I shall not tire you any further with more details; I hope to return to these questions here in the Physical Society, and to show how, on the basis of the underlying ideas, it is possible to develop a theory for the structure of atoms and molecules. Before closing I only wish to say that I hope I have expressed myself sufficiently clearly so that you have appreciated the extent to which these considerations conflict with the admirably coherent group of conceptions which have been rightly termed the classical theory of electrodynamics. On the other hand, by emphasizing this conflict, I have tried to convey to you the impression that it may be also possible in the course of time to discover a certain coherence in the new ideas.
[1] Address delivered before the Physical Society in Copenhagen, Dec. 20, 1913.
ESSAY II[2]
ON THE SERIES SPECTRA OF THE ELEMENTS
I.INTRODUCTION
The subject on which I have the honour to speak here, at the kind invitation of the Council of your society, is very extensive and it would be impossible in a single address to give a comprehensive survey of even the most important results obtained in the theory of spectra. In what follows I shall try merely to emphasize some points of view which seem to me important when considering the present state of the theory of spectra and the possibilities of its development in the near future. I regret in this connection not to have time to describe the history of the development of spectral theories, although this would be of interest for our purpose. No difficulty, however, in understanding this lecture need be experienced on this account, since the points of view underlying previous attempts to explain the spectra differ fundamentally from those upon which the following considerations rest. This difference exists both in the development of our ideas about the structure of the atom and in the manner in which these ideas are used in explaining the spectra.
We shall assume, according to Rutherford's theory, that an atom consists of a positively charged nucleus with a number of electrons revolving about it. Although the nucleus is assumed to be very small in proportion to the size of the whole atom, it will contain nearly the entire mass of the atom. I shall not state the reasons which led to the establishment of this nuclear theory of the atom, nor describe the very strong support which this theory has received from very different sources. I shall mention only that result which lends such charm and simplicity to the modern development of the atomic theory. I refer to the idea that the number of electrons in a neutral atom is exactly equal to the number, giving the position of the element in the periodic table, the so-called "atomic number." This assumption, which was first proposed by van den Broek, immediately suggests the possibility ultimately of deriving the explanation of the physical and chemical properties of the elements from their atomic numbers. If, however, an explanation of this kind is attempted on the basis of the classical laws of mechanics and electrodynamics, insurmountable difficulties are encountered. These difficulties become especially apparent when we consider the spectra of the elements. In fact, the difficulties are here so obvious that it would be a waste of time to discuss them in detail. It is evident that systems like the nuclear atom, if based upon the usual mechanical and electrodynamical conceptions, would not even possess sufficient stability to give a spectrum consisting of sharp lines.
In this lecture I shall use the ideas of the quantum theory. It will not be necessary, particularly here in Berlin, to consider in detail how Planck's fundamental work on temperature radiation has given rise to this theory, according to which the laws governing atomic processes exhibit a definite element of discontinuity. I shall mention only Planck's chief result about the properties of an exceedingly simple kind of atomic system, the Planck "oscillator." This consists of an electrically charged particle which can execute harmonic oscillations about its position of equilibrium with a frequency independent of the amplitude. By studying the statistical equilibrium of a number of such systems in a field of radiation Planck was led to the conclusion that the emission and absorption of radiation take place in such a manner, that, so far as a statistical equilibrium is concerned only certain distinctive states of the oscillator are to be taken into consideration. In these states the energy of the system is equal to a whole multiple of a so-called "energy quantum," which was found to be proportional to the frequency of the oscillator. The particular energy values are therefore given by the well-known formula
where
