﻿NUCLEUS 
  OF 
  THE 
  ATOM 
  CROWTHER 
  211 
  

  

  cases 
  is 
  due 
  to 
  this 
  electrostatic 
  repulsion, 
  and 
  the 
  " 
  collision 
  " 
  between 
  

   the 
  particles 
  thus 
  resembles 
  the 
  sweep 
  of 
  a 
  comet 
  through 
  the 
  solar 
  

   system; 
  the 
  only 
  difference 
  being 
  that 
  the 
  a 
  particle 
  is 
  repelled, 
  

   while 
  tlie 
  comet 
  is 
  attracted, 
  by 
  the 
  central 
  sun. 
  The 
  solution 
  of 
  the 
  

   problem 
  is 
  fully 
  worked 
  out 
  in 
  books 
  on 
  Dynamics, 
  and 
  its 
  extension 
  

   to 
  the 
  case 
  of 
  the 
  scattering 
  of 
  a 
  beam 
  of 
  a 
  particles 
  is 
  quite 
  simple. 
  

   It 
  can 
  thus 
  be 
  shown 
  that, 
  assuming 
  the 
  deflections 
  to 
  be 
  caused 
  by 
  an 
  

   electrostatic 
  force 
  varying 
  inversely 
  as 
  the 
  square 
  of 
  the 
  distance, 
  

   the 
  fraction 
  of 
  the 
  whole 
  number 
  of 
  particles 
  scattered 
  through 
  an 
  

   angle 
  greater 
  than 
  </> 
  by 
  a 
  sheet 
  of 
  matter 
  of 
  thickness 
  t 
  is 
  

  

  ■K 
  ni 
  jrpz 
  cot^ 
  n 
  where 
  n 
  is 
  the 
  number 
  of 
  atoms 
  per 
  c. 
  c. 
  m 
  the 
  

  

  material, 
  A^ 
  the 
  atomic 
  number, 
  and 
  7' 
  the 
  kinetic 
  energy 
  of 
  the 
  a 
  

   particle; 
  e 
  being, 
  as 
  usual, 
  the 
  unit 
  electronic 
  charge. 
  All 
  these 
  quan- 
  

   tities 
  are 
  well 
  known. 
  The 
  theory 
  has 
  been 
  tested 
  with 
  great 
  accu- 
  

   racy 
  by 
  Chadwick, 
  using 
  sheets 
  of 
  copper, 
  silver, 
  and 
  gold, 
  and 
  the 
  

   measured 
  deflections 
  were 
  found 
  to 
  agree 
  with 
  those 
  calculated 
  from 
  

   the 
  formula 
  to 
  an 
  accuracy 
  of 
  at 
  least 
  one 
  per 
  cent. 
  The 
  a 
  particle 
  

   and 
  the 
  nuclei 
  of 
  copper, 
  silver, 
  and 
  gold 
  thus 
  act 
  like 
  point 
  charges 
  

   repelling 
  each 
  other 
  in 
  accordance 
  with 
  the 
  law 
  of 
  inverse 
  squares 
  

   at 
  least 
  up 
  to 
  the 
  minimum 
  distance 
  of 
  approach 
  of 
  the 
  a 
  particle 
  

   to 
  the 
  nuclei 
  in 
  these 
  experiments. 
  This 
  minimum 
  distance 
  was 
  

   found, 
  by 
  calculation, 
  to 
  be 
  of 
  the 
  order 
  of 
  5X10"^^ 
  cm. 
  Since 
  the 
  

   inverse 
  square 
  law 
  could 
  certainly 
  not 
  apply 
  if 
  the 
  particles 
  came 
  

   into 
  actual 
  contact, 
  the 
  radii 
  of 
  the 
  nuclei 
  must 
  certainly 
  be 
  smaller 
  

   than 
  this 
  distance, 
  wliich 
  gives 
  us, 
  therefore, 
  an 
  upper 
  limit 
  to 
  the 
  

   size 
  of 
  the 
  nucleus. 
  The 
  radius 
  of 
  an 
  atomic 
  nucleus 
  is, 
  therefore, 
  

   certainly 
  less 
  than 
  one 
  two 
  thousandth 
  of 
  that 
  of 
  the 
  atom. 
  

  

  The 
  matter 
  can, 
  however, 
  be 
  pushed 
  a 
  little 
  further. 
  The 
  force 
  

   between 
  an 
  a 
  particle 
  and 
  a 
  nucleus 
  will 
  be 
  smaller 
  as 
  the 
  charge 
  

   on 
  the 
  nucleus 
  becomes 
  smaller, 
  that 
  is 
  to 
  say 
  as 
  the 
  atomic 
  number 
  

   of 
  the 
  atom 
  becomes 
  less. 
  Thus 
  the 
  smaller 
  the 
  atomic 
  number 
  of 
  the 
  

   scattering 
  element, 
  the 
  nearer 
  will 
  the 
  « 
  particle 
  be 
  able 
  to 
  approach 
  

   its 
  nucleus. 
  The 
  minimum 
  distance 
  of 
  approach 
  also 
  becomes 
  smaller 
  

   as 
  the 
  velocity 
  of 
  the 
  a 
  particle 
  increases. 
  Hence 
  by 
  using 
  scattering 
  

   substances 
  of 
  low 
  atomic 
  number 
  and 
  high 
  speed 
  a 
  particles 
  we 
  can 
  

   get 
  closer 
  and 
  closer 
  to 
  the 
  mysterious 
  world 
  we 
  are 
  investigating. 
  

   Some 
  experiments, 
  made 
  originally 
  by 
  Rutherford 
  and 
  extended 
  by 
  

   Chadwick 
  and 
  Bieler, 
  on 
  the 
  scattering 
  of 
  a 
  particles 
  by 
  hj^drogen 
  

   arc 
  of 
  peculiar 
  interest 
  in 
  this 
  connection. 
  

  

  The 
  problem 
  becomes 
  a 
  little 
  more 
  complex 
  when 
  the 
  a 
  particle 
  

   is 
  being 
  scattered 
  by 
  a 
  gas 
  the 
  particles 
  of 
  which 
  are 
  themselves 
  

   free 
  to 
  remove, 
  but 
  an 
  exact 
  solution 
  can 
  be 
  obtained, 
  on 
  the 
  same 
  

   assumptions 
  as 
  to 
  the 
  nature 
  of 
  the 
  collisions 
  as 
  were 
  made 
  in 
  the 
  

   previous 
  case. 
  The 
  hydrogen 
  nuclei 
  should 
  be 
  scattered 
  in 
  all 
  direc- 
  

   tions, 
  by 
  the 
  force 
  of 
  the 
  impact, 
  in 
  numbers 
  and 
  with 
  velocities 
  

  

  