600 Di fusion and Valency of the Radio-elements. 



this question, which is of great theoretical interest, we must 

 consider the factors that are operative in the diffusion of an 

 ion in infinitely dilute solution. 



We will compare the velocities of diffusion of: two ions 

 which have the same radius but different masses, under- 

 standing by " mass " the sum of the masses of the atom and 

 its hydration molecules, and b}^ "radius of the ion" the 

 radius of the atom plus surrounding water molecules. Ions 

 of chemically identical elements have the property that the 

 radii of the atoms are equal *, likewise their degrees of 

 hydration, and only their masses, that is the masses of the 

 nuclei, are different. 



In comparing the diffusion velocities of such cases we have 

 two extremes to consider. In the first case, the radius and 

 the mass of the diffusing particles are very great in com- 

 parison with those of the molecules of the solvent, and the 

 equation of Einstein and Smoluchowski f is valid, i. e., 



N 67rkr ' 



The mass of the diffusing particles does not come in this 

 formula, and the gravitational force vanishes compared with 

 the osmotic force, and therefore in this extreme case the 

 chemically identical elements must diffuse with exactly 

 the same velocity in spite of the irdifferent masses. 



The other extreme case is, that the radius and the mass of 

 the diffusing particles are very small in comparison with 

 those of the solvent, and here, as in the case of diffusion of 

 gas molecules in gases, the diffusion velocities are inversely 

 proportional to the square root of the mass, and therefore we 

 can expect a -J per cent, difference in the diffusion constant 

 for 1 per cent, difference in the atomic weight. 



The case of the two chemically identical elements such as 

 radium D and lead corresponds to neither of the above cases, 

 since the mass and the radius are not so large relatively as 

 demanded by the first case nor so small as required by the 

 second case. However, it is much nearer those conditions 

 for which the Einstein-Smoluchowski formula holds, in which 

 the mass does not influence the velocity of diffusion, and 

 therefore the possibility of separating chemically identical 

 elements by diffusion liquid in solution is very slight. 



In the case of the diffusion of these substances in the 

 gaseous form, the second of the above considerations is 



* N. Bohr, Phil. Mag. Sept. 1913. 



t A. Einstein, Ann. der Physik, xvii. p. 555 (1905). 



