Supplement to '' Nature,'' Jtily 7, 1923 



37 



of an electron to a helium nucleus is exactly equal 

 to 4 K, it becomes evident that spark spectra are due 

 to the ionised atom, and that their emission corresponds 

 to the last step hut one in the formation of the neutral 

 atom by the successive capture and binding of electrons. 



Absorption and Excitation of Spectral Lines. 



The interpretation of the origin of the spectra was 

 also able to explain the characteristic laws that govern 

 absorption spectra. As Kirchhoff and Bunsen had 

 already shown, there is a close relation between the 

 selective absorption of substances for radiation and 

 their emission spectra, and it is on this that the 

 application of spectrum analysis to the heavenly 

 bodies essentially rests. Yet on the basis of the 

 classical electromagnetic theory, it is impossible to 

 understand why substances in the form of vapour 

 show absorption for certain lines in their emission 

 spectrum and not for others. 



On the basis of the postulates given above we are, 

 however, led to assume that the absorption of radiation 

 corresponding to a spectral line emitted by a transition 

 from one stationary state of the atom to a state of 

 less energy is brought about by the return of the atom 

 frftm the last-named state to the first. We thus 

 understand immediately that in ordinary circumstances 

 a gas or vapour can only show selective absorption 

 for spectral lines that are produced by a transition 

 from a state corresponding to an earlier stage in the 

 binding process to the normal state. Only at higher 

 temperatures or under the influence of electric dis- 

 charges whereby an appreciable number of atoms are 

 being constantly disrupted from the normal state, 

 can we expect absorption for other lines in the emission 

 spectrum in agreement with the experiments. 



A most direct confirmation for the general inter- 

 pretation of spectra on the basis of the postulates 

 has also been obtained by investigations on the 

 excitation of spectral lines and ionisation of atoms 

 by means of impact of free electrons with given 

 velocities. A decided advance in this direction was 

 marked by the well-known investigations of Franck 

 and Hertz (1914). It appeared from their results 

 that by means of electron impacts it was impossible 

 to impart to an atom an arbitrary amount of energy, 

 but only such amounts as corresponded to a transfer 

 of the atom from its normal state to another stationary 

 state of the existence of which the spectra assure us, 

 and the energy of which can be inferred from the 

 magnitude of the spectral term. 



Further, striking evidence was afforded of the in- 

 dependence that, according to the postulates, must 

 be attributed to the processes which give rise to the 

 emission of the different spectral lines of an element. 



Thus it could be shown directly that atoms that were 

 transferred in this manner to a stationary state of 

 greater energy were able to return to the normal 

 state with emission of radiation corresponding to a 

 single spectral line. 



Continued investigations on electron impacts, in 

 which a large number of physicists have shared, have 

 also produced a detailed confirmation of the theory 

 concerning the excitation of series spectra. Especially 

 it has been possible to show that for the ionisation 

 of an atom by electron impact an amount of energy 

 is necessary that is exactly equal to the work required, 

 according to the theory, to remove the last electron 

 captured from the atom. This work can be determined 

 directly as the product of Planck's constant and the 

 spectral term corresponding to the normal state, 

 which, as mentioned above, is equal to the limiting 

 value of the frequencies of the spectral series connected 

 with selective absorption. 



The Quantum Theory of Multiply-Periodic 

 Systems. 



While it was thus possible by means of the funda- 

 mental postulates of the quantum theory to account 

 directly for certain general features of the properties 

 of the elements, a closer development of the ideas 

 of the quantum theory was necessary in order to 

 account for these properties in further detail. In the 

 course of the last few years a more general theo- 

 retical basis has been attained through the develop- 

 ment of formal methods that permit the fixation of 

 the stationary states for electron motions of a more 

 general type than those we have hitherto considered. 

 For a simply, periodic motion such as we meet in the 

 pure harmonic oscillator, and at least to a first ap- 

 proximation, in the motion of an electron about a 

 positive nucleus, the manifold of stationary states 

 can be simply co-ordinated to a series of whole 

 numbers. For motions of the more general class 

 mentioned above, the so-called multiply-periodic 

 motions, however, the stationary states compose a 

 more complex manifold, in which, according to 

 these formal methods, each state is characterised by 

 several whole numbers, the so-called " quantum 

 numbers." 



In the development of the theory a large number 

 of physicists have taken part, and the introduction 

 of several quantum numbers can be traced back to 

 the work of Planck himself. But the definite step 

 which gave the impetus to further work was made 

 by Sommerfeld (19 15) in his explanation of the fine 

 structure shown by the hydrogen lines when the 

 spectrum is observed with a spectroscope of high 

 resolving power. The occurrence of this fine structure 

 must be ascribed to the circumstance that we have 

 to deal, even in hydrogen, with a motion which is 

 not exactly simply periodic. In fact, as a consequence 

 of the change in the electron's mass with velocity 

 that is claimed by the theory of relativity, the electron 

 orbit will undergo a very slow precession in the orbital 

 plane. The motion will therefore be doubly periodic, 

 and besides a number characterising the term in the 

 Balmer formula, which we shall call the principal 

 quantum number because it determines in the main 

 the energy of the atom, the fixation of the stationary 



