﻿214 Theoretical Aspects of the Neon Spectrum. 



large number of lines will be obtained depending upon the 

 state of the atom when one or more electrons are removed 

 from it. There is another form of ionization which is worthy 

 of consideration. That is the case in which an electron has 

 succeeded in penetrating the atom and reached the nucleus, 

 thus temporarily reducing the positive charge and therefore 

 giving a negative ion. 



The fundamental mathematical expressions for such a case 

 are found by extending our formulae for the neutral atom 

 for the case where the charge on the nucleus is ' n ' instead 

 of ten. 



The angular velocities about the several axes will remain 

 unchanged ; and so only two equations will be required to 

 determine the new values assumed by ' c ' and ' r,' the radii 

 of the outer and inner shells respectively. 



We have three available equations ; and expressing them 

 in the notation previously used, we obtain : 



(4w-l> 2 Z e 2 eH_ e 2 (r + l) e 2 (r~l) 



4c 3 " ~ U 2 + 2s* + [ (r +■ l) 2 + s 2 ] *' 2 ~~ [ (r - I) 2 + s 2 ] 3 / 2 



+ 2mo?l, .... (la.) 



(4n-l> 2 / e 2 eH e 2 l eH 



4c 3 ~ - 4/ 2 + 2? + [(r + iy + s 2 y/ 2+ [{r-l) 2 + s 2 ] s < 2 



-hmco 1 2 l-\-?nco :i 2 l, . . (II a.) 



ne* <ke 2 (r + l) 4<? 2 (r-Q 



+ Vt*. 7\2 i .213/2 + 



+ 2mft> 1 V, . . . .(Ilia.) 



which are obtained from equations (I.), (II.), and (IV.), 

 replacing the nucleic charge of ' 10<? ' by ' ne 9 and remem- 

 bering that &) 1 = G) 2 . 



The result of the alteration will be that the electrons will 

 move further out from the nucleus, since i n } is of necessity 

 less than ten. In consequence of this, the frequency of the 

 spectral lines produced by such ionized atoms will be of a 

 lower frequency than those produced by the neutral atom. 

 There will in consequence be a larger number of lines in the 

 part of the spectrum of greater wave-length. It is for this 

 reason that there are so many lines in the orange, and red 

 in the case of neon. 



Feb. 13, 1922. 



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