292 PHENOMENA, ATOMS, AND MOLECULES 



The question arises : how much cadmium could have condensed on the 

 bulb in one minute while the lower part of the bulb was at 60° C. ? 



The vapor pressure of cadmium has been determined by Barus (9) 

 between the temperatures 549° and 770° C. If the logarithms of the 

 pressures are plotted against the reciprocals of the temperature, a straight 

 line is obtained from which the following equation for the vapor pressure 

 (in bars) is obtained as a function of absolute temperature 



6060 , , 



\ogp= 11.77 f- . (0 



At 60° C. the vapor pressure of cadmium is of the order of magnitude 

 of 4 X io~^ bars. Now the number of molecules of gas which strike a square 

 centimeter of surface per second is 



n = 2.6sXio^^ P/\/MT (2) 



Substituting M = 112, T = 333°, and /? = 4 X 10"'^, we find that with 

 saturated cadmium vapor at 60° C, n == 5 X 10'^^ atoms per second per 

 square centimeter. 



The maximum number of atoms of cadmium which can condense in 

 ond minute on a spot cooled in Hquid air when the lower part of the bulb 

 is at 60° C. is therefore 3.0 X lo^^ atoms per square centimeter. The 

 diameter of a cadmium atom is approximately 3.1 X 10"^ cm., so that it 

 would require i.o X 10^^ atoms to cover i square centimeter with a single 

 layer of atoms. 



Therefore the deposit which forms in one minute with the vapor from 

 cadmium at 60°, contains only enough cadmium atoms to cover 3/1000 

 of the surface of the glass. Yet this deposit serves as an effective nucleus 

 for the formation of a visible deposit. 



If the lower part of the bulb is heated to 78° instead of 60°, the nucleus 

 formed by applying liquid air for one minute causes a visible deposit to 

 grow more rapidly (with the lower part of the bulb at 170°). But the 

 nucleus obtained with temperatures above about 78° are not any more 

 effective than those formed at 78°. 



A calculation similar to that above shows that the deposit formed in 

 one minute at 78° contains 2.5 X lo-^^ atoms per square centimeter, or 

 enough to cover 25/1000 of the surface. If we consider that the surface 

 of the glass contains elementary spaces each capable of holding one 

 cadmium atom, the chance that any given cadmium atom will be adjacent 

 to another is i — (i — 0.025)'^, or 0.16. When the surface is allowed to 

 warm up, the single atoms evaporate, but the pairs remain. The surface is 

 then covered to the extent of 16% of 25/1000, or 4/1000. About 2% of 



