Chapter 04
Structure of the Atom
General Bibliography
1) Various wikipedia, as specified
2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated
Outline
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4.1 Atomic Models of Thomson & Rutherford
4.2 Rutherford Scattering
4.3 Classical Atomic Model
4.4 Bohr Model
4.5 Failures of the Bohr Model
4.6 Characteristic X-Ray Spectra
4.7 Atomic Excitations
4.1 Plum Pudding Model
J.J. Thomson
Positive pudding
with negative ‘raisins’
Electrons oscillate about
their equilibrium position
when heated and produce
EM radiation
If made oscillations about ~10-10 m,
could produce visible wavelengths, but never line spectra.
4.1 Geiger-Marsden-Rutherford
http://en.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiment
http://www.kutl.kyushu-u.ac.jp/seminar/MicroWorld1_E/Part2_E/P23_E/Geiger_Marsden_E.jpg
4.2 Geiger-Marsden-Rutherford
Assume massive positive objects
Coulomb force
2
 Z1Z 2e 2 
1

count rate  ~ 
4
 KE  sin  2
 
Derivation on pages 131-137
4.2 Geiger-Marsden-Rutherford
Example 4.4 & 4.5: Estimate distance of
closest approach for an alpha particle striking
an aluminum nucleus
KE = 7.7 MeV
s
4.3 Classical Atomic Model
v
r
Using Newtonian Mechanics & JJThomson’s anticipated sizes:
1. Estimate the speed of the orbiting electron
2. Total Energy of the system
4.3 Classical Atomic Model
Failures of the classical model:
1.
2.
4.4 Bohr’s Postulates
• A countable number of “stationary
states” exist. (electrons in a
selection of allowed orbit radii)
• EM radiation emitted when
electron jumps/transitions
between states
• Classical rules apply to stationary
states, but not during transitions
between states.
• …Angular momentum occurs in
integer multiples of h/2p.
n=1
n=2
n=3
4.4 Bohr Model
4p o  2
ao 
m e2
rn  n2 ao
En
e2
 
8p o ao n 2

 13.6
(in eV )
2
n
1 e2
vn 
n 4p o 
v1
e2
 
1
137
c 4p o c
4.4 Bohr Model
4.5 Successes & Failures of Bohr Model
Reduced Mass Correction
orbit radius
r  re
Coulombseparation r
me M
m agic fix m 
 e
me  M
4.5 Successes & Failures of Bohr Model
• + Rydberg Eqn predicts many lines of He
(except for a few extra lines)
• Higher resolution diffraction gratings in
advanced spectrographs indicated some
transitions were multiple (fine structure)
• Bohr’s “n” quantum number is only partially
associated with angular momentum (1s, 2s,
3s,… states do not have angular momentum)
• Worked best for single-electron atoms
– H+, He+, Li+
4.6 Characteristic X-Ray Spectra
4.7 Atomic Excitation