220 PHENOMENA, ATOMS, AND MOLECULES 



failure for two reasons. First, the method of mathematical expansion 

 which was used is not legitimate when applied to distances as short as 

 those hetween ions in salts ; and, second, Born assumed that the cubical 

 ions were all orientated so that their edges were parallel. This kind of 

 orientation would be unstable under the forces assumed, for these forces 

 would tend to orientate one cubical ion so that its corner would come 

 opposite the face of another ion, and in this case the repulsive force would 

 be replaced by an attractive force which would act in addition to the force 

 between the ionic charges. Although such orientation of ions as Born 

 assumes might conceivably exist in solid crystals from causes which he 

 does not discuss, it is clear that it cannot be the cause of the repulsive 

 forces, since the elimination of the orientation by melting the salt does not 

 greatly alter the density or the compressibility. 



Debye (7) has developed a theory which seems to give a better picture 

 of the repulsive forces. Assuming the electrons to move in orbits in accord 

 with Bohr's theory, he finds that the electric field around a molecule is a 

 pulsating or partly oscillating field increasing in amplitude very rapidly as 

 the surface of the molecule is approached. Thus when an electron ap- 

 proaches a molecule it acquires, in addition to any motion of translation 

 it may have, an oscillatory motion due to the pulsating field. Debye shows 

 that this oscillatory motion tends to be 180° out of phase with the field 

 producing it, and then shows, that because of the non-uniformity of the 

 electric field near an atom the resulting force will be one of repulsion. 



On this theory the repulsive forces between molecules are due to the 

 perturbations in the electron orbits in one molecule, caused by the motions 

 of the electrons in their orbits in the neighboring molecules. The repulsive 

 force thus does not originate from a molecule as a whole, but comes from 

 the close approach of electrons in the two molecules. This would seem to 

 indicate that we may profitably regard these forces as surface forces, and 

 should express them as functions of the distances between the surfaces of 

 the molecules rather than in terms of the distances between the centers. 

 This conception affords a justification, to a large extent, of the theory 

 which regarded molecules as rigid elastic spheres. 



Even if we accept Debye's picture of the origin of repulsive forces, 

 we see that it really only refers the cause back to the quantum theory, by 

 which the stable orbits of the electrons in the molecule are determined. At 

 present, however, problems of this kind are treated by wave mechanics 

 instead of by a consideration of orbits of electrons. For a few simple cases, 

 such as interactions between hydrogen molecules, Hund and London have 

 been able to calculate the forces by means of wave mechanics. But it will 

 probably be a long time before definite knowledge of repulsive forces can 

 be obtained in this way for more complicated molecules. 



