PHYS 252 General Physics IV

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PHYS 252 General Physics IV
Quantum Physics Atoms, molecules, and
solids Relativity Nuclear Physics Particle
physics Course webpage at http//fejer.ucol.mx/
fefo/
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Syllabus

• Instructor Alfredo Aranda (fefo) Email
  fefo_at_ucol.mx
• Office hours Open door policy webpage
  http//fejer.ucol.mx/fefo/
• Texts
• 1) Required Tipler P.A. and Mosca G., Physics
  for Scientists and Engineers, Vol. 2C, 5th ed.,
  Freeman and Company.
• 2) Optional Tipler P.A. and Llewellyn R.A.,
  Modern Physics, 5th ed., Freeman and Company.
• Objective This course will introduce students to
  the major developments of physics in the
  twentieth century. Among the principal topics for
  this semester are special relativity, quantum
  mechanics, solid state physics, nuclear physics,
  elementary particles and the quark structure of
  hadrons, and cosmology, including brief
  introductions to general relativity and
  astrophysics.
• 
  
• Exams 2 exams plus final exam.
• Grade Breakdown 2 Exams (20 each)
  40
• Homework
  30
• Final Exam
  30

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Syllabus

• Homework There will be two homework assignments
  per week. Discussion of homework with your
  classmates is encouraged. Late assignments will
  not be accepted after the due date.
• Grade Scale
• A 93-100, A- 90-92, B 85-89, B
  75-84, C 70-74, C 65-69, D 60-64
  
• Topical Outline of the Course
• Wave-Particle Duality and Quantum Mechanics
• Applications of the Schrödinger Equation
• Atoms Molecules
• Solids
• Relativity
• Nuclear Physics
• Elementary Particles and the Beginning of the
  Universe.

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Ch. 34Wave-Particle Duality Quantum Physics
Lecture 1 Waves, Particles, and Quantization
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Light

• The question of whether light consists of a beam
  of particles or waves in motion is one of the
  most interesting in the history of science.
• Isaac Newton used a particle theory of light to
  explain the laws of reflection and refraction
  however, for refraction, he needed to assume
  falsely that light travels faster in water or
  glass than in air.
• The wave theory proposed by Robert Hook and
  Christian Huygens can explain refraction by
  assuming that light travels slower in water or
  glass than in air.
• The diffraction of light and the existence of an
  interference pattern in the double slit
  experiment (1801,Thomas Young) give clear
  evidence that light has wave properties.
• The classical wave theory of light culminated in
  1860 when James Clerk Maxwell published his
  mathematical theory of electromagnetism. Light is
  an electromagnetic wave.

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The Photoelectric Effect
In 1887, in a corner of his physics
classroom at the Karlsruhe Polytechnic
University, Heinrich Hertz produced
electromagnetic waves using a spark gap, and
detected them with another loop and spark gap.
He later observed that when ultraviolet (UV)
light illuminated his spark gap he got better
sparks and that UV illumination could also
discharge an electroscope when charged negative
(but not positive). He had discovered the
photoelectric effect.
J. J. Thomson suspected that the UV light
was somehow causing metal surfaces to emit
electrons, and demonstrated that the particles
emitted had the same q/m as cathode rays.
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Characteristics of the Photoelectric Effect
Lenard was a student of Hertz, and in 1900
he investigated the photoelectric effect with the
apparatus shown. He illuminated the cathode with
UV and observed the cathode-to-anode current
produced, in the presence of a retarding
potential. He studied the current vs. wavelength
and vs. retarding potential. He found the
following

• The current I is proportional to light intensity
• The current I appears without delay as the light
  is turned on, even at low intensities
• There is no current unless frequency f gt ft
• The value of ft depends on the kind of metal of
  which the cathode is made
• When DV is negative, current stops at V0.
• The value of V0 is independent of intensity of UV
  but depends on metal type.

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Einsteins Postulates
Planck constant h6.626x10-34
J.s4.136x10-15 eV.s
To explain the photoelectric effect,
Einstein made 3 assumptions

• Light of frequency f consists of discrete quanta
  (photons) each with energy E hf hc/?
  that travel at the speed of light
• Light is emitted or absorbed only by emitting or
  absorbing complete quanta
• A light quantum, when absorbed by a metal,
  delivers all of its energy to one electron.

These were applied to the photoelectric
effect as follows
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• An electron in a metal receives a quantum of
  light and gains energy hf
• The more light, the greater the number of photons
  and electron current
• If F is the minimum energy necessary to remove
  an electron from a metal surface, the maximum
  kinetic energy of the electrons emitted is
• Photons with frequencies less than a threshold
  frequency ft and therefore with wavelengths
  greater than a threshold wavelength ?t, do not
  have enough energy to eject an electron from a
  particular metal

