232 PHENOMENA, ATOMS, AND MOLECULES 



between these molecules and the underlying surface are very large com- 

 pared to those that act between adjacent molecules, then, for example, we 

 may conclude that the rate of evaporation of the adsorbed molecules will 

 be proportional to 0. This simple conception leads to an adsorption isotherm 

 which has been found to hold experimentally in a large number of cases. 

 However, if the forces that act between adjacent adsorbed molecules are not 

 negligible, there will be large deviations from this simple law, but the theory 

 may be easily extended to take into account such forces. The forces may 

 be those of attraction, or, if the molecules become dipoles as a result of the 

 adsorption, or if they become crowded, their interaction may cause re- 

 pulsive forces. 



The second important case (14) to be considered is that in which the 

 forces that hold the second layer of molecules are greater than those which 

 hold the first ; or, more generally, the case in which the forces acting 

 between adjacent adsorbed molecules are greater than those with which 

 each of these is held on the underlying surface. There is then great 

 difficulty in getting any appreciable number of molecules in the first ad- 

 sorbed layer, and single molecules or atoms or groups of molecules in the 

 first layer act as nuclei from which large aggregates or crystals may de- 

 velop. The condensation of cadmium or mercury vapor on cooled glass 

 surfaces is an example of this type. It is possible to formulate the problem 

 quantitatively and to express the number of nuclei that will form per 

 second as a function of temperature and pressure. The calculated values 

 are in good agreement with those obtained by experiment. If definite num- 

 bers of isolated copper atoms are evaporated on to a clean surface, each one 

 serves as a nucleus for the formation of cadmium crystals, when the tem- 

 perature of the surface and the pressure of the cadmium vapor are carefully 

 regulated, and thus by dark field illumination of the surface the copper 

 atoms can be directly counted. Some experiments made several years ago 

 by Mr. Harold Mott-Smith have shown that this method can be developed 

 to count atoms just as the C. T. R. Wilson method can be used to count 

 ions. 



In case th.e adsorbed atoms on a metallic surface are electrically charged 

 or acquire large dipole moments, electrical forces are brought into play 

 which may make the principle of independent action inapplicable. For 

 example, the rate of evaporation of electrons from a tungsten surface at 

 high temperature is enormously increased b}- the presence of adsorbed 

 thorium (15) or caesium (16) atoms on the surface. But the increase in 

 the number of electrons which evaporate is not even approximately pro- 

 portional to the amount of thorium or caesium which is present on the 

 surface. The same is true for the evaporation of positive caesium ions from 

 a tungsten surface. In both of these cases, the heat of evaporation of 



