Supplement to ''Nature,'' July 7, 1923 



Zl 



2. While in contradiction to the classical 

 electromagnetic theory no radiation takes place 

 from the atom in the stationary states themselves, 

 t a process of transition between two stationary 

 states can be accompanied by the emission of 

 electromagnetic radiation, which will have the 

 same properties as that which would be sent 

 out according to the classical theory from an 

 electrified particle executing an harmonic vibra- 

 tion with constant frequency. This frequency v 

 has, however, no simple relation to the motion 

 of the particles of the atom, but is given by the 

 relation 



A.' = E'-E", 



where h is Planck's constant, and E' and E" are 

 the values of the energy of the atom in the two 

 stationary states that form the initial and final 

 state of the radiation process. Conversely, irradia- 

 tion of the atom with electromagnetic waves of 

 this frequency can lead to an absorption process, 

 whereby the atom is transformed back from the 

 latter stationary state to the former. 

 While the first postulate has in view the general 

 stability of the atom, the second postulate has chiefly 

 in view the existence of spectra with sharp lines. 

 Furthermore, the quantum theory condition entering 

 in the last postulate affords a starting point for the 

 interpretation of the laws of series spectra. The 

 most general of these laws, the combination principle 

 ; enunciated by Ritz, states that the frequency v for 

 j'leach of the lines in the spectrum of an element can 

 ' be represented by the formula 



v = T"-T', 

 where T" and T' are two so-called "spectral terms" 

 belonging to a manifold of such terms characteristic 

 of the substance in question. 



According to our postulates, this law finds an 

 immediate interpretation in the assumption that the 

 spectrum is emitted by transitions between a number 

 of stationary states in which the numerical value of 

 the energy of the atom is equal to the value of the 

 spectral term multiplied by Planck's constant. This 

 explanation of the combination principle is seen 

 io differ fundamentally from the usual ideas of 

 electrodynamics, as soon as we consider that there 

 is no simple relation between the motion of the atom 

 and the radiation sent out. The departure of our 

 considerations from the ordinary ideas of natural 

 I philosophy becomes particularly evident, however, 

 'when we observe that the occurrence of two spectral 

 I lines, corresponding to combinations of the same 

 spectral term with two other different terms, implies 

 [that the nature of the radiation sent out from the 

 atom is not determined only by the motion of the 



atom at the beginning of the radiation process, but 

 also depends on the state to which the atom is trans- 

 ferred by the process. 



At first glance one might, therefore, think that it 

 would scarcely be possible to bring our formal explana- 

 tion of the combination principle into direct relation 

 with our views regarding the constitution of the atom, 

 which, indeed, are based on experimental evidence 

 interpreted on classical mechanics and electrodynamics. 

 A closer investigation, however, should make it clear 

 that a definite relation may be obtained between the 

 spectra of the elements and the structure of their 

 atoms on the basis of the postulates. 



The Hydrogen Spectrum. 

 The simplest spectrum we know is that of hydrogen. 

 The frequencies of its lines may be represented with 

 great accuracy by means of Palmer's formula : 



v = K 



where K is a constant and n' and n" are two integers. 

 In the spectrum we accordingly meet a single series 

 of spectral terms of the form K/w^, which decrease 

 regularly with increasing term number n. In accord- 

 ance with the postulates, we shall therefore assume 

 that each of the hydrogen lines is emitted by a transi- 

 tion between two states belonging to a series of 

 stationary states of the hydrogen atom in which the 

 numerical value of the atom's energy is equal to hK/n^. 

 Following our picture of atomic structure, a hydrogen 

 atom consists of a positive nucleus and an electron 

 which — so far as ordinary mechanical conceptions are 

 applicable — will with great approximation describe a 

 periodic elliptical orbit with the nucleus at one focus. 

 The major axis of the orbit is inversely proportional 

 to the work necessary completely to remove the 

 electron from the nucleus, and, in accordance with 

 the above, this work in the stationary states is just 

 equal to hK/n^. We thus arrive at a manifold of 

 stationary states for which the major axis of the 

 electron orbit takes on a series of discrete values 

 proportional to the squares of the whole numbers. 

 The accompanying Fig. 2 shows these relations 

 diagrammatically. For the sake of simplicity the 

 electron orbits in the stationary states are represented 

 by circles, although in reality the theory places no 

 restriction on the eccentricity of the orbit, but only 

 determines the length of the major axis. The arrows 

 represent the transition processes that correspond to 

 the red and green hydrogen lines, Ha and H/3, the 

 frequency of which is given by means of the Balmer 

 formula when we put n" = 2 and n' = 3 and 4 respect- 

 ively. The transition processes are also represented 

 which correspond to the first three lines of the series 



