﻿Structure 
  of 
  the 
  Atom. 
  799 
  

  

  Since 
  e/m=5'3 
  x 
  10 
  17 
  , 
  C 
  = 
  10- 
  17 
  , 
  we 
  find 
  

  

  A 
  = 
  OT 
  x3'lxlO- 
  10 
  . 
  

  

  The 
  charge 
  on 
  a 
  corpuscle 
  is 
  4*7xl0~ 
  10 
  ; 
  the 
  force 
  at 
  a 
  

   distance 
  r, 
  calculated 
  by 
  the 
  ordinary 
  laws 
  of 
  Electrostatics 
  

   due 
  to 
  a 
  charge 
  me, 
  is 
  w 
  . 
  47 
  x 
  10~ 
  10 
  /r 
  2 
  . 
  "We 
  see, 
  then, 
  that 
  

   the 
  force 
  along 
  one 
  of 
  the 
  tubes 
  which 
  contain 
  the 
  corpuscles 
  

   which 
  give 
  the 
  hardest 
  characteristic 
  Rontgen 
  radiation, 
  

   the 
  K 
  radiation, 
  when 
  they 
  vibrate, 
  is 
  about 
  the 
  same 
  in 
  

   magnitude 
  as 
  would, 
  according 
  to 
  the 
  ordinary 
  laws 
  of 
  

   Electrostatics, 
  be 
  produced 
  by 
  a 
  charge 
  of 
  positive 
  electricity 
  

   between 
  \me 
  and 
  me. 
  If 
  Whiddington's 
  value 
  for 
  the 
  

   velocity 
  of 
  the 
  cathode 
  particles 
  is 
  too 
  great 
  by 
  about 
  

   20 
  per 
  cent, 
  the 
  charge 
  would 
  be 
  \me, 
  if 
  it 
  were 
  too 
  small 
  

   by 
  about 
  50 
  per 
  cent, 
  the 
  charge 
  would 
  be 
  me. 
  The 
  distance 
  

   from 
  the 
  centre 
  of 
  the 
  atom 
  at 
  which 
  the 
  corpuscles 
  which 
  

   produce 
  these 
  hard 
  rays 
  are 
  situated, 
  is 
  C/A 
  or 
  

  

  -3'2xl0- 
  8 
  cm. 
  

  

  m 
  

  

  Let 
  us 
  apply 
  this 
  result 
  to 
  the 
  case 
  of 
  hydrogen; 
  we 
  shall 
  

   suppose 
  that 
  in 
  this 
  case 
  me 
  = 
  A 
  or, 
  since 
  m—\, 
  A 
  = 
  e. 
  The 
  

   frequency 
  of 
  the 
  characteristic 
  radiation 
  is 
  (seep. 
  794) 
  given 
  

   by 
  the 
  equation 
  

  

  ma 
  4 
  m 
  C 
  3 
  

  

  since 
  a 
  = 
  C/A. 
  

  

  Putting 
  A 
  = 
  e, 
  and 
  substituting 
  the 
  values 
  for 
  C 
  and 
  e, 
  we 
  

   find 
  

  

  72 
  = 
  8-2 
  xlO 
  14 
  . 
  

  

  This 
  frequency 
  corresponds 
  to 
  light 
  just 
  in 
  the 
  ultra-violet. 
  

   The 
  most 
  interesting 
  tiling 
  about 
  this 
  result 
  is, 
  however, 
  

   that, 
  within 
  the 
  errors 
  of 
  experiment, 
  the 
  frequency 
  we 
  have 
  

   found 
  coincides 
  with 
  that 
  of 
  the 
  head 
  of 
  the 
  series 
  of 
  hydrogen 
  

   lines 
  given 
  by 
  Balmer's 
  law, 
  so 
  that 
  this 
  spectrum 
  represents 
  

   the 
  K 
  radiation 
  for 
  hydrogen. 
  As 
  hydrogen 
  possesses 
  in 
  the 
  

   Schumann 
  region 
  a 
  spectrum 
  of 
  still 
  greater 
  frequency, 
  it 
  

   seems 
  probable 
  that 
  the 
  K 
  radiation 
  may 
  not 
  be 
  the 
  hardest 
  

   type 
  of 
  characteristic 
  Rontgen 
  radiation. 
  

  

  If 
  for 
  helium 
  we 
  assume 
  k=\me, 
  the 
  corresponding 
  value 
  

   of 
  n 
  would 
  be 
  3*288 
  x 
  10 
  15 
  ; 
  this 
  corresponds 
  to 
  radiation 
  in 
  the 
  

   Schumann 
  region. 
  For 
  heavier 
  elements 
  the 
  frequency 
  

   would 
  be 
  of 
  an 
  order 
  corresponding 
  to 
  Rontgen 
  rays. 
  

  

  