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Chapter 04
Structure of the Atom
General Bibliography
1) Various wikipedia, as specified
2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated
Outline
• 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
 
 
2
sin
1
~ 4
2
2
2
1

 







KE
e
Z
Z
rate
count
Derivation on pages 131-137
Assume massive positive objects
Coulomb force
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
r
v
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
2
2
4
me
a o
o

p

o
n a
n
r 2

)
(
6
.
13
8 2
2
2
eV
in
n
n
a
e
E
o
o
n




p

o
n
e
n
v
p
4
1 2

137
1
4
2
1



c
e
c
v
o
p

4.4 Bohr Model
4.5 Successes & Failures of Bohr Model
r
separation
Coulomb
r
r
radius
orbit e

Reduced Mass Correction
e
e
e
M
m
M
m
m
fix
magic 



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

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Chapter04.ppt

  • 1. Chapter 04 Structure of the Atom General Bibliography 1) Various wikipedia, as specified 2) Thornton-Rex, Modern Physics for Scientists & Eng, as indicated
  • 2. Outline • 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
  • 3. 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.
  • 5. 4.2 Geiger-Marsden-Rutherford     2 sin 1 ~ 4 2 2 2 1           KE e Z Z rate count Derivation on pages 131-137 Assume massive positive objects Coulomb force
  • 6. 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
  • 7. 4.3 Classical Atomic Model r v Using Newtonian Mechanics & JJThomson’s anticipated sizes: 1. Estimate the speed of the orbiting electron 2. Total Energy of the system
  • 8. 4.3 Classical Atomic Model Failures of the classical model: 1. 2.
  • 9. 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
  • 10. 4.4 Bohr Model 2 2 4 me a o o  p  o n a n r 2  ) ( 6 . 13 8 2 2 2 eV in n n a e E o o n     p  o n e n v p 4 1 2  137 1 4 2 1    c e c v o p 
  • 12. 4.5 Successes & Failures of Bohr Model r separation Coulomb r r radius orbit e  Reduced Mass Correction e e e M m M m m fix magic    
  • 13. 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+