus is spherically symmetrical. Later, we shall see that the situation becomes considerably more complicated in the case of multielectron atoms.
The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. This is because the classical quantum theory of Bohr does not take the theory of relativity into account. In this paper, the kinetic energy and momentum of an electron in a hydrogen atom are treated relativistically. A clearer argument is developed while also referring to papers published in the past. The energy levels of a hydrogen atom predicted by this paper almost match the theoretical values of Bohr. It is difficult to experimentally distinguish the two. However, this paper predicts the existence of an n = 0 energy level that cannot be predicted even with Dirac’s relativistic quantum mechanics. The only quantum number treated in this paper is n. This point falls far short of a finished quantum mechanics. However, even in discussion at the level of this paper, it can be concluded that quantum mechanics is an incomplete theory.