﻿46 Dr. H. Stanley Allen on the 



Substituting the value of a) derived from the quadratic 

 equation (3) we find 



w 27rWEVr A // A V A""] 3 , in 



W = ^^j ? — L2MB±VV2MEJ ~MEJ " (11) 



We now proceed to express the quantity inside the square 

 bracket, which may be denoted by x, as a continued fraction 



of the form x = 7 .... 



a+ u+ a + 



Since x= — - -. , x is the root of the quadratic equation 



a t- + x 



ax 2 + abx — b = 0, and therefore 



/> \ 2 b 

 + : 



9' 



So we find a — 1 and b = 

 Hence 



A 

 ME* 



W = 



2TT 2 me 2 Wa 



rVr 



or approximately 



w = 



1+ 



A 



ME" 1 " 



'27r' 2 l 



[1-¥T 



(12) 



(13) 



An examination of the numerical magnitude of the 

 quantities involved in the term ME/A shows that in general 

 the value of this term must be less than unity. 



In Bohr's theory monochromatic radiation is supposed to 

 be emitted during the passage from one steady state of 

 motion of the electron to another. How this change takes 

 place is left undetermined, but it is assumed that the amount 

 of energy radiated, that is the difference between the energy 

 in the first orbit and that in the second, is exactly one 

 quantum. That is 



hv = SW = W 2 -W 1 (14) 



The frequency of the radiation is therefore given by 



2ttWE 2 fa 2 x 2 ? ' W\ ,_ 



v= v xw-^ry' ' ' (15) 



or approximately 



2w 2 me 2 E 2 f a 2 a l ~) , . 



A :5 



*-S 



[>%}• 



