﻿'. 
  N. 
  Bohr 
  on 
  the 
  Constitution 
  

  

  of 
  the 
  more 
  special 
  assumptions, 
  viz. 
  that 
  the 
  different 
  

   stationary 
  states 
  correspond 
  to 
  the 
  emission 
  of 
  a 
  different 
  

   number 
  of 
  Planck's 
  energy-quanta, 
  and 
  that 
  the 
  frequency 
  of 
  

   the 
  radiation 
  emitted 
  during 
  the 
  passing 
  of 
  the 
  system 
  from 
  

   a 
  state 
  in 
  which 
  no 
  energy 
  is 
  yet 
  radiated 
  out 
  to 
  one 
  of 
  the 
  

   stationary 
  states, 
  is 
  equal 
  to 
  half 
  the 
  frequency 
  of 
  revolution 
  

   of 
  the 
  electron 
  in 
  the 
  latter 
  state. 
  We 
  can, 
  however 
  (see 
  

   § 
  3), 
  also 
  arrive 
  at 
  the 
  expressions 
  (3) 
  for 
  the 
  stationary 
  

   states 
  by 
  using 
  assumptions 
  of 
  somewhat 
  different 
  form. 
  

   We 
  shall, 
  therefore, 
  postpone 
  the 
  discussion 
  of 
  the 
  special 
  

   assumptions, 
  and 
  first 
  show 
  how 
  by 
  the 
  help 
  of 
  the 
  above 
  

   principal 
  assumptions, 
  and 
  of 
  the 
  expressions 
  (3) 
  for 
  the 
  

   stationary 
  states, 
  we 
  can 
  account 
  for 
  the 
  line-spectrum 
  of 
  

   hydrogen. 
  

  

  § 
  2. 
  Emission 
  of 
  Line-spectra. 
  

  

  Spectrum 
  of 
  Hydrogen. 
  — 
  General 
  evidence 
  indicates 
  that 
  

   an 
  atom 
  of 
  hydrogen 
  consists 
  simply 
  of 
  a 
  single 
  electron 
  

   rotating 
  round 
  a 
  positive 
  nucleus 
  of 
  charge 
  e*. 
  The 
  re- 
  

   formation 
  of 
  a 
  hydrogen 
  atom, 
  when 
  the 
  electron 
  has 
  been 
  

   removed 
  to 
  great 
  distances 
  away 
  from 
  the 
  nucleus 
  — 
  e. 
  g. 
  by 
  

   the 
  effect 
  of 
  electrical 
  discharge 
  in 
  a 
  vacuum 
  tube 
  — 
  will 
  

   accordingly 
  correspond 
  to 
  the 
  binding 
  of 
  an 
  electron 
  by 
  a 
  

   positive 
  nucleus 
  considered 
  on 
  p. 
  5. 
  If 
  in 
  (3) 
  we 
  put 
  E 
  = 
  ^, 
  

   we 
  get 
  for 
  the 
  total 
  amount 
  of 
  energy 
  radiated 
  out 
  by 
  the 
  

   formation 
  of 
  one 
  of 
  the 
  stationary 
  states, 
  

  

  W,= 
  

  

  hh 
  2 
  

  

  The 
  amount 
  of 
  energy 
  emitted 
  by 
  the 
  passing 
  of 
  the 
  

   system 
  from 
  a 
  state 
  corresponding 
  to 
  t 
  = 
  Tj 
  to 
  one 
  corre- 
  

   sponding 
  to 
  t 
  = 
  t 
  2 
  , 
  is 
  consequently 
  

  

  If 
  now 
  we 
  suppose 
  that 
  the 
  radiation 
  in 
  question 
  is 
  homo- 
  

   geneous, 
  and 
  that 
  the 
  amount 
  of 
  energy 
  emitted 
  is 
  equal 
  to 
  

   hv, 
  where 
  v 
  is 
  the 
  frequency 
  of 
  the 
  radiation, 
  we 
  get 
  

  

  W 
  T 
  -Wr=hv, 
  

  

  * 
  See 
  f. 
  inst. 
  N. 
  Bohr, 
  Phil. 
  Mag. 
  xxy. 
  p. 
  24 
  (1913). 
  The 
  conclusion 
  

   drawn 
  in 
  the 
  paper 
  cited 
  is 
  strongly 
  supported 
  by 
  the 
  fact 
  that 
  hydrogen, 
  

   in 
  the 
  experiments 
  on 
  positive 
  rays 
  of 
  Sir 
  J. 
  J. 
  Thomson, 
  is 
  the 
  only 
  

   element 
  which 
  never 
  occurs 
  with 
  a 
  positive 
  charge 
  corresponding 
  to 
  the 
  

   loss 
  of 
  more 
  than 
  one 
  electron 
  (comp. 
  Phil. 
  Mag. 
  xxiv. 
  p. 
  672 
  (1912)). 
  

  

  