Transcript Walker3_Lecture_Ch30

Lecture Outlines
Chapter 30
Physics, 3rd Edition
James S. Walker
© 2007 Pearson Prentice Hall
This work is protected by United States copyright laws and is provided solely for
the use of instructors in teaching their courses and assessing student learning.
Dissemination or sale of any part of this work (including on the World Wide Web)
will destroy the integrity of the work and is not permitted. The work and materials
from it should never be made available to students except by instructors using
the accompanying text in their classes. All recipients of this work are expected to
abide by these restrictions and to honor the intended pedagogical purposes and
the needs of other instructors who rely on these materials.
Chapter 30
Quantum Physics
Units of Chapter 30
• 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
Units of Chapter 30
• The de Broglie Hypothesis and WaveParticle Duality
• The Heisenberg Uncertainty Principle
• Quantum Tunneling
30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
An ideal blackbody absorbs all the light that is
incident upon it.
30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
An ideal blackbody is also
an ideal radiator. If we
measure the intensity of the
electromagnetic radiation
emitted by an ideal
blackbody, we find:
30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
This illustrates a remarkable experimental
finding:
The distribution of energy in blackbody
radiation is independent of the material from
which the blackbody is constructed — it
depends only on the temperature, T.
The peak frequency is given by:
30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
The peak wavelength increases linearly with
the temperature. This means that the
temperature of a blackbody can be
determined by its color.
Classical physics calculations were
completely unable to produce this
temperature dependence, leading to
something called the “ultraviolet
catastrophe.”
30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
Classical predictions were that the intensity
increased rapidly with frequency, hence the
ultraviolet catastrophe.
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:
The constant h in this equation is known as
Planck’s constant:
30-1 Blackbody Radiation and Planck’s
Hypothesis of Quantized Energy
Planck’s constant is a very tiny number; this
means that the quantization of the energy of
blackbody radiation is imperceptible in most
macroscopic situations. It was, however, a
most unsatisfactory solution, as it appeared
to make no sense.
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:
30-2 Photons and the Photoelectric Effect
Therefore, a more intense beam of light will
contain more photons, but the energy of each
photon does not change.
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:
30-2 Photons and the Photoelectric Effect
This diagram shows the basic layout of a
photoelectric effect experiment.
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.
30-2 Photons and the Photoelectric Effect
Explanations:
1. 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.
30-2 Photons and the Photoelectric Effect
2. A more intense beam means more photons,
and therefore more ejected electrons.
30-3 The Mass and Momentum of a Photon
Photons always travel at the speed of light (of
course!). What does this tell us about their mass
and momentum?
The total energy can be written:
Since the left side of the equation must be
zero for a photon, it follows that the right side
must be zero as well.
30-3 The Mass and Momentum of a Photon
The momentum of a photon can be written:
Dividing the momentum by the energy and
substituting, we find:
30-3 The Mass and Momentum of a Photon
Finally, we can write the momentum of a
photon in the following way:
30-4 Photon Scattering and the Compton
Effect
The Compton effect occurs when a photon
scatters off an atomic electron.
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:
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:
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 Xrays can diffract from crystal planes:
30-5 The de Broglie Hypothesis and WaveParticle Duality
The same patterns can be observed using either
particles or X-rays.
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.
30-5 The de Broglie Hypothesis and WaveParticle Duality
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.
30-5 The de Broglie Hypothesis and WaveParticle Duality
These images show the gradual creation of an
electron diffraction pattern.
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.
30-6 The Heisenberg Uncertainty Principle
The width of the central maximum is given by:
Therefore, it would be possible to have a
narrower central peak by using light of a
shorter wavelength. However, from the de
Broglie relation, as the wavelength goes
down, the momentum goes up:
30-6 The Heisenberg Uncertainty Principle
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.
30-6 The Heisenberg Uncertainty Principle
Mathematically,
30-6 The Heisenberg 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.
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.
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.
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:
• Planck’s hypothesis:
Summary of Chapter 30
• Light is composed of photons, each with
energy:
• In terms of wavelength:
• Photoelectric effect: photons eject
electrons from metal surface.
• Minimum energy: work function, W0
• Minimum frequency:
Summary of Chapter 30
• Photons have zero rest mass.
• Photon momentum, frequency, and
wavelength:
• Compton effect: a photon scatters off an
atomic electron, and exits with a longer
wavelength:
Summary of Chapter 30
• de Broglie hypothesis: particles have
wavelengths, depending on their momentum:
• Both X-rays and electrons can be
diffracted by crystals.
• Light and matter display both wavelike
and particle-like properties.
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.