﻿304 
  Dr. 
  L. 
  Vegard 
  on 
  the 
  X-Ray 
  Spectra 
  

  

  incident 
  rays 
  surpasses 
  that 
  o£ 
  the 
  L-radiation 
  of 
  the 
  sub- 
  

   stance 
  ; 
  and 
  Wagner 
  * 
  and 
  de 
  Broglie 
  t 
  have 
  by 
  means 
  of 
  

   the 
  reflexion 
  method 
  observed 
  two 
  absorption 
  bands 
  in 
  the 
  

   L-region 
  and 
  accurately 
  determined 
  the 
  sharp 
  edges 
  L^ 
  

   and 
  La 
  2) 
  which 
  have 
  just 
  the 
  sufficient 
  frequency 
  to 
  give 
  

   absorption. 
  The 
  measurements 
  of 
  Wagner 
  and 
  de 
  Broglie 
  

   show 
  that 
  the 
  frequency 
  La 
  x 
  is 
  just 
  a 
  little 
  greater 
  than 
  L 
  y 
  , 
  

   and 
  La 
  2 
  just 
  greater 
  than 
  L$. 
  

  

  If 
  we 
  stick 
  to 
  the 
  assumption 
  that 
  one 
  quantum 
  Jiv 
  is 
  

   sufficient 
  to 
  excite 
  radiation, 
  an 
  energy 
  quantum 
  hvy 
  or 
  hv 
  2 
  , 
  

   cannot 
  produce 
  L 
  a 
  if 
  this 
  line 
  is 
  emitted 
  by 
  an 
  electron 
  

   recombining 
  to 
  a 
  broken 
  K-ring. 
  Now 
  absorption 
  takes 
  

   place 
  when 
  the 
  radiation 
  falls 
  upon 
  atoms 
  in 
  the 
  normal 
  

   state, 
  and 
  we 
  caunot 
  assume 
  that 
  atoms 
  are 
  found 
  in 
  the 
  

   normal 
  state 
  with 
  a 
  broken 
  K-ring 
  aud 
  the 
  recombining 
  

   electron 
  in 
  some 
  secondary 
  circuit. 
  

  

  We 
  might 
  then 
  naturally 
  try 
  to 
  follow 
  up 
  the 
  idea 
  

   suggested 
  by 
  Bohr 
  to 
  explain 
  Kossel's 
  frequency 
  relations, 
  

   and 
  assume 
  the 
  electron 
  removed 
  from 
  the 
  K-ring 
  to 
  be 
  

   replaced 
  by 
  electrons 
  belonging 
  to 
  some 
  outer 
  system. 
  If, 
  

   however, 
  we 
  uphold 
  Bohr's 
  first 
  assumption 
  that 
  each 
  

  

  electron 
  in 
  the 
  normal 
  state 
  has 
  an 
  angular 
  momentum 
  ~— 
  , 
  

  

  LIT 
  

  

  there 
  seems 
  to 
  be 
  no 
  possibility 
  of 
  explaining 
  the 
  high- 
  

   frequency 
  spectra 
  by 
  interchange 
  of 
  electrons 
  from 
  outer 
  to 
  

   inner 
  systems. 
  

  

  Suppose 
  we 
  have 
  a 
  ring 
  of 
  p 
  electrons, 
  and 
  inside 
  this, 
  

   systems 
  which 
  are 
  made 
  up 
  of 
  r 
  electrons 
  surrounding 
  the 
  

   nucleus. 
  Outside 
  the 
  p-ring 
  follows 
  a 
  ring 
  of 
  q 
  electrons. 
  

   According 
  to 
  Bohr 
  J, 
  when 
  the 
  diameters 
  of 
  the 
  rings 
  are 
  

   not 
  nearly 
  equal, 
  the 
  forces 
  due 
  to 
  the 
  external 
  systems 
  can 
  

   be 
  neglected, 
  and 
  the 
  effect 
  of 
  inner 
  systems 
  is 
  approximately 
  

   equivalent 
  to 
  a 
  reduction 
  of 
  the 
  charge 
  of 
  the 
  nucleus 
  equal 
  

   to 
  the 
  charge 
  of 
  the 
  inner 
  electrons. 
  

  

  Hence 
  the 
  effective 
  nucleus 
  charge 
  of 
  the 
  p-ring 
  : 
  

  

  N 
  p 
  = 
  N-r; 
  

   of 
  the 
  q-ring 
  : 
  

  

  N 
  =N-(p 
  + 
  r). 
  

  

  We 
  now 
  regard 
  the 
  system 
  when 
  one 
  electron 
  is 
  removed 
  

   from 
  the 
  p-ring. 
  The 
  energy 
  of 
  the 
  p- 
  and 
  q-ring 
  is 
  then 
  : 
  

  

  ■W 
  2 
  = 
  W 
  p 
  ^ 
  + 
  W 
  q 
  = 
  ARj^-lXN^S^O' 
  + 
  ^N.-S,) 
  2 
  }. 
  

  

  * 
  Loc. 
  cit. 
  

   t 
  Loc. 
  cit. 
  

   \ 
  K 
  Bohr, 
  Phil. 
  Mag. 
  xxvi. 
  p. 
  476 
  (1913). 
  

  

  