Download Chapter 30 Quantum Physics

12/7/2011
Units of Chapter 30
Chapter 30
Quantum Physics
• Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
• Photons and the Photoelectric Effect
• The Mass and Momentum of a
Photon
• Photon Scattering and the Compton
Effect
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Copyright © 2010 Pearson Education, Inc.
Units of Chapter 30
• The de Broglie Hypothesis and WaveParticle Duality
• The Heisenberg Uncertainty Principle
• Quantum Tunneling
Development of Quantum Physics
• Problems remained from classical mechanics
that relativity didn’t explain
• Blackbody Radiation
– The electromagnetic radiation emitted by a heated
object
• Photoelectric Effect
– Emission of electrons by an illuminated metal
• Spectral Lines
– Emission of sharp spectral lines by gas atoms in an
electric discharge tube
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Development of Quantum Physics
• 1900 to 1930
– Development of ideas of quantum mechanics
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30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
An ideal blackbody absorbs all the light that is
incident upon it.
• Also called wave mechanics
• Highly successful in explaining the behavior of atoms,
molecules, and nuclei
• Quantum Mechanics reduces to classical mechanics
when applied to macroscopic systems
• Involved a large number of physicists
– Planck introduced basic ideas
– Mathematical developments and interpretations involved
such people as Einstein, Bohr, Schrödinger, de Broglie,
Heisenberg, Born and Dirac
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30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
Classical physics calculations were completely unable to
produce this temperature dependence, leading to
something called the “ultraviolet catastrophe.”
An ideal blackbody is also
an ideal radiator. If we
measure the intensity of the
electromagnetic radiation
emitted by an ideal
blackbody, we find:
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30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
Planck discovered that he could reproduce the
experimental curve by assuming that the
radiation in a blackbody came in quantized
energy packets, depending on the frequency:
Rayleigh
-Jeans
Planck
8π f
c3
2
k BT
hf
8πf 2
hf (e k BT − 1) −1
c3
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30-2 Photons and the Photoelectric Effect
The photoelectric effect occurs when a beam of light
strikes a metal, and electrons are ejected.
Each metal has a minimum amount of energy required
to eject an electron, called the work function, W0. If the
electron is given an energy E by the beam of light, its
maximum kinetic energy is:
The constant h in this equation is known as
Planck’s constant:
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30-2 Photons and the Photoelectric Effect
Classical predictions:
1. Any beam of light of any color can eject
electrons if it is intense enough.
2. The maximum kinetic energy of an ejected
electron should increase as the intensity
increases.
Observations:
1. Light must have a certain minimum frequency
in order to eject electrons.
2. More intensity results in more electrons of the
same energy.
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Copyright © 2010 Pearson Education, Inc.
30-2 Photons and the Photoelectric Effect
Einstein suggested that the quantization of light was
real; that light came in small packets, now called
photons, of energy:
A more intense beam of
light will contain more
photons, but the energy
of each photon does not
change.
Example: A laser emits 2.5 W of light energy at the wavelength
of 532 nm, determine the number of photons given off by the
laser per second.
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30-2 Photons and the Photoelectric Effect
30-3 The Mass and Momentum of a Photon
Explanations:
Photons always travel at the speed of light (of
course!). What does this tell us about their mass
and momentum?
Each photon’s energy is determined by its frequency. If it
is less than the work function, electrons will not be
ejected, no matter how intense the beam.
The total energy can be written:
Example: A sodium surface is illuminated with light of wavelength 300
nm. The work function of solium is 2.46 eV. Calculate (a) the energy
of each photon in electron volts, (b) the maximum kinetic energy of the
ejected photoelectrons, and (c) the cutoff wavelength for the sodium.
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Since the left side of the equation must be
zero for a photon, it follows that the right side
must be zero as well.
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30-3 The Mass and Momentum of a Photon
Energy-momentum equation in Relativity:
2
2
2
E = E 0+ p c
2
30-4 Photon Scattering and the Compton
Effect
The Compton effect occurs when a photon
scatters off an atomic electron.
With E0 = m0c2 = 0,
And finally,
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30-4 Photon Scattering and the Compton
Effect
In order for energy to be conserved, the energy
of the scattered photon plus the energy of the
electron must equal the energy of the incoming
photon. This means the wavelength of the
outgoing photon is longer than the wavelength
of the incoming one:
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Copyright © 2010 Pearson Education, Inc.
