496 



NATURE 



[December 30, 191 5 



The conception of free electrons in metals affords a 

 ready explanation of many of their electrical proper- 

 ties. Let us consider for a moment what will happen 

 if we put two different metals, A and B, into contact. 

 Both A and B contain electrons, but one, A say, has 

 more per unit volume than the other ; thus the pres- 

 sure of the electrons in A is greater than that of the 

 electrons in B. Thus, when the two metals are put in 

 contact, electrons will rush out of A into B. As these 

 electrons carry negative electricity with them, B will 

 be negatively electrified, and its electrification will 

 increase until the repulsion it exerts on the electrons 

 in A is sufficient to balance the excess of pressure, 

 and to prevent any more electrons from passing from 

 A to B. Those that do pass, however, will establish 

 a difference of potential between A and B, and in this 

 way we have a simple explanation of the difference 

 of potential arising from the contact of metals. 



Again, when an electric current passes through an 

 unequally heated metal, electrons will drift from places 

 of high to places of low potential, and carry heat with 

 them ; thus the passage of a current of electricity 

 through an unequally heated conductor will alter the 

 flow of heat. This is a well-known effect; it was 



/O 20 SO fO SO 60 70 80 90 /OO 

 Fig. I.— Conductivities of alloys of bismuth and lead. 



discovered by Lord Kelvin, and is known as the 

 Thomson effect. Closely connected with this is the 

 effect produced when we suddenly heat one part of a 

 conductor._ This will raise the temperature of the 

 electrons in that part and increase their pressure; 

 they will overflow into other parts of the conductor, 

 and the charges they carry will produce electromotive 

 forces arising from unequal heatings. These, too, 

 are a well-known feature of metallic conduction. 



We _ thus see that the characteristic features of 

 metallic conduction can be explained in a general way 

 by the theory that free electrons are dispersed through 

 the metal. We have not, however, considered as yet 

 how many of these free electrons would be required 

 to produce conductivity as great as that of metals. 

 This is a very important point, for these free electrons 

 will produce other effects besides electrical ones. 

 While their presence endows the metal with electrical 

 conductivity, the property we wish to explain, it also 

 endows it with other properties which have to be 

 explained away. We have to satisfy ourselves that 

 the number of electrons required for metallic con- 

 duction is so small that the undesirable effects are 

 negligible. Let us consider for a moment the nature 

 oT some of these effects. We have supposed the elec- 

 trons to be in temperature equilibrium with the metal, 

 so that when we heat the metal we also heat the 

 electrons. Now, to raise the temperature of a number 

 of electrons requires just as much energy as to raise 

 NO. 2409, VOL. 96] 



that of the same number of molecules of air — the 

 specific heat of electrons is the same as that of the 

 same number of air molecules. And it might, and in 

 certain cases we shall see that it does, happen that so 

 many electrons were required to explain the metallic 

 conduction that their specific heat would be consider- 

 ably greater than the observed specific heat of the 

 metal. This is even the case when we suppose that 

 the increase in the temperature does not increase the 

 number of the electrons. The production of free 

 atoms from the metal is, however, a case of dissocia- 

 tion, a neutral atom of the metal dissociating into an 

 electron and a positively charged atom. The dissocia- 

 tion might be expected to increase with temperature, 

 so that when we raise the temperature we have to 

 supply not merely the work required to raise the tem- 

 perature of the electrons already present, but also the 

 work required to detach fresh electrons, and this addi- 

 tional work will increase the apparent specific heat; 

 thus the effective specific heat of a number of electrons 

 may be considerably greater than that of the same 

 number of molecules of air. 



Another point, too, has to be taken into considera- 

 tion : every electron present in the metal requires the 

 presence of one positively electrified atom. If there 

 are as many electrons as atoms, then, supposing each 

 atom carries only one charge, every one of the metallic 

 atoms must be charged with positive electricity; if 

 there were six times as many electrons as atoms, each 

 atom would have on the average to be charged with 

 six units of electricity. So that any great excess of 

 electrons over atoms is only possible if the atoms can 

 receive positive charges which are many multiples of 

 one unit. Now there are strong reasons for thinking 

 that the number of positive charges on an atom, or, 

 what is the same thing, the number of electrons which 

 can be taken out of it, cannot, at any rate in the cir- 

 cumstances of the atoms in the metal, be any very 

 large multiple of the atomic unit of electricity. It is 

 true that we have reason to believe that there are in 

 an atom a number of electrons equal to half the 

 atomic weight, but the great majority of those are 

 deeply seated and require the expenditure of large 

 amounts of energy before they can be liberated. The 

 number of electrons which can be detached from an 

 atom of a metal in normal circumstances is prob- 

 ably quite small ; and it would be a grave difficulty if, 

 in order to explain metallic conductivity, we had to 

 assume that the number of electrons was largely in 

 excess of the number of atoms. 



Let us now proceed to calculate the number of elec- 

 trons required to explain metallic conduction. We 

 have seen that the specific conductivity of a metal is 

 equal to nfee, where n is the number of electrons per 

 unit volume, fe the drift of the electrons under unit 

 electric force (fe is called the mobility of the electron), 

 and e the charge on the electron. We know the specific 

 conductivity, and e, and hence we can determine 

 nh. I will, for the sake of definiteness, take the case 

 of silver at 0° C. For this metal, nfe = 3-9x 10^®. The 

 specific resistance gives us only the value of the pro- 

 duct nk. To determine n we must, from other 

 sources, form an estimate of fe. I will consider two 

 methods : the first, an indirect one based on values 

 of fe derived from experiments made on gases. The 

 drift fe, which can be compared with the terminal 

 velocity acquired by a weight falling through a viscous 

 liquid, depends upon the effects of the collisions which 

 the electrons make with the atoms of the metal 

 through which they are moving. Maxwell proved 

 that where a particle drifts through a gas with a 

 velocity tt, it loses momentum at the rate /3u ; j8 is a 

 coefficient directly proportional to the number of mole- 

 cules per unit volume of the gas through which the 



