Electron Theory of Chemistry to Solids. 



739 



instead of being concentrated at points were uniformly dis- 

 tributed over the layer, the electric force produced by the 

 electricity below the surface layer of electrons would be an 

 attraction equal to 2tto; where a is the surf ace density of the 

 layer when there are N/2 atoms per unit area. Hence, if 

 d be the distance between two atoms, a m = e/2d 2 ' i hence the 

 force acting on each surface electron is irc 2 /d 2 . This is the 

 attraction due to the forces varying inversely as the square 

 of the distance ; it must be balanced bv the repulsive force 

 varying inversely as the cube of the distance which the atoms 

 exert on the electrons. If we suppose that the distance 

 between the surface layer of electrons and the layer of 

 atoms immediately beneath them is the same as that in the 

 body of the crystal between a layer of electrons and the 

 adjacent layer of atoms, we find that the repulsive force is 

 greater than 7re 2 /d' 2 } the attractive one. The upper layer of 

 electrons will hence move further away from the atoms, so 

 that the distance of the electrons in the outer layer from the 

 nearest atoms is greater than it is for the electrons in the 

 interior. Thus the potential energy of an atom on the surface 

 will be greater than that of an atom in the interior ; as the 

 atoms on the surface have an abnormally large amount. of 

 energy, there will be in the expression for the energy of the 

 solid a term proportional to the surface. This term will be 

 proportional to the surface tension, so that the surface 

 tension possessed by the substance can be calculated. I 

 must leave this, however, for another occasion. 



Another possible way of arranging the atoms and the 

 electrons when they are equal in number is that shown in 

 fig. 4, where the A's represent atoms and the E's electrons. 



; 







Fig. 4. 



E 



A 





E 



j 



E 



/ 



A 



/ 















/ 



E 





A 



/" 



/ 



We shall consider the conditions for stability and the 

 properties of this system. 



Let. us take the coordinate axes parallel to the axes of the 

 lattices, and the origin at an electron. The electrons may 

 -be divided into two classes : in the first class the coordinates 



3B2 



