34 



Supplement to *' Nature,'' Jtt/y 7, 1923 



of ultra-violet lines found by Lyman in 1914, of which 

 the frequencies are given by the formula when n is put 

 equal to i, as well as to the first line of the infra-red 

 series discovered some years previously by Paschen, 

 which are given by the formula if n" is put equal to 3. 

 This explanation of the origin of the hydrogen 

 spectrum leads us quite naturally to interpret this 

 spectrum as the manifestation of a process whereby 

 the electron is bound to the nucleus. While the 

 largest spectral term with term number i corresponds 

 to the final stage in the binding process, the small 

 spectral terms that have larger values of the term 

 number correspond to stationary states which represent 

 the initial states of the binding process, where the 



Fig. 2. 



electron orbits still have large dimensions, and where 

 the work required to remove an electron from the 

 nucleus is still small. The final stage in the binding 

 process we may designate as the normal state of the 

 atom, and it is distinguished from the other stationary 

 states by the property that, in accordance with the 

 postulates, the state of the atom can only be changed 

 by the addition of energy whereby the electron is 

 transferred to an orbit of larger dimensions correspond- 

 ing to an earlier stage of the binding process. 



The size of the electron orbit in the normal state 

 calculated on the basis of the above interpretation 

 of the spectrum agrees roughly with the value for the 

 dimensions of the atoms of the elements that have 

 been calculated by the kinetic theory of matter from the 

 properties of gases. Since, however, as an immediate 

 consequence of the stability of the stationary states 

 that is claimed by the postulates, we must suppose 

 that the interaction between two atoms during a 

 collision cannot be completely described with the aid 

 of the laws of classical mechanics, such a comparison 

 as this cannot be carried further on the basis of such 

 considerations as those just outlined. 



A more intimate connexion between the spectra 

 and the atomic model has been revealed, however, 



by an investigation of the motion in those station 

 states where the term number is large, and wl 

 the dimensions of the electron orbit and the frequt i 

 of revolution in it vary relatively little when wc 

 from one stationary state to the next following, it 

 was possible to show that the frequency of the radiation 

 sent out during the transition between two station, 

 states, the difference of the term numbers of wHk n 

 is small in comparison to these numbers themseh'es, 

 tended to coincide in frequency with one of 

 harmonic components into which the electron motion 

 could be resolved, and accordingly also with the 

 frequency of one of the wave trains in the radiation 

 which would be emitted according to the laws of 

 ordinary electrodynamics. 



The condition that such a coincidence should occur 

 in this region where the stationary states differ but 

 little from one another proves to be that the constant 

 in the Balmer formula can be expressed by means of 

 the relation 



K = 





where e and m are respectively the charge and mass 

 of the electron, while h is Planck's constant. This 

 relation has been shown to hold to within the con- 

 siderable accuracy with which, especially through the 

 beautiful investigations of Millikan, the quantities 

 e, m, and k are known. 



This result shows that there exists a connexion 

 between the hydrogen spectrum and the model for 

 the hydrogen atom which, on the whole, is as close 

 as we might hope considering the departure of the 

 postulates from the classical mechanical and electro-; 

 dynamic laws. At the same time, it affords somej 

 indication of how we may perceive in the quantum 

 theory, in spite of the fundamental character of thisj 

 departure, a natural generalisation of the fundamental 

 concepts of the classical electrodynamic theor\-. To 

 this most important question we shall return later^ 

 but first we will discuss how the interpretation of 

 the hydrogen spectrum on the basis of the postulates 

 has proved suitable in several ways, for elucidating the 

 relation between the properties of the different elements.' 



Relationships between the Elements. 

 The discussion above can be applied immediately 

 to the process whereby an electron is bound to a 

 nucleus with any given charge. The calculations 

 show that, in the stationary state corresponding tc 

 a given value of the number n, the size of the orbit 

 will be inversely proportional to the nuclear charge 

 while the work necessary to remove an electron wil 

 be directly proportional to the square of the nucleai 

 charge. The spectrum that is emitted during t]K 

 binding of an electron by a nucleus with charge > 



