﻿184 
  Dr. 
  R. 
  T. 
  Beatty 
  on 
  the 
  

  

  to 
  be 
  disposed 
  round 
  the 
  surface 
  of 
  the 
  atom 
  and 
  to 
  play 
  a 
  

   part 
  in 
  the 
  refraction 
  of 
  light 
  and 
  in 
  chemical 
  processes. 
  

  

  Now 
  the 
  smaller 
  the 
  radii 
  of 
  the 
  inner 
  rings 
  of 
  electrons 
  

   the 
  less 
  effect 
  will 
  they 
  have 
  in 
  determining 
  the 
  energy 
  

   required 
  for 
  ionization. 
  Thus 
  imagine 
  a 
  central 
  charge 
  be 
  

   surrounded 
  by 
  a 
  ring 
  of 
  radius 
  b, 
  containing 
  four 
  electrons, 
  

   a 
  fifth 
  electron 
  lying 
  at 
  a 
  greater 
  distance 
  a 
  from 
  the 
  

   centre, 
  on 
  a 
  line 
  joining 
  the 
  centre 
  and 
  one 
  of 
  the 
  inner 
  

   electrons. 
  

  

  The 
  energy 
  to 
  remove 
  the 
  outer 
  electron 
  to 
  infinity 
  will 
  

   be 
  

  

  2 
  n 
  

  

  a~+b~ 
  v/^+^J 
  

  

  La 
  a 
  — 
  b 
  a 
  + 
  

   a 
  L 
  a 
  J 
  

  

  w 
  

  

  ,2 
  

  

  neglecting 
  higher 
  powers 
  of 
  - 
  than 
  the 
  second. 
  If 
  the 
  four 
  

  

  inner 
  electrons 
  were 
  removed 
  along 
  with 
  four 
  units 
  of 
  the 
  

   central 
  charge, 
  the 
  energy 
  for 
  ionization 
  would 
  be 
  

  

  e* 
  

   a 
  

  

  Hence 
  if 
  6= 
  — 
  , 
  the 
  error 
  produced 
  by 
  regarding 
  the 
  atom 
  

  

  as 
  simplified 
  in 
  this 
  way 
  would 
  be 
  1 
  per 
  cent. 
  

  

  If 
  the 
  central 
  charge 
  were 
  9e, 
  with 
  eight 
  electrons 
  in 
  the 
  

   inner 
  ring 
  and 
  one 
  electron 
  at 
  ten 
  times 
  the 
  distance 
  from 
  

   the 
  centre, 
  we 
  find 
  

  

  W=^[l--039l. 
  

  

  In 
  this 
  case 
  if 
  we 
  regard 
  the 
  atom 
  as 
  consisting 
  of 
  a 
  charge 
  

   -f- 
  e, 
  with 
  only 
  one 
  electron 
  

  

  a 
  

  

  so 
  that 
  the 
  error 
  introduced 
  by 
  the 
  assumption 
  is 
  4 
  per 
  cent. 
  

  

  Hence 
  a 
  knowledge 
  of 
  the 
  number 
  of 
  electrons 
  in 
  the 
  

   outer 
  ring 
  and 
  of 
  the 
  atomic 
  radius 
  should 
  enable 
  us 
  to 
  

   give 
  an 
  approximation 
  to 
  the 
  energy 
  required 
  for 
  ionization. 
  

  

  Values 
  of 
  the 
  atomic 
  radii 
  have 
  been 
  given 
  for 
  the 
  gases 
  

   of 
  the 
  helium 
  group* 
  and 
  for 
  mercury 
  vapour 
  f. 
  

  

  The 
  value 
  for 
  mercury, 
  however, 
  is 
  not 
  reliable 
  J. 
  

  

  The 
  results 
  for 
  the 
  helium 
  group 
  were 
  obtained 
  under 
  the 
  

  

  * 
  E,ankine, 
  Proc. 
  Roy. 
  Soc. 
  A. 
  lxxxiii. 
  p. 
  524. 
  

  

  t 
  Koch, 
  Wied. 
  Ann. 
  xix. 
  p. 
  857. 
  

  

  X 
  See 
  Meyer, 
  ' 
  Kinetic 
  Theory 
  of 
  Gases,' 
  pp. 
  197-296. 
  

  

  