﻿Theory of the Metallic State. 12& 



question of the atomic heat of metals. Measurement shows 

 that there cannot be more than one free electron per hundred 

 atoms if the electron obeys the law of the equipartition of 

 energy, for the atomic heat of metals corresponds in every 

 respect to that of metalloids. As shown above, the con- 

 ductivity leads to the conclusion that there are more free 

 electrons than atoms. If one gives up the law of the equi- 

 partition of energy, which at first sight seems the simplest 

 way out of the difficulty, one cannot explain the conduction 

 of heat and the Wiedemann-Franz constant. Thus the 

 electrical conductivity leads to a large number of free 

 electrons. Its temperature coefficient leads to no specific 

 heat. But the heat conduction cannot be explained except 

 by a normal specific heat. Again, the measured heat 

 capacities are incompatible with a large number of electrons 

 or with a normal specific heat. 



The expression free electron, suggesting, and intending to 

 suggest, an electron normally not under the action of any 

 force, like an atom in a monatomic gas, might almost be 

 called a contradiction in terms. If one assumes that the 

 electrons are not attracted by the ions (and this assumption 

 is essential, for otherwise they would recombine with them), 

 the forces between the electrons themselves will prevent 

 their being free in the true sense. Indeed, the force pre- 

 venting one electron from moving between two others 

 at a distance of 3 . 10~ 8 cm., corresponding to about one 

 electron per atom, is so great that the equipartition energy 



on 



«— T could only shift it by about 1/20 of the distance apart. 



These figures may be modified, of course, by assuming the 

 ions at a distance to attract the electrons, and some such 

 supposition must be made, as the electrons would otherwise 

 not remain in the metal at all. But the forces exerted by 

 the neighbouring electrons whose repulsion is not neutralized 

 are sufficient to prevent any similarity to a gas. The 

 hypothesis put forward in this paper is, that far from forming 

 a sort of perfect gas the electrons in a metal may be looked 

 upon as a perfect solid. 



This conception would appear not to lead to any serious 

 contradictions, and even to supply an explanation for one or 

 two phenomena which the old theory hardly touches upon. 



The following assumptions would appear to be necessary 

 to explain the facts : — 



1. Though attracted, according to the inverse square law. 

 by ions at distances sensibly greater than the atom's radius, 

 the electrons are repelled at distances less than r , by a force 



Phil. Mag. S. 6. Vol. -29. No. 169. Jan. 1915. K 



