316 Mr. J. Frenkel on the Surface Electric 



It would be of course unreasonable to expect a complete 

 coincidence between thein, since the equations (A) and (B) 

 were deduced for an isolated atom, subject to no external 

 forces, while such forces are very intense in a solid or liquid 

 body. We should expect the conditions underlying these 

 equations to be realized when the metal is vaporized and 

 the interaction between its atoms becomes feeble. In fact,, 

 experiments on the single-line spectra, excited by slow 

 cathode rays in the vapours of Hg, Zn, Cd, and other metals 

 of the same group, indicate that the frequency and energy 

 of the light emitted corresponds to the transition of one of 

 the electrons from the fourth stationary orbit on the third 

 one * (7 = 3). The radius of this third orbit 



( )a 

 r »= 2 -0-25 ? 2 ' 83xl0 ~ 8 Cm " (se ° P ' 312) ' 



is, thus, the normal atomic radius of the di-valent metals in 

 the gaseous state. When the metal is condensed, these 

 orbits imust contract, being too large compared with the 

 inter-atomic distances, and the electrons are forced to remain 

 on the second stationary orbits with a radius 



4 

 r 2 — -r 3 = l-26xl0" 8 cm. 



This tendency of the external electrons towards stationary 

 orbits of higher order (second, third) seems to constitute a 

 general, fundamental property of the metallic atoms, distin- 

 guishing them from the atoms of dielectrics, ivhich, under 

 ordinary conditions, keep their external electrons on the first 

 stationary orbit (corresponding to i—1). 



As the work required to remove an electron from its orbit, 

 i. e. to ionize the atom, is inversely proportional to the 

 radius, we see at once that the ionizing potentials of metals 

 although increasing with the valency, must be much smaller 

 than those of the dielectrics, a conclusion which is fully 



* Franck & Hertz, Verh. d. D. Phys. Ges. xv. p. 34 (1913) ; McLennan 

 (and others), Proc. Eoy. Soc. v. 92, Oct. J 916.— The frequency is 



represented by the formula v—i-, Sj — {-, P] , or approximately 



v = Ak (™ — jy ) > where k is Rydberg's constant. This corresponds ta 



the energy hv, acquired by an electron moving through a potential 



fall of 300— =2:4 volts, or (approximately), to the energy necessary to 



remove the electron from the third orbit, as can be calculated by means 

 of formula (15), taking k = 2 and 2'= 3. 



