﻿of 
  Atoms 
  and 
  Molecules. 
  5 
  

  

  orbit 
  ; 
  then, 
  from 
  Planck's 
  theory, 
  we 
  might 
  expect, 
  that 
  the 
  

  

  amount 
  of 
  energy 
  emitted 
  by 
  the 
  process 
  considered 
  is 
  equal 
  

  

  to 
  tJiv, 
  where 
  h 
  is 
  Planck's 
  constant 
  and 
  r 
  an 
  entire 
  number. 
  

  

  If 
  we 
  assume 
  that 
  the 
  radiation 
  emitted 
  is 
  homogeneous, 
  the 
  

  

  second 
  assumption 
  concerning 
  the 
  frequency 
  of 
  the 
  radiation 
  

  

  suggests 
  itself, 
  since 
  the 
  frequency 
  of 
  revolution 
  of 
  the 
  

  

  electron 
  at 
  the 
  beginning 
  of 
  the 
  emission 
  is 
  0. 
  The 
  question, 
  

  

  however, 
  of 
  the 
  rigorous 
  validity 
  of 
  both 
  assumptions, 
  and 
  

  

  also 
  of 
  the 
  application 
  made 
  of 
  Planck's 
  theory, 
  will 
  be 
  more 
  

  

  closely 
  discussed 
  in 
  § 
  3. 
  

  

  Putting 
  w 
  7 
  co 
  

  

  » 
  VV=T/i 
  9 
  -, 
  (2) 
  

  

  we 
  get 
  by 
  help 
  of 
  the 
  formula 
  (1) 
  

  

  ±irhne*W 
  n 
  tVi 
  2 
  

  

  ,,. 
  > 
  « 
  = 
  

  

  T 
  

  

  A\ 
  = 
  275—3 
  co= 
  — 
  — 
  , 
  2a=-- 
  r 
  - 
  .. 
  (3) 
  

  

  - 
  2 
  /r 
  t 
  6 
  Il 
  6 
  27r 
  l 
  mehj 
  

  

  If 
  in 
  these 
  expressions 
  we 
  give 
  r 
  different 
  values, 
  we 
  get 
  

   a 
  series 
  of 
  values 
  for 
  W, 
  co, 
  and 
  a 
  corresponding 
  to 
  a 
  series 
  

   of 
  configurations 
  of 
  the 
  system. 
  According 
  to 
  the 
  above 
  

   considerations, 
  we 
  are 
  led 
  to 
  assume 
  that 
  these 
  configurations 
  

   will 
  correspond 
  to 
  states 
  of 
  the 
  system 
  in 
  which 
  there 
  is 
  

   no 
  radiation 
  of 
  energy; 
  states 
  which 
  consequently 
  will 
  be 
  

   stationary 
  as 
  long 
  as 
  the 
  system 
  is 
  not 
  disturbed 
  from 
  out- 
  

   side. 
  We 
  see 
  that 
  the 
  value 
  of 
  "W 
  is 
  greatest 
  if 
  t 
  has 
  its 
  

   smallest 
  value 
  1. 
  This 
  case 
  will 
  therefore 
  correspond 
  to 
  

   the 
  most 
  stable 
  state 
  of 
  the 
  system, 
  i. 
  e. 
  will 
  correspond 
  to 
  

   the 
  binding 
  of 
  the 
  electron 
  for 
  the 
  breaking 
  up 
  of 
  which 
  the 
  

   greatest 
  amount 
  of 
  energy 
  is 
  required. 
  

  

  Putting 
  in 
  the 
  above 
  expressions 
  t=1 
  and 
  E 
  = 
  £, 
  and 
  

   introducing 
  the 
  experimental 
  values 
  

  

  <? 
  = 
  4-7.10- 
  10 
  ; 
  - 
  = 
  5'31.10 
  17 
  , 
  A 
  = 
  6-5.10- 
  27 
  , 
  

   m 
  

  

  we 
  get 
  

  

  1 
  W 
  

  

  2a=l-l 
  . 
  10" 
  8 
  cm., 
  co 
  = 
  6~2 
  . 
  10 
  15 
  , 
  - 
  =13 
  volt. 
  

  

  sec. 
  e 
  

  

  We 
  see 
  that 
  these 
  values 
  are 
  of 
  the 
  same 
  order 
  of 
  magni- 
  

   tude 
  as 
  the 
  linear 
  dimensions 
  of 
  the 
  atoms, 
  the 
  optical 
  

   frequencies, 
  and 
  the 
  ionization-potentials. 
  

  

  The 
  general 
  importance 
  of 
  Planck's 
  theory 
  for 
  the 
  dis- 
  

   cussion 
  of 
  the 
  behaviour 
  of 
  atomic 
  systems 
  was 
  originally 
  

   pointed 
  out 
  by 
  Einstein*. 
  The 
  considerations 
  of 
  Einstein 
  

  

  * 
  A. 
  Einstein, 
  Ann. 
  d. 
  Fhys. 
  xvii. 
  p. 
  132 
  (1905): 
  xx. 
  p. 
  199 
  (1906); 
  

   xxii. 
  p. 
  180(1907). 
  

  

  