﻿of 
  Atoms 
  and 
  Molecules, 
  3 
  

  

  for 
  a 
  theory 
  of 
  the 
  constitution 
  of 
  atoms. 
  It 
  will 
  further 
  

   be 
  shown 
  that 
  from 
  this 
  theory 
  we 
  are 
  led 
  to 
  a 
  theory 
  of 
  the 
  

   constitution 
  of 
  molecules. 
  

  

  In 
  the 
  present 
  first 
  part 
  of 
  the 
  paper 
  the 
  mechanism 
  of 
  

   the 
  binding 
  of: 
  electrons 
  by 
  a 
  positive 
  nucleus 
  is 
  discussed 
  in 
  

   relation 
  to 
  Planck's 
  theory. 
  It 
  will 
  be 
  shown 
  that 
  it 
  is 
  

   possible 
  from 
  the 
  point 
  of 
  view 
  taken 
  to 
  account 
  in 
  a 
  simple 
  

   wav 
  for 
  the 
  law 
  of 
  the 
  line 
  spectrum 
  of 
  hydrogen. 
  Further, 
  

   reasons 
  are 
  given 
  for 
  a 
  principal 
  hypothesis 
  on 
  which 
  the 
  

   considerations 
  contained 
  in 
  the 
  following 
  parts 
  are 
  based. 
  

  

  I 
  wish 
  here 
  to 
  express 
  my 
  thanks 
  to 
  Prof. 
  Rutherford 
  for 
  

   his 
  kind 
  and 
  encouraging 
  interest 
  in 
  this 
  work. 
  

  

  Part 
  I. 
  — 
  Binding 
  of 
  Electrons 
  by 
  Positive' 
  Nuclei. 
  

   § 
  1. 
  General 
  Considerations, 
  

  

  The 
  inadequacy 
  of 
  the 
  classical 
  electrodynamics 
  in 
  ac- 
  

   countino" 
  for 
  the 
  properties 
  of 
  atoms 
  from 
  an 
  atom-model 
  as 
  

   Rutherford's, 
  will 
  appear 
  very 
  clearly 
  if 
  we 
  consider 
  a 
  simple 
  

   svstem 
  consisting 
  of 
  a 
  positively 
  charged 
  nucleus 
  of 
  very 
  

   small 
  dimensions 
  and 
  an 
  electron 
  describing 
  closed 
  *orbits 
  

   around 
  it. 
  For 
  simplicity, 
  let 
  us 
  assume 
  that 
  the 
  mass 
  of 
  

   the 
  electron 
  is 
  negligibly 
  small 
  in 
  comparison 
  with 
  that 
  of 
  

   the 
  nucleus, 
  and 
  further, 
  that 
  the 
  velocity 
  of 
  the 
  electron 
  is 
  

   small 
  compared 
  with 
  that 
  of 
  light. 
  

  

  Let 
  us 
  at 
  first 
  assume 
  that 
  there 
  is 
  no 
  energy 
  radiation. 
  

   In 
  this 
  case 
  the 
  electron 
  will 
  describe 
  stationary 
  elliptical 
  

   orbits. 
  The 
  frequency 
  of 
  revolution 
  co 
  and 
  the 
  major-axis 
  

   of 
  the 
  orbit 
  2a 
  will 
  depend 
  on 
  the 
  amount 
  of 
  energy 
  W 
  

   which 
  must 
  be 
  transferred 
  to 
  the 
  system 
  in 
  order 
  to 
  remove 
  

   the 
  electron 
  to 
  an 
  infinitely 
  great 
  distance 
  apart 
  from 
  the 
  

   nucleus. 
  Denoting 
  the 
  charge 
  of 
  the 
  electron 
  and 
  of 
  the 
  

   nucleus 
  by 
  — 
  e 
  and 
  E 
  respectively 
  and 
  the 
  mass 
  of 
  the 
  electron 
  

   by 
  m, 
  we 
  thus 
  get 
  

  

  V2 
  Wl 
  _ 
  eft 
  „. 
  

  

  7T 
  eft 
  Vm' 
  W 
  

  

  Further, 
  it 
  can 
  easily 
  be 
  shown 
  that 
  the 
  mean 
  value 
  of 
  the 
  

   kinetic 
  energy 
  of 
  the 
  electron 
  taken 
  for 
  a 
  whole 
  revolution 
  

   is 
  equal 
  to 
  W. 
  We 
  see 
  that 
  if 
  the 
  value 
  of 
  W 
  is 
  not 
  given, 
  

   there 
  will 
  be 
  no 
  values 
  of 
  co 
  and 
  a 
  characteristic 
  for 
  the 
  

   system 
  in 
  question. 
  

  

  Let 
  us 
  now, 
  however, 
  take 
  the 
  effect 
  of 
  the 
  energy 
  radia- 
  

   tion 
  into 
  account, 
  calculated 
  in 
  the 
  ordinary 
  way 
  from 
  the 
  

   acceleration 
  of 
  the 
  electron. 
  In 
  this 
  case 
  the 
  electron 
  will 
  

  

  B 
  2 
  

  

  