F, called the work function, is a characteristic
of the particular metal.
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A Testable Prediction
In addition to explaining Lenards
observations of the photoelectric effect,
Einstein was able to make a testable prediction
of an effect that Lenard had not studied.
Einstein predicted that the stopping potential V0
should depend linearly on the frequency f of the
light illuminating the cathode. In particular,
Einstein predicted that a plot of Kmax vs.
frequency f should be a straight line that has
slope h.
Robert Millikan took up the challenge and
did a careful measurement of the stopping
potential vs. frequency. Some of his data is
shown in the figure. He also used the graphs
slope (h/e) to obtain h.
Planck constant h6.626x10-34
J.s4.136x10-15 eV.s
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Photons
Einstein received the 1921 Nobel Prize, not
for his theory of relativity, but for his
explanation of the photoelectric effect. While
Planck had introduced quantization, Einstein had
shown convincingly that energy is quantized and
that light, even while exhibiting interference,
comes in particle-like energy packets, now called
photons. What are photons? Certainly not
classical particles. When traveling through a
double slit, even one photon at a time, they
build up an interference pattern. The
implication is that each photon travels through
both slits and interferes with itself.
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Example The Photon Ratein a Laser Beam
A 1.0 mW light beam from a helium-neon laser
(l 633 nm) shines on a screen. How many
photons strike the screen each second?
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Photodetectors
Modern light detectors, whether photodiodes
or CCD arrays in cameras, are descendents of the
photoelectric effect. Typically, incident light
ejects electrons into a region of a semiconductor
which results in charge storage or current flow.
However, it normally requires many photons to
produce a detectable signal. Can single
photons of visible light be detected? Yes! A
device called a photomultiplier tube has good
detection efficiency for single photons. It
contains a low-work-function photocathode and a
ladder of multiplying electrodes, each
producing several output electrons from each
incoming electron. The result is an electrical
pulse at the anode that signals the arrival of a
single photon at the photocathode. Such devices
are widely used in experimental nuclear and
particle physics.
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The Compton Effect
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Thomson and the Electron
Shortly after Roentgens discovery of
X-rays, J. J. Thompson began using them to study
electrical conduction in gas. He found that
X-rays could discharge an electroscope and
concluded that they must be making air molecules
into ions that made the air conductive. The
implication was that atoms had constituents that
could be split apart. Thomson also
investigated the current associated with cathode
rays by placing collecting electrodes inside the
tube. He found that the current flowed when the
rays were magneticallydeflected to theelectrode
andstopped whenthey weredeflected away.
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Thomsons Crossed-Field Experiment
Thomson built a discharge tube containing a
pair of parallel-plate deflection electrodes,
which at very low pressures could deflect the
cathode rays. Then he applied a perpendicular
magnetic field and found the field values for E
and B at which the magnetic and electrical forces
cancelled, so that the beam went straight
through. Then he turned off the electric field
an noted the radius of curvature r of the beam in
the magnetic field.
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The de Broglie Wavelength
In 1924 Louis de Broglie, then a graduate
student, hypothesized that if light could exhibit
particle-like properties and act as a photon,
then perhaps particles could exhibit wave-like
properties and have a definite wavelength.
In particular, he proposed that the
connection to wavelength was through the
momentum of theparticle-waves in both cases. He
reasoned thatfor light, the momentum is p E/c
hf/c h/l, and that this same relation might
hold for particles like electrons. Thus l
h/p, where l is the de Broglie wavelength of the
particle. He showed that an electron of such
a wavelength fits neatly into the circumference
of an atomic orbit in the Bohr model. Later,
Davisson and Germer measured l from electron
diffraction, which proved to be precisely the de
Broglie wavelength.
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Example The de Broglie Wavelength of a Smoke
Particle
One of the smallest composite microscopic
particles we could imagine using in an experiment
would be a particle of smoke or soot. These are
about 1 mm in diameter, barely at the resolution
limit of most microscopes. A particle of this
size with the density of carbon has a mass of
about 10-18 kg. What is the de Broglie
wavelength for such a particle, if it is moving
slowly at 1 mm/s?
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The Davisson-Germer Experiment
In 1927, Davisson and Germer were studying
how electrons scattered from metal surfaces.
When they used a particular nickel crystal, they
observed clear maxima and minima. In effect,
they had observed Bragg diffraction of electron
waves.
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Electron Interference Diffraction
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Example The de Broglie Wavelength of an Electron
An electron (mass 9.11x10-31 kg) used in the
Davisson-Germer experiment has a speed of
4.35x106 m/s. What is the de Broglie
wavelength of such an electron?
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Interference andDiffraction of Matter
Subsequently, G. P. Thompson showed electron
diffraction when the electrons pass through a
crystal. He observed Laue-type spots in the
diffraction pattern. The figures below show
diffraction patterns when different beams are
passed through an aluminum foil (made of randomly
oriented micro-crystals)
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Interference andDiffraction of Matter (2)
Actually, it is not necessary to use
crystals to demonstrate the interference of
particle waves, if the wavelengths are made long
enough (by using very slow moving particles).
The figures below show two-slit interference
patterns.
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Electron Interference
These figures show the build up of the
electron two-slit interference pattern as the
electrons arrive at the detector.
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Electron Microscope
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End of Lecture 1
Before the next lecture, read TM, Chapter
34.6-10.