72 Dr. Eva von Bahr on the Quantum-theory and 



the quantum-theory, since the rotation of a molecule — with 

 charged atoms — causes radiation, and that, even with in- 

 finitely thick gas-layers, we do not get emission o£ shorter 

 wave-lengths. 



In the hope of finding this quantum effect, the disciples 

 of Nernst have since made investigations into the specific 

 heat of gases at low temperatures. The results obtained with 

 hydrogen are particularly interesting. For this gas A. 

 Eucken* has shown that, with a falling temperature, the 

 specific heat rapidly declines, at about 70° abs. asymptotically 

 approaching the value for the monatomic gases. Practically 

 this value is reached at 60° abs. Attempts to find — by the 

 aid of the quantum- theory — a formula that represents the 

 results arrived at have been made by Einstein and Stern t, 

 as well as by Ehrenfest %. The latter proceeds from the 

 assumption that the energy of rotation of the molecules is 



distributed according to quanta (Jiv), putting \{2ttv) 2 .l = n~^> 



where n is a whole number, h Planck's constant — and that 

 consequently the frequencies of rotation (y) of the molecules 

 do not vary continuously, but can only have certain fixed 

 values. 



Strong support for the assumption of discontinuity in 

 the distribution of the rotation-frequencies is afforded by 

 investigations into the absorption of the ultra-red rays by 

 the gases. It is proposed here to give a summary of the 

 most important results of these investigations, with special 

 reference to their significance for the quantum-theory. 



Since Rubens and v. Wartenberg § found that certain 

 gases show strong absorption even in the case of rays of very 

 long wave-length (100-350/a), it has been generally presumed 

 that this absorption is caused by the rotation of the gas 

 molecules, while, on the other hand, the absorption in the 

 case of shorter wave-lengths (2-20 fi) is caused by the 

 vibrations of the atoms within the molecule. N. Bjerrum || , 

 however, has drawn attention to the fact that absorption in 

 the case of short wave-lengths is also probably dependent on 

 the rotation — to a certain extent. 



If the vibration-frequency of the atoms is v , and at the 

 same time the molecules rotate with a frequency. of v, then, 



* A. Eucken, JBerl. Akad. Ber. 1912, p. 141. 

 f A. Einstein u. O. Stern, Ann. de Phys. xl. p. 551 (1913). 

 % P. Ehrenfest, Verli. d. Deutsch. phys. Ges. xv. p. 451 (1913). 

 § II. Rubens u. H. v. Wartenberg, Verh. d. Deutsch. phys. Ges. xiii. 

 p. 796 (1911). 



|| N. Bjerrum, Nernst Festschrift, Halle a. S. 1912, p. 90. 



