﻿Structure 
  of 
  tlie 
  Atom. 
  797 
  

  

  A 
  cathode 
  ray 
  striking 
  against 
  an 
  atom 
  will 
  penetrate 
  into 
  

   it 
  until 
  stopped 
  by 
  the 
  repulsive 
  force, 
  then 
  from 
  the 
  action 
  

   of 
  this 
  force 
  it 
  will 
  be 
  repelled 
  and 
  ejected 
  from 
  the 
  atom. 
  

   As 
  long 
  as 
  the 
  corpuscle 
  is 
  inside 
  the 
  atom 
  it 
  will 
  be 
  

   accelerated 
  and 
  will 
  therefore 
  emit 
  radiation, 
  this 
  radiation 
  

   constitutes 
  the 
  Rontgen 
  rays. 
  

  

  If 
  the 
  cathode 
  particle 
  approaches 
  the 
  atom 
  radially, 
  its 
  

   equation 
  of 
  motion 
  is 
  

  

  d?x__Ce 
  

   m 
  dt 
  2 
  ~ 
  **? 
  

  

  where 
  x 
  is 
  the 
  distance 
  from 
  the 
  centre 
  at 
  the 
  time 
  t. 
  

   Integrating 
  this 
  equation 
  we 
  get 
  

  

  /dx\ 
  2 
  Ce 
  T72 
  

  

  where 
  V 
  is 
  the 
  velocity 
  of 
  the 
  corpuscle 
  before 
  it 
  strikes 
  the 
  

   atom. 
  

  

  Integrating 
  this 
  equation, 
  and 
  taking 
  £ 
  = 
  when 
  the 
  cor- 
  

   puscle 
  is 
  at 
  its 
  least 
  distance 
  from 
  the 
  centre 
  of 
  the 
  atom, 
  

   we 
  have 
  

  

  — 
  V2f2 
  i 
  (yg 
  —Y 
  2 
  (t 
  2 
  +- 
  } 
  

  

  We 
  see 
  from 
  this 
  that 
  the 
  time 
  during 
  which 
  the 
  cathode 
  

   particle 
  is 
  in 
  the 
  neighbourhood 
  of 
  the 
  place 
  where 
  it 
  is 
  

   nearest 
  to 
  the 
  centre 
  of 
  the 
  atom 
  (i. 
  e. 
  the 
  time 
  when 
  its 
  

   acceleration 
  is 
  greatest, 
  and 
  its 
  radiation 
  therefore 
  the 
  most 
  

   vigorous) 
  is 
  measured 
  by 
  

  

  -J, 
  

  

  Ue 
  

  

  \/Cem 
  = 
  

  

  \ 
  ri 
  "mV 
  2 
  y 
  ^' 
  l 
  ~irmN 
  2 
  ' 
  

  

  If 
  we 
  take 
  2ir 
  times 
  this 
  time 
  as 
  corresponding 
  to 
  the 
  time 
  

   of 
  vibration 
  of 
  the 
  Rontgen 
  rays, 
  n 
  the 
  " 
  frequency 
  " 
  of 
  the 
  

   rays 
  will 
  be 
  given 
  by 
  the 
  equation 
  

  

  mV 
  2 
  ?nV 
  2 
  

  

  or 
  — 
  —=z/m. 
  

  

  2h 
  

  

  Thus 
  Planck's 
  relation 
  holds 
  between 
  the 
  "frequency" 
  of 
  

   the 
  Rontgen 
  rays 
  and 
  the 
  kinetic 
  energy 
  of 
  the 
  cathode 
  

   particles 
  which 
  produce 
  them. 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  26. 
  No. 
  154. 
  Oct. 
  1913. 
  3 
  H 
  

  

  