Electron Theory of Chemistry to Solids, 741 



this to the atoms which are nearest, next nearest, and next 

 next nearest to the electron the restoring force is 



(2e 2 c 8 e 2 c 8 e 2 c\ _ e 2 e 

 p \W + 2Td^25o¥) = 262p 'd^ 



Hence the equation for p is 



d 2 p e 2 / n rto c 



P 

 m d? 



-^(2.62.^2-08); 



so that for the equilibrium to be stable, 



The frequency p of the greatest vibration is given by the 

 equation 



To express d in terms of M and A, the molecular weight 



and density of the solid, we notice that the atoms may be 



arranged in face-centred cubes with a side 2d, and that each 



of: these cubes will contain four atoms. Hence the number 



of atoms in unit volume is 4 x (l/8^ 3 ), and this equals A/M. 



1 2A 

 Hence ^s = ~m > so ^ na ^ the critical frequency is given by 



ill as in the case considered on p. 732 # the shortest distance 

 between an atom and an electron is much the same in the 

 -solid and gaseous state, cjd will be nearly unity, so that 



mp 2 = 5*24^62 approximately. 



This is practically identical with the critical frequency for 

 the other arrangement of electrons, so that the selective 

 photo-electric effect will not distinguish between them. 



We proceed to consider the value of the bulk modulus 

 given by the new arrangement. We calculate, as before, the 

 potential energy of the system of electrons and atoms. We 

 divide the system up in cells, but now the cells, instead 

 of being cubes with electrons at the corners and atoms 

 .at the centre, are face-centred cubes whose side is equal 

 to 2d and which have atoms at the middle points of the 

 sides and also at the centre. I find in this way that the 

 potential energy due to the forces varying inversely as 