30-5 The de Broglie Hypothesis and WaveParticle Duality
In 1923, de Broglie proposed that, as waves can exhibit
particle-like behavior, particles should exhibit wave-like
behavior as well.
He proposed that the same relationship between
wavelength and momentum should apply to massive
particles as well as photons:
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30-5 The de Broglie Hypothesis and WaveParticle Duality
Indeed, we can even
perform Young’s twoslit experiment with
particles of the
appropriate
wavelength and find
the same diffraction
pattern.
This is even true if we have a particle beam so
weak that only one particle is present at a time
– we still see the diffraction pattern produced
by constructive and destructive interference.
Also, as the diffraction pattern builds, we
cannot predict where any particular particle will
land, although we can predict the final
appearance of the pattern.
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Copyright © 2010 Pearson Education, Inc.
30-5 The de Broglie Hypothesis and WaveParticle Duality
These images show the gradual creation of an electron
diffraction pattern.
Low Energy Electron
Diffraction (LEED)
pattern from Silicon
(111) surface.
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30-5 The de Broglie Hypothesis and WaveParticle Duality
The same patterns can be observed using either
particles or X-rays.
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30-5 The de Broglie Hypothesis and WaveParticle Duality
30-5 The de Broglie Hypothesis and WaveParticle Duality
The correctness of this assumption has been verified
many times over. One way is by observing diffraction.
We already know that X-rays can diffract from crystal
planes:
Example: A beam of neutrons with a de Broglie wavelength of 0.240 nm
diffracts from a crystal of table salt, which has an interionic spacing of
0.283 nm. (a) What is the speed of the neutrons? (b) What is the angle of
the second interference maximum?
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30-6 The Heisenberg Uncertainty Principle
The uncertainty just mentioned – that we
cannot know where any individual electron
will hit the screen – is inherent in quantum
physics, and is due to the wavelike properties
of matter.
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30-6 The Heisenberg Uncertainty Principle
30-6 The Heisenberg Uncertainty Principle
Mathematically,
When the electrons diffract through the slit, they
acquire a y-component of momentum that they
had not had before. This leads to the uncertainty
principle:
If we know the position of a particle with greater
precision, its momentum is more uncertain; if
we know the momentum of a particle with
greater precision, its position is more uncertain.
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Copyright © 2010 Pearson Education, Inc.
30-6 The Heisenberg Uncertainty Principle
Thought Experiment – the
Uncertainty Principle
The uncertainty principle can be cast in
terms of energy and time rather than position
and momentum:
The effects of the uncertainty principle are
generally not noticeable in macroscopic
situations due to the smallness of Planck’s
constant, h.
•
•
•
•
A thought experiment for viewing an electron with a powerful
microscope
In order to see the electron, at least one photon must bounce off it
During this interaction, momentum is transferred from the photon to
the electron
Therefore, the light that allows you to accurately locate the electron
changes the momentum of the electron
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30-7 Quantum Tunneling
Waves can “tunnel” through narrow gaps of
material that they otherwise would not be able
to traverse. As the gap widens, the intensity of
the transmitted wave decreases exponentially.
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30-7 Quantum Tunneling
Given their wavelike properties, it is not surprising that
particles can tunnel as well. A practical application is the
scanning tunneling microscope, which can image single
atoms using the tunneling of electrons.
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Summary of Chapter 30
• An ideal blackbody absorbs all light incident
on it. The distribution of energy within it as a
function of frequency depends only on its
temperature.
• Frequency of maximum radiation:
Summary of Chapter 30
• Light is composed of photons, each with
energy:
• In terms of wavelength:
• Photoelectric effect: photons eject
electrons from metal surface.
• Planck’s hypothesis:
• Minimum energy: work function, W0
• Minimum frequency:
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Copyright © 2010 Pearson Education, Inc.
Summary of Chapter 30
• Photons have zero rest mass.
Summary of Chapter 30
• de Broglie hypothesis: particles have
wavelengths, depending on their momentum:
• Photon momentum, frequency, and
wavelength:
• Compton effect: a photon scatters off an
atomic electron, and exits with a longer
wavelength:
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• Both X-rays and electrons can be
diffracted by crystals.
• Light and matter display both wavelike
and particle-like properties.
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Summary of Chapter 30
• The position and momentum of waves and
particles cannot both be determined
simultaneously with arbitrary precision:
• Nor can the energy and time:
• Particles can “tunnel” through a region that
classically would be forbidden to them.
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