Physics. — ''The spectrum of a rotating molecule according to the 

 theory of quanta." By J. M. Burgers, (Coramunicated bj 



Piof. H. A. LORENTZ). 



(Communicated in the meeting of May 26, 1917). 



§ 1. Introduction. 



N. Bjerrum has drawn attention to the fact that if a molecule 

 which carries a vibrating resonator, rotates, this rotation exerts an 

 influence upon the frequency of the light emitted'). If tiie frequency 

 of the resonator is \\ *), the angular velocity of the molecule being 

 oi=:1jiv', the frequencies: x\, v^-\-v\ \\ —v will be found in 

 the light emitted by the system. Molecules of this kind will also 

 absorb the frequencies v^, \\ -\- v', \\ — v' from radiation which falls 

 upon them. Starting from this principle Bjerrum has explained the 

 structure of the bands which are found in the infra-red absorption 

 spectra of certain gases. It was assumed that the velocity of rotation 

 of the molecule is determined by a condition taken from the theory 

 of quanta, so that to can only have values which are an integral 

 multiple of a certain quantity Wq. In the spectrum of such a gas 

 a line of the frequency x\ will be accompanied by a set of equi- 

 distant satellites, given by the general formula : 



The bands observed in the absorption spectra of water vapour and 

 other gases actually have a structure that may be described by this 

 form\ila '). 



On the principles of the theory of quanta, however, one will 

 be inclined to assume that a given spectral line is not emitted by 

 a vibrating electron; but that it is emitted when the electron passes 

 from a certain definite state of motion discontinuously to another 



1) N. Bjerrum, Nernst-b'estschrift p. 93 (1912). — Lord Rayleigh was the 

 first to point out this influence of the rotation (Scientific Papers, IV, p. 17). - Com- 

 pare also: W. G. Mandeesloot, De breedte van spektraallijnen (Diss.^Utrecht 1914). 



3) In this paper "frequency" will always denote the number of vibrations per 

 second. 



3) Cf. for instance: Eva von Bahr, Verb. Deutsch.Phys. Ges. 15, p. 710, 1150, 

 (1913); H. Rubens & G. Hettner, Sitz. Ber. Berl. Akad. p. 167, 1916. 



