﻿of 
  Atoms 
  and 
  Molecules. 
  489- 
  

  

  At 
  distances 
  from 
  the 
  nucleus 
  great 
  compared 
  with 
  the 
  

   radius 
  of 
  the 
  bound 
  electron, 
  the 
  system 
  2(1) 
  will, 
  to 
  a 
  close 
  

   approximation, 
  act 
  on 
  an 
  electron 
  as 
  a 
  simple 
  nucleus 
  of 
  

   charge 
  e. 
  For 
  a 
  system 
  consisting 
  of 
  two 
  electrons 
  and 
  a 
  

   nucleus 
  of 
  charge 
  2<?, 
  we 
  may 
  therefore 
  assume 
  the 
  existence 
  

   of 
  a 
  series 
  of 
  stationary 
  states 
  in 
  w 
  r 
  hich 
  the 
  electron 
  most 
  

   lightlv 
  bound 
  moves 
  approximately 
  in 
  the 
  same 
  way 
  as 
  the 
  

   electron 
  in 
  the 
  stationary 
  states 
  of 
  a 
  hydrogen 
  atom. 
  Such 
  

   an 
  assumption 
  has 
  already 
  been 
  used 
  in 
  Part 
  I. 
  in 
  an 
  attempt 
  

   to 
  explain 
  the 
  appearance 
  of 
  Rydberg's 
  constant 
  in 
  the 
  

   formula 
  for 
  the 
  line-spectrum 
  of 
  any 
  element. 
  We 
  can, 
  

   however, 
  hardly 
  assume 
  the 
  existence 
  of 
  a 
  stable 
  configur- 
  

   ation 
  in 
  which 
  the 
  two 
  electrons 
  have 
  the 
  same 
  angular 
  

   momentum 
  round 
  the 
  nucleus 
  and 
  move 
  in 
  different 
  orbits, 
  

   the 
  one 
  outside 
  the 
  other. 
  In 
  such 
  a 
  configuration 
  the 
  

   electrons 
  would 
  be 
  so 
  near 
  to 
  each 
  other 
  that 
  the 
  deviations 
  

   from 
  circular 
  orbits 
  would 
  be 
  very 
  great. 
  For 
  the 
  permanent 
  

   state 
  of 
  a 
  neutral 
  helium 
  atom, 
  we 
  shall 
  therefore 
  adopt 
  the 
  

   configuration 
  

  

  2(2) 
  a=0-571a 
  0j 
  a) 
  = 
  3-06a> 
  , 
  W 
  = 
  6'13W 
  . 
  

  

  Since 
  

  

  W[2@] 
  - 
  W[2(i)] 
  =2-13W 
  , 
  

  

  we 
  see 
  that 
  both 
  electrons 
  in 
  a 
  neutral 
  helium 
  atom 
  are 
  more 
  

   firmlv 
  bound 
  than 
  the 
  electron 
  in 
  a 
  hydrogen 
  atom. 
  Using 
  

   the 
  values 
  on 
  p. 
  488, 
  we 
  get 
  

  

  TAT 
  W 
  

  

  2-13 
  . 
  -H* 
  =27 
  volts 
  and 
  2-13-^=6-6 
  . 
  10 
  15 
  ^- 
  : 
  

  

  e 
  h 
  sec 
  - 
  

  

  these 
  values 
  are 
  of 
  the 
  same 
  order 
  of 
  magnitude 
  as 
  the 
  value 
  

   observed 
  for 
  the 
  ionization 
  potential 
  in 
  helium, 
  20*5 
  volt 
  *,. 
  

   and 
  the 
  value 
  for 
  the 
  frequency 
  of 
  the 
  ultra-violet 
  ab- 
  

   sorption 
  in 
  helium 
  determined 
  by 
  experiments 
  on 
  dispersion 
  

  

  5-9 
  . 
  10 
  15 
  — 
  t 
  

  

  sec. 
  

   The 
  frequency 
  in 
  question 
  may 
  be 
  regarded 
  as 
  corre- 
  

   sponding 
  to 
  vibrations 
  in 
  the 
  plane 
  of 
  the 
  ring 
  (see 
  p. 
  480). 
  

   The 
  frequency 
  of 
  vibration 
  of 
  the 
  whole 
  ring 
  perpendicular 
  

   to 
  the 
  plane, 
  calculated 
  in 
  the 
  ordinary 
  way 
  (see 
  p. 
  482), 
  is 
  

  

  * 
  J. 
  Franck 
  u. 
  G. 
  Hertz, 
  Verh. 
  d. 
  Deatsch. 
  Phys. 
  Ges. 
  xt. 
  p. 
  34 
  (1913). 
  

  

  t 
  C. 
  and 
  M. 
  Cuthbertson, 
  Proc. 
  Roy. 
  Soc. 
  A. 
  Ixxxir. 
  p. 
  13 
  1 
  1910). 
  (In 
  

   a 
  previous 
  paper 
  (Phil. 
  Mag. 
  Jan. 
  1913) 
  the 
  author 
  took 
  the 
  values 
  for 
  

   the 
  refractive 
  index 
  in 
  helium, 
  given 
  by 
  M. 
  and 
  C. 
  Cuthbertson, 
  as 
  

   corresponding 
  to 
  atmospheric 
  pressure 
  ; 
  these 
  values, 
  however, 
  refer 
  to 
  

   double 
  atmospheric 
  pressure. 
  Consequently 
  the 
  value 
  there 
  given 
  for 
  the 
  

   number 
  of 
  electrons 
  in 
  a 
  helium 
  atom 
  calculated 
  from 
  Drude's 
  theory 
  has 
  

   to 
  be 
  divided 
  by 
  2.) 
  

  

  