﻿Distribution of Electrons in Na and CI Atoms. 441 



the atomic radius is expected to be. For any given value 

 of 6 we have 



</>l </>2 </>3 </>t $5 



+/^ (5) 



We chose from the experimental curve six values of 6 

 evenly spaced over the range of values at our disposal, and 

 for each of these values read from the curve the value of F. 

 Since definite radii have been assumed for the shells, the 



values of — j-^~ , etc., can be calculated for each value of 6. 

 9i 



Hence, for each value of 0, we have an equation involving 

 numerical coefficients and the quantities a, b, c, d, e,f\ so that 

 if six such equations are formed we may calculate these 

 quantities. 



If Z is the total number of electrons in the atom w r e have 



Z=a+b + c + d + e+f, ...... (6) 



and this will be taken as one of our equations (corresponding 

 to # — 0). In calculating the results for sodium and chlorine 

 we have assumed the atom to be ionized, and have taken 

 Zci = 18 and Z^ a = 10. 



It will be evident that this method of solution is somewhat 

 arbitrary, and that the results we get will depend on the 

 particular radii assumed for the shells. By assuming various 

 radii for the shells, however, and solving the simultaneous 

 equations for the number of electrons on each, we find that 

 the solutions agree in the number of electrons assigned to 

 various regions of the atom. 



As a test of the method of analysis, a model atom was 

 taken which w T as supposed to have electrons arranged as 

 follows : — 



2 on a shell 0"05 A radius. 

 5 „ „ 0-35 



3 „ „ 0-70 



The F curve for this model was calculated. Then the simul- 

 taneous equations for the electron distribution were solved, 

 just as if this curve had been one found experimentally. 

 This was done for two arbitrarily chosen sets of radii, taken 

 out to well beyond the shell at 0*70 A. 



