﻿478 
  Dr. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  electrons 
  in 
  the 
  rings, 
  however, 
  there 
  will, 
  in 
  general, 
  he 
  

   more 
  than 
  one 
  configuration 
  which 
  will 
  satisfy 
  the 
  condition 
  

   of 
  the 
  angular 
  momentum 
  together 
  with 
  the 
  condition 
  of 
  

   stability. 
  

  

  In 
  § 
  3 
  and 
  § 
  4 
  it 
  will 
  be 
  shown 
  that, 
  on 
  the 
  general 
  view 
  

   of 
  the 
  formation 
  of 
  the 
  atoms, 
  we 
  are 
  led 
  to 
  indications 
  of 
  

   the 
  arrangement 
  of 
  the 
  electrons 
  in 
  the 
  rings 
  which 
  are 
  con- 
  

   sistent 
  with 
  those 
  suggested 
  by 
  the 
  chemical 
  properties 
  of 
  

   the 
  corresponding 
  element. 
  

  

  In 
  § 
  5 
  it 
  will 
  be 
  shown 
  that 
  it 
  is 
  possible 
  from 
  the 
  theory 
  

   to 
  calculate 
  the 
  minimum 
  velocity 
  of 
  cathode 
  rays 
  necessary 
  

   to 
  produce 
  the 
  characteristic 
  Rontgen 
  radiation 
  from 
  the 
  

   element, 
  and 
  that 
  this 
  is 
  in 
  approximate 
  agreement 
  with 
  the 
  

   experimental 
  values. 
  

  

  In 
  § 
  6 
  the 
  phenomena 
  of 
  radioactivity 
  will 
  be 
  briefly 
  con- 
  

   sidered 
  in 
  relation 
  to 
  the 
  theory. 
  

  

  § 
  2. 
  Configuration 
  and 
  Stability 
  of 
  the 
  Systems. 
  

  

  Let 
  us 
  consider 
  an 
  electron 
  of 
  charge 
  e 
  and 
  mass 
  m 
  which 
  

  

  moves 
  in 
  a 
  circular 
  orbit 
  of 
  radius 
  a 
  with 
  a 
  velocity 
  v 
  small 
  

  

  compared 
  with 
  the 
  velocity 
  of 
  light. 
  Let 
  us 
  denote 
  the 
  

  

  e 
  2 
  

   radial 
  force 
  acting 
  on 
  the 
  electrons 
  by 
  — 
  2 
  F 
  ; 
  F 
  will 
  in 
  

  

  general 
  be 
  dependent 
  on 
  a. 
  The 
  condition 
  of 
  dynamical 
  

   equilibrium 
  gives 
  

  

  m 
  v 
  2 
  e 
  2 
  T 
  ., 
  

  

  — 
  = 
  - 
  2 
  F 
  - 
  

  

  a 
  a- 
  

  

  Introducing 
  the 
  condition 
  of 
  universal 
  constancy 
  of 
  the 
  

   angular 
  momentum 
  of 
  the 
  electron, 
  we 
  have 
  

  

  h 
  

  

  mva= 
  — 
  . 
  

  

  Z7T 
  

  

  From 
  these 
  two 
  conditions 
  we 
  now 
  get 
  

  

  a= 
  f 
  F" 
  1 
  and 
  v=~¥; 
  . 
  . 
  (1) 
  

  

  and 
  for 
  the 
  frequency 
  of 
  revolution 
  co 
  consequently 
  

  

  4:7r 
  2 
  e 
  4 
  m 
  

  

  o) 
  = 
  

  

  ~h 
  6 
  

  

  F 
  2 
  (2) 
  

  

  If 
  F 
  is 
  known, 
  the 
  dimensions 
  and 
  frequency 
  of 
  the 
  corre- 
  

   sponding 
  orbit 
  are 
  simply 
  determined 
  by 
  (1) 
  and 
  (2). 
  For 
  a 
  

  

  