THE QUANTUM PHYSICS OF SOLIDS 649 



even to single atoms so long as no attempt was made to investigate 

 the internal structure of the atom. Considering the atom to be a 

 perfectly elastic miniature billiard ball having size, mass, and velocity 

 but no internal properties, classical mechanics was able to handle in a 

 statistical fashion the dynamics of large systems of atoms in a gaseous 

 form and to deduce a number of valid conclusions concerning the 

 specific heat, gas laws, viscosity, and diffusion constants of gases. 

 On the other hand, failure attended all endeavors to apply these laws 

 to the swarm of electrons surrounding a nucleus. A system of this 

 sort is unstable classically and can never come to thermal equilibrium. 

 Applying the classical laws of statistical mechanics, one finds that 

 some of the electrons will move very close to the nucleus, the energy 

 lost in this process being acquired by other electrons which move farther 

 out. According to classical mechanics this process will continue with- 

 out ever reaching equilibrium and during it the atom will be thoroughly 

 torn apart. 



Another difficulty in the classical theory arises from the electro- 

 dynamics of an accelerated electron. An electron moving in the field 

 of a nucleus is accelerated, and classical electromagnetic theory pre- 

 dicts that under these circumstances electromagnetic energy will be 

 radiated — the atom being in effect a microscopic radio transmitting 

 station in which the charging currents in the antenna are represented 

 by the motions of the electrons. According to this theory an atomic 

 system would continually radiate energy, and it could be proved that 

 no equilibrium like that actually observed between matter and radia- 

 tion would ever be achieved. 



Thus, classical mechanics and electromagnetics were incapable of 

 taking the electrons and nuclei as building blocks and constructing 

 solids or even atoms from them. To put it bluntly, the classical laws 

 were wrong; although adequate for large-scale phenomena, they were 

 inapplicable to phenomena of an atomic scale. 



Nevertheless, modified applications of the classical theory had a great 

 number of successes in the atomic theory of solids. Dealing with the 

 atoms as elastic idealized billiard balls led to the correct value for the 

 specific heat of solids, at least at normal temperatures, and the electron 

 theory of conduction in metals was in many respects quite successful. 

 None of the successes of the conduction theory were completely 

 satisfying, however, because the assumptions needed to explain one 

 set of facts were incompatible with other sets of facts and the whole 

 field was greatly lacking in unity. According to this classical theory 

 a metal contained free electrons which could move under the influence 

 of an electric field and thus conduct a current. Their motion was 



