﻿Structure 
  of 
  the 
  Atom. 
  795 
  

  

  this 
  work, 
  which 
  we 
  shall 
  denote 
  by 
  w, 
  is 
  proportional 
  to 
  1/T, 
  

   the 
  frequency 
  of 
  the 
  vibration 
  ; 
  if 
  1/T 
  = 
  n, 
  we 
  have 
  

  

  IV 
  = 
  7T 
  \Ji^tm 
  ,n. 
  

   We 
  shall 
  choose 
  C 
  so 
  that 
  

  

  it 
  sjGem 
  = 
  h, 
  

  

  where 
  A 
  is 
  Planck's 
  constant6*5 
  X 
  10~ 
  27 
  ; 
  putting 
  <? 
  = 
  4*7 
  x 
  10 
  -10 
  , 
  

   e/)n 
  = 
  5 
  m 
  'd 
  x 
  10 
  17 
  , 
  we 
  find 
  C 
  = 
  10~ 
  17 
  . 
  Let 
  us 
  now 
  consider 
  

   some 
  of* 
  the 
  properties 
  which 
  an 
  atom 
  in 
  which 
  there 
  are 
  

   forces 
  of 
  this 
  kind 
  would 
  possess. 
  Take, 
  first, 
  the 
  photo- 
  

   electric 
  effect. 
  Suppose 
  light 
  of 
  frequency 
  n 
  falls 
  upon 
  the 
  

   atom, 
  it 
  will 
  find 
  some 
  corpuscle 
  with 
  which 
  it 
  is 
  in 
  resonance 
  

   and 
  communicate 
  energy 
  to 
  it. 
  The 
  corpuscle 
  will 
  not 
  be 
  

   able 
  to 
  get 
  out 
  of 
  the 
  tube 
  of 
  attractive 
  force 
  in 
  which 
  it 
  is 
  

   situated 
  unless 
  it 
  receives 
  sufficient 
  energy 
  to 
  get 
  sideways 
  

   out 
  of 
  the 
  tube. 
  This 
  amount 
  of 
  energy 
  is, 
  as 
  we 
  have 
  seen, 
  

   Ae/a 
  = 
  Ce/a 
  2 
  = 
  2w. 
  When 
  the 
  energy 
  reaches 
  this 
  value 
  the 
  

   corpuscle 
  gets 
  out 
  of 
  the 
  tube, 
  its 
  kinetic 
  energy 
  being 
  

   exhausted 
  in 
  the 
  process. 
  It 
  now 
  comes 
  under 
  the 
  un- 
  

   controlled 
  action 
  of 
  the 
  repulsive 
  force 
  and 
  acquires 
  kinetic 
  

   energy, 
  the 
  kinetic 
  energy 
  when 
  the 
  corpuscle 
  leaves 
  the 
  

   atom 
  being 
  equal 
  to 
  the 
  work 
  done 
  by 
  the 
  repulsive 
  forces 
  

   on 
  the 
  corpuscle 
  as 
  it 
  moves 
  from 
  r 
  = 
  a 
  to 
  r 
  = 
  infinity 
  ; 
  this 
  

   work 
  is 
  equal 
  to 
  Qe/2a 
  2 
  = 
  w, 
  and 
  this, 
  as 
  we 
  have 
  seen, 
  is 
  equal 
  

   to 
  hn, 
  where 
  n 
  is 
  the 
  frequency 
  of 
  the 
  vibration 
  and 
  li 
  Planck's 
  

   constant. 
  Thus 
  we 
  see 
  that 
  the 
  kinetic 
  energy 
  with 
  which 
  

   the 
  corpuscle 
  is 
  expelled 
  is 
  proportional 
  to 
  the 
  frequency 
  of 
  

   the 
  light 
  and 
  is 
  equal 
  to 
  the 
  frequency 
  multiplied 
  by 
  Planck's 
  

   constant. 
  This 
  is 
  the 
  well-known 
  law 
  of 
  Photo-Electricity. 
  

  

  Though 
  the 
  energy 
  communicated 
  to 
  the 
  corpuscle 
  by 
  the 
  

   light 
  would, 
  in 
  the 
  first 
  instance, 
  appear 
  as 
  an 
  increased 
  radial 
  

   velocity, 
  we 
  can 
  easily 
  conceive 
  ways 
  by 
  which 
  the 
  radial 
  

   velocity 
  might, 
  without 
  loss 
  of 
  energy, 
  be 
  turned 
  into 
  a 
  side- 
  

   ways 
  velocity. 
  For 
  example, 
  if 
  when 
  the 
  corpuscle 
  was 
  

   passing 
  through 
  the 
  position 
  of 
  equilibrium 
  it 
  came 
  under 
  

   the 
  influence 
  of 
  some 
  casual 
  magnetic 
  force 
  at 
  right 
  angles 
  

   to 
  the 
  direction 
  in 
  which 
  it 
  w 
  r 
  as 
  moving, 
  the 
  corpuscle 
  would 
  

   be 
  deflected 
  and 
  the 
  radial 
  velocity 
  would 
  be 
  diminished, 
  

   while 
  the 
  sideways 
  velocity 
  would 
  increase 
  without 
  there 
  

   being 
  any 
  change 
  in 
  the 
  kinetic 
  energy. 
  Thus 
  we 
  see 
  that 
  

   it 
  is 
  quite 
  possible 
  for 
  a 
  corpuscle 
  when 
  acted 
  upon 
  by 
  

   light 
  to 
  continually 
  acquire 
  kinetic 
  energy 
  without 
  any 
  

   commensurate 
  increase 
  in 
  the 
  amplitude 
  of 
  the 
  radial 
  

   displacement. 
  

  

  