﻿Theory of Spectral Series. G63 



We have also f> — m~Et/Y where V r = |7rR 3 is the volume of 

 the sphere, R its radius, and E is the charge in the sphere of 

 one atom. 



Also p = 2T/R and v= ^epfd7rc 2 M. 



Solving all these equations for v we easily obtain 



v = a — b'/m 2 , 

 where a' and V are constants as in the hydrogen spectrum. 



Some important facts receive a satisfactory explanation" 

 on the above theory. In flames, alkali metal salts only give 

 one or two lines. This is because the salt vapour is very 

 dilute and mixed with a relatively enormous amount of 

 flame gases, so that it is extremely unlikely that more than 

 one or two metal atoms should combine together. The 

 greatest number of lines in the series is observed when the 

 metal is heated in an exhausted tube. In this ease the 

 vapour is saturated and condensing in the cooler parts, so 

 that the conditions are very favourable to the formation of 

 molecules containing many atoms. 



The flame lines appear to be emitted by uncharged mole- 

 cules, so that for these lines we should have n=0. We can 

 write n + 1 or n + 2 for n in the formulae for v in order to 

 make them applicable when n = Q. 



The three hydrogen series are given by the formulae 



-»G- 



■i) 





m - 



= 3, 



4, 5, . 



"G- 



. 1 

 " (m -HO' 



w) 



m- 



- 9 



o, 1, . 



-(}- 



" m 2 ) 





m- 



= 4, 



5,6,. 



The chief series may be supposed due to uncharged mole- 

 cules containing an even number of atoms. The second 

 series to uncharged molecules containing an odd number of 

 atoms, and the third series to molecules each having lost 

 one electron and containing an even number of atoms. All 

 three series can then be represented by the formula 



N \(n + 2)» UW/ 



where n is the number of electrons lost by each molecule 

 and in the number of atoms per molecule. 



The first series due to the combination of ordinary mole- 

 cules H 2 is naturally the one usually obtained. 



