﻿4 
  Dr. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  no 
  longer 
  describe 
  stationary 
  orbits. 
  W 
  will 
  continuously 
  

   increase, 
  and 
  the 
  electron 
  will 
  approach 
  the 
  nucleus 
  de- 
  

   scribing 
  orbits 
  of 
  smaller 
  and 
  smaller 
  dimensions, 
  and 
  with 
  

   greater 
  and 
  greater 
  frequency 
  ; 
  the 
  electron 
  on 
  the 
  average 
  

   gaining 
  in 
  kinetic 
  energy 
  at 
  the 
  same 
  time 
  as 
  the 
  whole 
  

   system 
  loses 
  energy. 
  This 
  process 
  will 
  go 
  on 
  until 
  the 
  

   dimensions 
  of 
  the 
  orbit 
  are 
  of 
  the 
  same 
  order 
  of 
  magni- 
  

   tude 
  as 
  the 
  dimensions 
  of 
  the 
  electron 
  or 
  those 
  of 
  the 
  nucleus. 
  

   A 
  simple 
  calculation 
  shows 
  that 
  the 
  energy 
  radiated 
  out 
  

   during 
  the 
  process 
  considered 
  will 
  be 
  enormously 
  great 
  

   compared 
  with 
  that 
  radiated 
  out 
  by 
  ordinary 
  molecular 
  

   processes. 
  

  

  It 
  is 
  obvious 
  that 
  the 
  behaviour 
  of 
  such 
  a 
  system 
  will 
  be 
  

   very 
  different 
  from 
  that 
  of 
  an 
  atomic 
  system 
  occurring 
  in 
  

   nature. 
  In 
  the 
  first 
  place, 
  the 
  actual 
  atoms 
  in 
  their 
  per- 
  

   manent 
  state 
  seem 
  to 
  have 
  absolutely 
  fixed 
  dimensions 
  and 
  

   frequencies. 
  Further, 
  if 
  we 
  consider 
  any 
  molecular 
  process, 
  

   the 
  result 
  seems 
  always 
  to 
  be 
  that 
  after 
  a 
  certain 
  amount 
  of 
  

   energy 
  characteristic 
  for 
  the 
  systems 
  in 
  question 
  is 
  radiated 
  

   out, 
  the 
  systems 
  will 
  again 
  settle 
  down 
  in 
  a 
  stable 
  state 
  of 
  

   equilibrium, 
  in 
  which 
  the 
  distances 
  apart 
  of 
  the 
  particles 
  are 
  

   of 
  the 
  same 
  order 
  of 
  magnitude 
  as 
  before 
  the 
  process. 
  

  

  Now 
  the 
  essential 
  point 
  in 
  Planck's 
  theory 
  of 
  radiation 
  is 
  

   that 
  the 
  energy 
  radiation 
  from 
  an 
  atomic 
  system 
  does 
  not 
  

   take 
  place 
  in 
  the 
  continuous 
  way 
  assumed 
  in 
  the 
  ordinary 
  

   electrodynamics, 
  but 
  that 
  it, 
  on 
  the 
  contrary, 
  takes 
  place 
  in 
  

   distinctly 
  separated 
  emissions, 
  the 
  amount 
  of 
  energy 
  radiated 
  

   out 
  from 
  an 
  atomic 
  vibrator 
  of 
  frequency 
  v 
  in 
  a 
  single 
  

   emission 
  being 
  equal 
  to 
  rhv, 
  where 
  t 
  is 
  an 
  entire 
  number, 
  

   and 
  h 
  is 
  a 
  universal 
  constant*. 
  

  

  Returning 
  to 
  the 
  simple 
  case 
  of 
  an 
  electron 
  and 
  a 
  positive 
  

   nucleus 
  considered 
  above, 
  let 
  us 
  assume 
  that 
  the 
  electron 
  at 
  

   the 
  beginning 
  of 
  the 
  interaction 
  with 
  the 
  nucleus 
  was 
  at 
  a 
  

   great 
  distance 
  apart 
  from 
  the 
  nucleus, 
  and 
  had 
  no 
  sensible 
  

   velocity 
  relative 
  to 
  the 
  latter. 
  Let 
  us 
  further 
  assume 
  that 
  

   the 
  electron 
  after 
  the 
  interaction 
  has 
  taken 
  place 
  has 
  

   settle°d 
  down 
  in 
  a 
  stationary 
  orbit 
  around 
  the 
  nucleus. 
  We 
  

   shall, 
  for 
  reasons 
  referred 
  to 
  later, 
  assume 
  that 
  the 
  orbit 
  in 
  

   question 
  is 
  circular 
  ; 
  this 
  assumption 
  will, 
  however, 
  make 
  no 
  

   alteration 
  in 
  the 
  calculations 
  for 
  systems 
  containing 
  only 
  a 
  

   single 
  electron. 
  

  

  Let 
  us 
  now 
  assume 
  that, 
  during 
  the 
  binding 
  of 
  the 
  electron, 
  

   a 
  homogeneous 
  radiation 
  is 
  emitted 
  of 
  a 
  frequency 
  v, 
  equal 
  

   to 
  half 
  the 
  frequency 
  of 
  revolution 
  of 
  the 
  electron 
  in 
  its 
  final 
  

  

  * 
  See 
  f. 
  irist., 
  M. 
  Planck, 
  Ann. 
  d. 
  Phys. 
  xxxi. 
  p. 
  758 
  (1910) 
  ; 
  xxxvii. 
  

   y. 
  6-42 
  (1912) 
  ; 
  Verh. 
  deutsch. 
  Phys. 
  Ges. 
  1911, 
  p. 
  138. 
  

  

  