344 Frequency of Electrons in the Neon Atom. 



Solving this equation in" r " we find that it is. satisfied 

 when r=6'l x 10 -9 cm. 



From equation (VI.) we may obtain an equation for w l : 



flX \ *- A j 39 _ Mr+l) _ i(r-l) _ \ 



Putting 6 = 4-774 x 10" 10 E.S.U. and m = 8*8 x lO" 28 grm. 

 we find that o) 1 = 6'28 X 10 ie radians/sec. 



Subtracting equation (II.) from equation (I.) we find 

 that 



»/)■ 



Substituting in this equation for e, r, I, s,m, and co^ we 

 find that &) 3 = 4'58 X 10 16 radians/sec. 



From this we can now find the frequency about the axes 

 ZZ' and YY' Oh) and about the axis XX' (n 3 ). 



Also we may calculate the. instantaneous linear velocities 

 of the electrons in the outer or inner shells. Taking the 

 case of the outer shell we determine the linear velocity due 

 to rotation about ZZ / or YY' M and due to rotation about 



xx' o 3 ). 



Tabulating the results we find that : — 



Frequency of the electrons about XX ; 



= ? 2 3 = -73xl0 16 . 

 Frequency of the electrons about YY / and ZZ' 



= ni=l-00xl0 16 . 

 Angular velocity of the electrons about XX' 



= o>' 3 = 4-58xlO l6 rad./sec. 

 Angular velocity of the electrons about YY' and ZZ' 



= © 1 = 6'28xl0 16 rad./sec. 

 Instantaneous linear velocity of the outer electrons 



about XX' = v 3 ^ 2-98 x 10 8 cms./sec. 

 Instantaneous linear velocity of the outer electrons 



about YY and ZZ / = v 1 = 4'08 x 10 8 cms./sec. 

 Instantaneous linear velocity of the inner electrons 

 about YY' and ZZ' = 3*83 x 10 8 cms./sec. 



The value of iC v" will be seen to be small compared with 

 the velocity of light, in consequence of which it follows that 

 we have committed no appreciable error in not correcting 

 for the variation of mass with velocity according to the 

 equation m v = m (l — y 2 /c 2 )* where "c" is the velocity of 

 light. 



October 15, 1921 



