﻿226 
  ANNUAL 
  EEPORT 
  SMITHSONIAN 
  INSTITUTION, 
  1929 
  

  

  is 
  not 
  quite 
  as 
  sharp 
  as 
  the 
  photograph 
  taken 
  with 
  the 
  X 
  rays, 
  we 
  can 
  

   see 
  distinctly 
  the 
  central 
  image, 
  and. 
  several 
  rings 
  of 
  diffracted 
  elec- 
  

   trons. 
  If 
  Plate 
  5, 
  Figure 
  2, 
  demonstrated 
  the 
  wave 
  character 
  of 
  X 
  

   rays, 
  does 
  not 
  Plate 
  5, 
  Figure 
  3, 
  prove 
  equallj^ 
  definitely 
  the 
  wave 
  

   character 
  of 
  electrons? 
  

  

  We 
  are 
  thus 
  faced 
  with 
  the 
  fact 
  that 
  the 
  fundamental 
  things 
  in 
  

   nature, 
  matter, 
  and 
  radiation, 
  present 
  to 
  us 
  a 
  dual 
  aspect. 
  In 
  certain 
  

   ways 
  they 
  act 
  like 
  particles, 
  in 
  others 
  like 
  waves. 
  The 
  experiments 
  

   teU 
  us 
  that 
  we 
  must 
  seize 
  both 
  horns 
  of 
  the 
  dilemma. 
  

  

  A 
  SUGGESTED 
  SOLUTION 
  

  

  During 
  the 
  last 
  year 
  or 
  two 
  there 
  has 
  gradually 
  developed 
  a 
  solution 
  

   of 
  this 
  puzzle, 
  which 
  though 
  at 
  first 
  rather 
  difficult 
  to 
  grasp, 
  seems 
  to 
  be 
  

   free 
  from 
  logical 
  contradictions 
  and 
  essentially 
  capable 
  of 
  describing 
  

   the 
  phenomena 
  which 
  our 
  experiments 
  reveal. 
  A 
  mere 
  mention 
  of 
  

   some 
  of 
  the 
  names 
  connected 
  with 
  tliis 
  development 
  will 
  suggest 
  some- 
  

   thing 
  of 
  the 
  complexities 
  through 
  which 
  the 
  theory 
  has 
  gradually 
  

   gone. 
  There 
  are 
  Duane, 
  Slater, 
  and 
  Swann 
  in 
  this 
  country, 
  De 
  

   Broglie 
  in 
  France, 
  Heisenberg 
  and 
  Schrodinger 
  in 
  Germany, 
  Bohr 
  in 
  

   Denmark, 
  Dirac 
  in 
  England, 
  among 
  others, 
  who 
  have 
  contributed 
  to 
  

   the 
  growth 
  of 
  this 
  explanation. 
  

  

  The 
  point 
  of 
  departure 
  of 
  this 
  theorj^ 
  is 
  the 
  mathematical 
  proof 
  

   that 
  the 
  dynamics 
  of 
  a 
  particle 
  may 
  be 
  expressed 
  in 
  terms 
  of 
  the 
  pro- 
  

   pagation 
  of 
  a 
  group 
  of 
  waves. 
  That 
  is, 
  the 
  particle 
  may 
  be 
  replaced 
  

   by 
  a 
  wave 
  train 
  — 
  the 
  two, 
  so 
  far 
  as 
  their 
  motion 
  is 
  concerned, 
  may 
  be 
  

   made 
  mathematically 
  equivalent. 
  The 
  motion 
  of 
  a 
  particle 
  such 
  as 
  

   an 
  electron 
  or 
  a 
  photon 
  in 
  a 
  straight 
  line 
  is 
  represented 
  by 
  a 
  plane 
  

   wave. 
  The 
  wave 
  length 
  is 
  determined 
  by 
  the 
  momentum 
  of 
  the 
  

   particle, 
  and 
  the 
  length 
  of 
  the 
  train 
  of 
  waves 
  by 
  the 
  precision 
  with 
  

   which 
  the 
  momentum 
  is 
  known. 
  In 
  the 
  case 
  of 
  the 
  photon, 
  this 
  

   wave 
  may 
  be 
  taken 
  as 
  the 
  ordinary 
  electromagnetic 
  wave. 
  The 
  

   wave 
  corresponding 
  to 
  the 
  moving 
  electron 
  is 
  called 
  by 
  the 
  name 
  of 
  

   its 
  inventor, 
  a 
  De 
  Broglie 
  wave. 
  

  

  Consider, 
  for 
  example, 
  the 
  deflection 
  of 
  a 
  photon 
  by 
  an 
  electron 
  on 
  

   this 
  basis, 
  that 
  is, 
  the 
  scattering 
  of 
  an 
  X 
  ray. 
  The 
  incident 
  photon 
  

   is 
  represented 
  by 
  a 
  train 
  of 
  plane 
  electromagnetic 
  waves. 
  The 
  recoU- 
  

   ing 
  electron 
  is 
  lilvcwise 
  represented 
  by 
  a 
  train 
  of 
  plane 
  De 
  Broglie 
  waves 
  

   propagated 
  in 
  the 
  direction 
  of 
  recoil. 
  These 
  electron 
  waves 
  form 
  a 
  

   kind 
  of 
  grating 
  by 
  which 
  the 
  incident 
  electromagnetic 
  waves 
  are 
  

   diffracted. 
  The 
  diffracted 
  waves 
  represent 
  in 
  turn 
  the 
  deflected 
  

   photon. 
  They 
  are 
  increased 
  in 
  wave 
  length 
  by 
  the 
  dift'raction 
  because 
  

   the 
  grating 
  is 
  receding, 
  resulting 
  in 
  a 
  Doppler 
  effect. 
  

  

  In 
  this 
  solution 
  of 
  the 
  problem 
  we 
  note 
  that 
  before 
  we 
  could 
  deter- 
  

   mine 
  the 
  du'ection 
  in 
  which 
  the 
  X 
  ray 
  was 
  to 
  be 
  deflected, 
  it 
  was 
  

   necessary 
  to 
  know 
  the 
  direction 
  of 
  recoil 
  of 
  the 
  electron. 
  In 
  this 
  

  

  