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 thisnuclear 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 explanationof 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 formulawhereis a whole number,the frequency of vibration of the oscillator, andis Planck's constant.
If we attempt to use this result to explain the spectra of the elements, however, we encounter difficulties, because the motion of the particles in the atom, in spite of its simple structure, is in general exceedingly complicated compared with the motion of a Planckoscillator. The question then arises, how Planck's result ought to be generalized in order to make its application possible. Different points of view immediately suggest themselves. Thus we might regard this equation as a relation expressing certain characteristic properties of the distinctive motions of an atomic system and try to obtain the general form of these properties. On the other hand, we may also regard equation (1) as a statement about a property of the process of radiation and inquire into the general laws which control this process.
In Planck's theory it is taken for granted that the frequency of the radiation emitted and absorbed by the oscillator is equal to its own frequency, an assumption which may be writtenif in order to make a sharp distinction between the frequency of the emitted radiation and the frequency of the particles in the atoms, we here and in the following denote the former byand the latter by.We see, therefore, that Planck's result may be interpreted to mean, that the oscillator can emit and absorb radiation only in "radiation quanta" of magnitudeIt is well known that ideas of this kind led Einstein to a theory of the photoelectric effect. This is of great importance, since it represents the first instance in which the quantum theory was applied to a phenomenon of non-statistical character. I shall not here discuss the familiar difficulties to which the "hypothesis of light quanta" leads in connection with the phenomena of interference, for the explanation of which the classical theory of radiation has shown itself to be so remarkably suited. Above all I shall not consider the problem of the nature of radiation, I shall only attempt to show how it has been possible in a purely formal manner to develop a spectral theory, the essential elements of which may be considered as a simultaneous rational development of the two ways of interpreting Planck's result.