﻿20 
  Dr. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  § 
  5. 
  The 
  permanent 
  State 
  of 
  an 
  Atomic 
  System. 
  

  

  We 
  shall 
  now 
  return 
  to 
  the 
  main 
  object 
  of 
  this 
  paper 
  — 
  the 
  

  

  discussion 
  of 
  the 
  " 
  permanent 
  " 
  state 
  of 
  a 
  system 
  consisting 
  

  

  of 
  nuclei 
  and 
  bound 
  electrons. 
  For 
  a 
  system 
  consisting 
  of 
  a 
  

  

  nucleus 
  and 
  an 
  electron 
  rotating 
  round 
  it, 
  this 
  state 
  is, 
  

  

  according 
  to 
  the 
  above, 
  determined 
  by 
  the 
  condition 
  that 
  the 
  

  

  angular 
  momentum 
  of 
  the 
  electron 
  round 
  the 
  nucleus 
  is 
  

  

  h 
  

   equal 
  to 
  ^— 
  . 
  

  

  On 
  the 
  theory 
  of 
  this 
  paper 
  the 
  only 
  neutral 
  atom 
  which 
  

   contains 
  a 
  single 
  electron 
  is 
  the 
  hydrogen 
  atom. 
  The 
  per- 
  

   manent 
  state 
  of 
  this 
  atom 
  should 
  correspond 
  to 
  the 
  values 
  of 
  

   a 
  and 
  co 
  calculated 
  on 
  p. 
  5. 
  Unfortunately, 
  however, 
  we 
  

   know 
  very 
  little 
  of 
  the 
  behaviour 
  of 
  hydrogen 
  atoms 
  on 
  

   account 
  of 
  the 
  small 
  dissociation 
  of 
  hydrogen 
  molecules 
  at 
  

   ordinary 
  temperatures. 
  In 
  order 
  to 
  get 
  a 
  closer 
  comparison 
  

   with 
  experiments, 
  it 
  is 
  necessary 
  to 
  consider 
  more 
  complicated 
  

   systems. 
  

  

  Considering 
  systems 
  in 
  which 
  more 
  electrons 
  are 
  bound 
  by 
  

   a 
  positive 
  nucleus, 
  a 
  Configuration 
  of 
  the 
  electrons 
  which 
  

   presents 
  itself 
  as 
  a 
  permanent 
  state 
  is 
  one 
  in 
  which 
  the 
  

   electrons 
  are 
  arranged 
  in 
  a 
  ring 
  round 
  the 
  nucleus. 
  In 
  the 
  

   discussion 
  of 
  this 
  problem 
  on 
  the 
  basis 
  of 
  the 
  ordinary 
  

   electrodynamics, 
  we 
  meet 
  — 
  apart 
  from 
  the 
  question 
  of 
  the 
  

   energy 
  radiation 
  — 
  with 
  new 
  difficulties 
  due 
  to 
  the 
  question 
  

   of 
  the 
  stability 
  of 
  the 
  ring. 
  Disregarding 
  for 
  a 
  moment 
  this 
  

   latter 
  difficulty, 
  we 
  shall 
  first 
  consider 
  the 
  dimensions 
  and 
  

   frequency 
  of 
  the 
  systems 
  in 
  relation 
  to 
  Planck's 
  theory 
  of 
  

   radiation. 
  

  

  Let 
  us 
  consider 
  a 
  ring 
  consisting 
  of 
  n 
  electrons 
  rotating 
  

   round 
  a 
  nucleus 
  of 
  charge 
  E, 
  the 
  electrons 
  being 
  arranged 
  

   at 
  equal 
  angular 
  intervals 
  around 
  the 
  circumference 
  of 
  a 
  

   circle 
  of 
  radius 
  a. 
  

  

  The 
  total 
  potential 
  energy 
  of 
  the 
  system 
  consisting 
  of 
  the 
  

   electrons 
  and 
  the 
  nucleus 
  is 
  

  

  wh 
  

  

  ere 
  

  

  *=■-?<■-«*, 
  

  

  l^' 
  1 
  S7T 
  

  

  = 
  7 
  2, 
  cosec 
  — 
  , 
  

   4 
  s 
  =i 
  n 
  

  

  For 
  the 
  radial 
  force 
  exerted 
  on 
  an 
  electron 
  by 
  the 
  nucleus 
  

   and 
  the 
  other 
  electrons 
  we 
  get 
  

  

  Jb 
  = 
  -j- 
  = 
  ,&—esn). 
  

  

  n 
  da 
  or 
  ( 
  

  

  