﻿Theory of the Metallic State. 137 



In addition to this the electron space-lattice may be expected 



to have a large number of proper frequencies, which will 



modify the coefficient of reflexion. The proper frequencies 



must actually become most numerous in the region in which 



the deviations really commence. As will be shown, their 



9N 

 number should be — -» v 2 dv. 



Putting in the values assumed above this is of the order 



2 1 aa o 



' d\ \ being measured in Angstrom units, 10~ 10 metre. 



Thus for waves 1 mm. long there would still be 2 . 10 5 fre- 

 quencies per tenth-metre. Planck's infinite number of 

 resonators of different frequencies may thus have a physical 

 meaning, though in our case the number is confined to 3N, 

 and the frequencies are less than v m . 



Photoelectric Effect. — One would need special assumptions 

 to calculate the proper frequencies of the electron space- 

 lattice as Born and Karman did for atomic space-lattices. 

 Fortunately, however, we can use the method which Debye 

 proved was permissible as a first approximation for atomic 

 space-lattices, namely that used by Rayleigh in developing 

 the first radiation formula. According to this, the number 

 of proper frequencies in any interval dv is 4:7rp 3 ^fc*/ 2 v-dv 

 per cm. 3 . 



The factor /3 3 / 2 /C3/2 is 3 , q being the velocity of sound in 



the space-lattice, which, as shown above, is determined 

 by the atomic volume and the dielectric constant. Now if 

 light he allowed to fall on the metal, it may happen that a 

 sufficiently intense wave is induced in the space-lattice to 

 disrupt it and project an electron. This is the more likely 

 to happen the more proper frequencies there are in the 

 space-lattice in resonance with the incident light-wave. 

 For a given metal this number is proportional to v 2 . The 

 probability of a resonator getting the energy necessary 

 to free an electron hv is inversely proportional to v. 

 Thus the photoelectric current should be proportional to 

 the frequency, which is confirmed by experiments. On the 

 other hand, as shown above, other things being equal, the 

 number of proper frequencies of a given colour is inversely 

 proportional to the third power of the velocity of sound, or 

 roughly to the atomic volume. Thus the theory also accounts 

 for the observed fact that the photoelectric sensibility for rod 

 light is greatest with the alkali metals whose atomic volume 

 is greatest. This point of view disposes at once of the 



