﻿of 
  Atoms 
  and 
  Molecules, 
  499 
  

  

  with 
  experiments 
  if 
  we 
  consider 
  the 
  innermost 
  ring 
  and 
  as 
  a 
  

   first 
  approximation 
  neglect 
  the 
  repulsion 
  from 
  the 
  electrons 
  

   in 
  comparison 
  with 
  the 
  attraction 
  of 
  the 
  nucleus. 
  Let 
  us 
  

   consider 
  a 
  simple 
  system 
  consisting 
  of 
  a 
  bound 
  electron 
  

   rotating 
  in 
  a 
  circular 
  orbit 
  round 
  a 
  positive 
  nucleus 
  of 
  

   charge 
  Ne. 
  From 
  the 
  expressions 
  (1) 
  on 
  p. 
  478 
  we 
  get 
  for 
  

   the 
  velocity 
  of 
  the 
  electron, 
  putting 
  F 
  = 
  N, 
  

  

  i7=?^N=2-1.10 
  8 
  K 
  

   /i 
  

  

  The 
  total 
  energy 
  to 
  he 
  transferred 
  to 
  the 
  system 
  in 
  order 
  

   to 
  remove 
  the 
  electron 
  to 
  an 
  infinite 
  distance 
  from 
  the 
  

   nucleus 
  is 
  equal 
  to 
  the 
  kinetic 
  energy 
  of 
  the 
  bound 
  electron. 
  

   If, 
  therefore, 
  the 
  electron 
  is 
  removed 
  to 
  a 
  great 
  distance 
  

   from 
  the 
  nucleus 
  by 
  impact 
  of 
  another 
  rapidly 
  moving 
  elec- 
  

   tron, 
  the 
  smallest 
  kinetic 
  energy 
  possessed 
  by 
  the 
  latter 
  

   when 
  at 
  a 
  great 
  distance 
  from 
  the 
  nucleus 
  must 
  necessarily 
  

   be 
  equal 
  to 
  the 
  kinetic 
  energy 
  of 
  the 
  bound 
  electron 
  before 
  

   the 
  collision. 
  The 
  velocity 
  of 
  the 
  free 
  electron 
  therefore 
  

   must 
  be 
  at 
  least 
  equal 
  to 
  v. 
  

  

  According 
  to 
  Whiddington's 
  experiments 
  * 
  the 
  velocity 
  of 
  

   cathode 
  rays 
  just 
  able 
  to 
  produce 
  the 
  characteristic 
  Rbntgen 
  

   radiation 
  of 
  the 
  so-called 
  K-type 
  — 
  the 
  hardest 
  type 
  of 
  radia- 
  

   tion 
  observed 
  — 
  from 
  an 
  element 
  of 
  atomic 
  weight 
  A 
  is 
  for 
  

   elements 
  from 
  Al 
  to 
  Se 
  approximately 
  equal 
  to 
  A. 
  10 
  8 
  cm./sec. 
  

   As 
  seen 
  this 
  is 
  equal 
  to 
  the 
  above 
  calculated 
  value 
  for 
  v, 
  if 
  

  

  ^T 
  A 
  

  

  we 
  put 
  JN 
  = 
  - 
  . 
  

  

  Since 
  we 
  have 
  obtained 
  approximate 
  agreement 
  with 
  

   experiment 
  by 
  ascribing 
  the 
  characteristic 
  Rontgen 
  radia- 
  

   tion 
  of 
  the 
  K-type 
  to 
  the 
  innermost 
  ring, 
  it 
  is 
  to 
  be 
  expected 
  

   that 
  no 
  harder 
  type 
  of 
  characteristic 
  radiation 
  wlil 
  exist. 
  

   This 
  is 
  strongly 
  indicated 
  by 
  observations 
  of 
  the 
  penetrating 
  

   power 
  of 
  7 
  raysf. 
  

  

  It 
  is 
  worthy 
  of 
  remark 
  that 
  the 
  theory 
  gives 
  not 
  only 
  

   nearly 
  the 
  right 
  value 
  for 
  the 
  energy 
  required 
  to 
  remove 
  an 
  

   electron 
  from 
  the 
  outer 
  ring, 
  but 
  also 
  the 
  energy 
  required 
  

   to 
  remove 
  an 
  electron 
  from 
  the 
  innermost 
  ring. 
  The 
  

   approximate 
  agreement 
  between 
  the 
  calculated 
  and 
  experi- 
  

   mental 
  values 
  is 
  all 
  the 
  more 
  striking 
  when 
  it 
  is 
  recalled 
  

   that 
  the 
  energies 
  required 
  in 
  the 
  two 
  cases 
  for 
  an 
  element 
  of 
  

   .atomic 
  weight 
  70 
  differ 
  hx 
  a 
  ratio 
  of 
  1000. 
  

  

  In 
  connexion 
  with 
  this 
  it 
  should 
  be 
  emphasized 
  that 
  the 
  

  

  * 
  R. 
  Whiddington, 
  Proc. 
  Roy. 
  Soc. 
  A. 
  lxxxv. 
  p. 
  323 
  (1911). 
  

   t 
  Comp. 
  E. 
  Rutherford, 
  Phil. 
  Mag. 
  xxiv. 
  p. 
  453 
  (1912). 
  

  

  