Download CHAPTER 3: The Experimental Basis of Quantum

CHAPTER 3
Prelude to Quantum Theory
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
Discovery of the X-Ray and the Electron
Determination of Electron Charge
Line Spectra
Quantization
Blackbody Radiation
Photoelectric Effect
X-Ray Production
Compton Effect
Pair Production and Annihilation
Max Karl Ernst Ludwig Planck
(1858-1947)
Problems due Wednesday Sept. 24th: Chapter 3: 7, 9, 14, 15, 16,
18, 19, 24, 25, 26
Photons also have momentum!
Use our expression for the relativistic
energy to find the momentum of a photon,
which has no mass:
E  (mc )  p c
2
2 2
Alternatively:
When
radiation
pressure is
important:
2 2

E h h
p 

c
c 
h 2
p
 k
2 
Comet tails (other forces are small)
Viking spacecraft (would've missed Mars by 15,000 km)
Stellar interiors (resists gravity)
3.8: Compton Effect
Ep, pp
Photons have energy and momentum:
E  hc / 
p h/
When a photon enters matter, it can
interact with one of the electrons. The
laws of conservation of energy and
momentum apply, as in any elastic
collision between two particles.
This yields the change in
wavelength of the scattered
photon, known as the
Compton effect:
Ee, pe
Ep’ , pp ’
Read: section 3.4 Kane
3.9: Pair Production and Annihilation
In 1932, C. D. Anderson observed a
positively charged electron (e+) in
cosmic radiation. This particle, called a
positron, had been predicted to exist
several years earlier by P. A. M. Dirac.
A photon’s energy can be converted
entirely into an electron and a positron
in a process called pair production:
Paul Dirac
(1902 - 1984)
Pair Production
in Empty Space
h
Conservation of energy for pair
production in empty space is:
E
E+
h  E  E
The total energy for a particle is:
So:
E  p c
This yields a lower limit on the photon energy:
Momentum conservation yields:
h  p c  p c
h  pc cos( )  p c cos( )
This yields an upper limit on the photon energy:
h  p c  p c
A contradiction! And hence the conversion of energy and momentum
for pair production in empty space is impossible!
Pair Production
in Matter
In the presence of matter, the
nucleus absorbs some energy
and momentum.
The photon energy required for
pair production in the presence
of matter is:
h  E  E  K .E.(nucleus)
h  2me c 2  1.022 MeV
Pair Annihilation
A positron passing through matter
will likely annihilate with an
electron. The electron and positron
can form an atom-like configuration
first, called positronium.
Pair annihilation in empty space
produces two photons to conserve
momentum. Annihilation near a
nucleus can result in a single
photon.
hv
hv
Pair Annihilation
Conservation of energy:
2me c 2  hv1  hv2
Conservation of momentum:
hv1 hv2

0
c
c
So the two photons will have the
same frequency:
v1  v2  v
The two photons from positronium
annihilation will move in opposite
directions with an energy:
hv  me c 2  0.511 MeV
hv
hv
CHAPTER 4
Structure of the Atom
4.1 The Atomic Models of Thomson and
Rutherford
4.2 Rutherford Scattering
4.3 The Classic Atomic Model
4.4 The Bohr Model of the Hydrogen Atom
4.5 Successes & Failures of the Bohr Model
4.6 Characteristic X-Ray Spectra and Atomic
Number
4.7 Atomic Excitation by Electrons
Niels Bohr (1885-1962)
The opposite of a correct statement is a false statement. But the opposite of
a profound truth may well be another profound truth.
An expert is a person who has made all the mistakes that can be made in a
very narrow field.
Never express yourself more clearly than you are able to think.
Prediction is very difficult, especially about the future.
- Niels Bohr
Structure of the Atom
Evidence in 1900 indicated that
the atom was not a fundamental unit:
1)
There seemed to be too many kinds
of atoms, each belonging to a distinct chemical
element (way more than earth, air, water, and fire!).
2)
Atoms and electromagnetic phenomena were intimately related
(magnetic materials; insulators vs. conductors; different emission
spectra).
3)
Elements combine with some elements but not with others, a
characteristic that hinted at an internal atomic structure
(valence).
4)
The discoveries of radioactivity, x rays, and the electron (all
seemed to involve atoms breaking apart in some way).
Knowledge of atoms in 1900
Electrons (discovered in
1897) carried the negative
charge.
Electrons were very light,
even compared to the atom.
Protons had not yet been
discovered, but clearly
positive charge had to be
present to achieve charge
neutrality.
Thomson’s
Atomic Model
Thomson’s “plum-pudding”
model of the atom had the
positive charges spread
uniformly throughout a
sphere the size of the atom,
with electrons embedded in
the uniform background.
In Thomson’s view, when the atom was heated, the electrons could
vibrate about their equilibrium positions, thus producing
electromagnetic radiation.
Unfortunately, Thomson couldn’t explain spectra with this model.
Experiments of Geiger and Marsden
Rutherford, Geiger, and Marsden
conceived a new technique for
investigating the structure of
matter by scattering a particles
from atoms.
Experiments of Geiger and Marsden 2
Geiger showed that many a particles were scattered from thin
gold-leaf targets at backward angles greater than 90°.
Electrons can’t
back-scatter a
particles.
Before
After
Calculate the maximum scattering angle—
corresponding to the maximum momentum change.
It can be shown that the maximum
momentum transfer to the a particle is:
Dpmax  2me va
Determine max by letting
Dpmax be perpendicular to
the direction of motion:
 max
Dpa 2me va



pa
M a va
too small!