Complete Photoelectric Emission. 151 



are absorbed according to an exponential law, although such 

 an assumption can be regarded as only a very rough kind 

 of approximation when applied to the very slowly moving 

 electrons with which we are now dealing. In reality the 

 problem involved here is a very complex one : the stream of 

 electrons which travels in a given direction is depleted in 

 number both through the electrons being stopped and through 

 scattering, and it also suffers loss of energy. Little is known 

 definitely either as to the relative importance or as to the 

 precise effect of these different actions. In addition, the 

 electrons which escape lose most of their energy in passing- 

 through the surface ; although this fact need not prevent 

 their absorption being approximately exponential when they 

 are travelling in the interior. In any event, the exponential 

 law of internal absorption is the only assumption with which 

 it is possible to arrive at any result in the present state of the 

 subject. 



Consider first the case of a beam of light of definite 

 frequency incident normally, and let I be the energy crossing 

 unit area just within the surface of the metal in unit time. 

 Of the electrons ejected from atoms in a layer of infinitesimal 

 thickness perpendicular to the beam, let the proportion e~ ax 

 reach a parallel plane at a distance x from the layer. Let /3 

 be the coefficient of absorption of the light and N the 

 number of electrons ejected from the atoms of the metal when 

 unit energy is absorbed by them from the light. A calcu- 

 lation following well-known lines, which allows for the 

 absorption of both light and electrons in accordance with 

 the assumptions just indicated, shows that the number Nj of 

 electrons which reach unit area of the surface bounding the 

 metal in unit time is given by 



N '=^ N w 



We assume that a definite fraction, 7, of these escape from 

 the surface. In general 7 will be a function of the frequency 

 of! the light, and will be different for different materials. 



Using Planck's notation, the intensity i v dv of the isotropic 

 natural radiation inside the material, within the frequency 

 range from v to v-t-dv, is 



. , r 2 h?dv ' 



where r is the real part of the complex refractive index of 

 the material. A calculation similar to that leading to (2) 



