314 Mr. J. Frenkel on the Surface Electric 



intrinsic potentials, are of the right order of magnitude 

 (about 1 volt). 



Thus, the agreement of the theory with the facts is, on 

 the whole, very satisfactory. 



§ 7. Let us now turn to the atomic radii (column VI. of 

 Table II.). The main fact is, again, the right order of 

 magnitude of all the values found for different atoms. 

 Another striking fact is that the atomic radii regularly 

 decrease as the valency increases. This result was antici- 

 pated in § 4. It was pointed out there that, " as the inter- 

 ference between the rings of neighbouring atoms increases 

 with the number of electrons in them, the ratio of their 

 radius to their mutual distance must decrease," and it was 

 thought possible to explain by this circumstance the too 

 high values obtained for the intrinsic potentials of Zn, Al, 

 and Pb, on the assumption that r, the atomic radius, was 



equal to R = - 3/ - ? where 2R, is the mean interatomic 



distance. (This assumption would give for the intrinsic 

 potential of Pt a value about five times as large as that 

 calculated from the surface-tension.) The quantitative 

 examination of this question from the point of view of Bohr's 

 theory of atomic dynamics leads to the same result. 



If k equidistant electrons of charge —e and mass m rotate 

 with an angular velocity a> in a circle of radius r with an 

 immobile nucleus of charge ice at the centre, the condition 

 of equilibrium between the attraction to the centre and the 

 centrifugal force is expressed by the equation 



e 2 



( K - s «)-2T mc ° 2r > ( A ) 



1 K ~ * ITT S 6 2 



where si— , X cosec , and the term — ■—- corresponds to 



A i=1 K r 2 1 



the mutual repulsion of the electrons. According to Bohr *, 

 this motion is stationary (unaffected by radiation) then only, 

 when the angular momentum of each electron is an integral 



multiple of ^— , where h is Planck's constant, that is when 

 mr*a> = i^. (i=l,2,3, ...)• • • . (B) 

 From (A) and (B) we get for the possible values of r, 



* Phil. Mag. toI. xxvi. pp. 1 & 476 (1913). 



