﻿and 
  the 
  Constitution 
  of 
  the 
  Atom. 
  325 
  

  

  As 
  I 
  haye 
  already 
  shown 
  in 
  previous 
  papers 
  *, 
  an 
  electron 
  

   moving 
  with 
  an 
  angular 
  momentum 
  which 
  is 
  a 
  fraction 
  of 
  

   h/27r 
  would 
  possess 
  a 
  very 
  great 
  kinetic 
  energy 
  and 
  move 
  

   in 
  an 
  orbit 
  with 
  very 
  small 
  diameter. 
  Now 
  according 
  to 
  

   Rutherford 
  f 
  and 
  his 
  collaborators 
  the 
  radioactive 
  elements 
  

   give 
  7-radiations 
  which 
  are 
  very 
  much 
  more 
  penetrating 
  than 
  

   those 
  of 
  the 
  K-series, 
  and 
  we 
  might 
  ask 
  whether 
  these 
  

   7-radiations 
  could 
  be 
  due 
  to 
  electronic 
  systems 
  moving 
  

   inside 
  the 
  K-ring 
  and 
  with 
  an 
  angular 
  momentum 
  

  

  n 
  h 
  

  

  m 
  2tt 
  ' 
  

  

  where 
  n 
  and 
  m 
  are 
  whole 
  numbers 
  and 
  

  

  m 
  > 
  n. 
  

  

  This 
  assumption, 
  however, 
  would 
  meet 
  with 
  the 
  difficulty 
  

   that 
  for 
  elements 
  of 
  high 
  atomic 
  numbers 
  the 
  velocity 
  would 
  

   soon 
  exceed 
  the 
  velocity 
  of 
  light. 
  The 
  velocity 
  of 
  an 
  electron 
  

  

  moving 
  inside 
  the 
  K-ring 
  with 
  an 
  angular 
  momentum- 
  

  

  would 
  be 
  27rm 
  

  

  v 
  = 
  2.10 
  8 
  (N-fl)m. 
  

  

  For 
  uranium 
  N 
  = 
  92, 
  and 
  if 
  v 
  is 
  to 
  be 
  smaller 
  than 
  the 
  

   velocity 
  of 
  light, 
  we 
  must 
  have 
  

  

  m 
  < 
  1-6. 
  

  

  It 
  might, 
  however, 
  be 
  argued 
  that 
  electrons 
  bound 
  up 
  in 
  

   the 
  atom 
  may 
  acquire 
  velocities 
  greater 
  than 
  that 
  of 
  light, 
  

   because 
  they 
  are 
  not 
  setting 
  up 
  any 
  radiating 
  electromagnetic 
  

   field 
  when 
  moving 
  in 
  a 
  stationary 
  state. 
  Of 
  course, 
  when 
  an 
  

   electron 
  is 
  set 
  free 
  in 
  the 
  form 
  of 
  a 
  /S-ray, 
  the 
  ordinary 
  

   electromagnetic 
  field 
  would 
  be 
  active 
  ; 
  the 
  electron 
  would 
  

   meet 
  a 
  sudden 
  retarding 
  impulse 
  which 
  at 
  once 
  would 
  reduce 
  

   its 
  velocity 
  to 
  less 
  than 
  that 
  of 
  light. 
  Or 
  we 
  might 
  say, 
  at 
  

   the 
  very 
  moment 
  of 
  release 
  the 
  electron 
  moves 
  according 
  

   to 
  the 
  principle 
  of 
  relativity, 
  which 
  makes 
  the 
  light 
  velocity 
  

   an 
  upper 
  limit. 
  

  

  The 
  line 
  X 
  = 
  0'072 
  . 
  10" 
  8 
  cm. 
  observed 
  by 
  Rutherford 
  and 
  

  

  * 
  L. 
  Vegard, 
  Phil. 
  Mag. 
  xxix. 
  p. 
  651 
  (1915) 
  ; 
  Ann. 
  d. 
  Phys. 
  liii. 
  p. 
  27 
  

   (1917). 
  

  

  t 
  E. 
  Rutherford 
  and 
  E. 
  N. 
  da 
  C. 
  Andrade, 
  Phil. 
  Mag. 
  xxviii. 
  p. 
  263 
  

   (1914). 
  

  

  Phil 
  Mag. 
  S. 
  6. 
  Vol. 
  35. 
  No. 
  208. 
  April 
  1918. 
  2 
  A 
  

  

  