306 Mr. J. Frenkel on the Surface Electric 



Table I. — Atomic volumes and intrinsic potentials. 



I. 



Element. 



II. 

 Valency 



(■)■ 



III. 



Atomic 



volume. 



A/8. 



IV. 



P 1 



V. 



Intrinsic 

 potential 

 (calcul.). 



VI. 



Intrinsic 

 potential 

 (observed). 



VII. 



Ionizing 

 potential. 





Na 



1. 



23-7 ~ l cm. 



1-6 XlO _ 'cm. 



1-7 volts. 



1-81 





Li 



- 1 



11-9 



1-27 X 10" S 



2-14 



2-21 





Hg 



o 



14-8 



1-4 XlO" 8 



4-2 





49. 



Zn 



2 



95 



1-25X10" 8 



52 



3-1 



396 



Al 



3 



104 



1-21X10" 8 



6-7 





■ 



Pb 



4 



18-3 



1-46 X 10" s 



7-4 







It will be seen that the calculated values of V for Na and 

 Li are in excellent agreement with Millikan's values (§ 1)*. 

 As to the other values (except that for Hg, which also seems 

 of the correct magnitude), they are obviously too high, and 

 increase too rapidly with tc. This circumstance is easily 

 explained by the fact that r is, in general, less than It and 



that the ratio ^ decreases as k increases 



In fact, the inter 



ference between the external electronic rings of neighbour- 

 ing atoms must, obviously, increase with the number (k) of 

 electrons in these rings ; their diameters must, therefore, 

 contract compared with the interatomic distances — or rather 

 conversely — the distances between the atoms must increase, 

 compared with their diameters, as the valency k increases. 



How far these considerations correspond to the facts will 

 be seen from the next Table (II.), in which the atomic radii 

 are calculated by means of the strict equation (8) from the 

 known values of the intrinsic potentials, as derived directly 

 from the thermionic effect f. It must be emphasized that 

 these values, obtained at very high temperatures after an 

 almost complete expulsion of occluded gases, are really 

 characteristic of the metal itself, and are, consequently, 

 much more reliable than those derived from the photo- 

 electric effect. 



* This close agreement is, probably, merely accidental, because 

 (1) Millikan's values do not relate to pure Na or Li. i. e. free from 

 absorbed gases, (2) r cannot be exactly equal to E. The coincidence of 

 the ratios, theoretical and experimental, is, however, very significant. 



t H. Lester, Phil. Mag. March 1916, and Baedecker, Elchtr. Erschein- 

 migen in metallischen Leitern (1911). 



