Chapter 40 Introduction to quantum physics

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• Chapter 40 Introduction to quantum physics
• March 4, 6 Blackbody radiation
• Introduction to quantum physics
• The need for quantum mechanics.
• Attempts to apply the laws of classical physics
  to explain the behavior of matter on the atomic
  scale were consistently unsuccessful.
• Problems
• Blackbody radiation
• Photoelectric effect
• Emission of light from atoms, etc.
• 2) The quantum mechanics revolution.
• Occurred between 1900 and 1930. Quantum mechanics
  was very successful in explaining the behavior of
  particles of microscopic size.

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40.1 Blackbody radiation and Plancks hypothesis

• Thermal radiation The electromagnetic emission
  from an object.
• Covers all the spectrum.
• At room temperature, the wavelengths of the
  radiation are mainly in the infrared. As the
  surface temperature increases, the wavelength
  shifts to red and then white.
• Classical physics could not describe the observed
  distribution of the radiation emitted by a
  blackbody.

Blackbody An ideal system that absorbs all
radiation incident on it. Blackbody radiation
The electromagnetic radiation emitted by a
blackbody.
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Blackbody approximation A hollow object with a
small hole. The intensity of blackbody radiation
is found to vary with temperature and wavelength.
Two significant experimental results 1) The
total power of the emitted radiation increases
with temperature.
Quiz 40.1
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An early classical attempt to explain blackbody
radiation Rayleigh-Jeans law
Ultraviolet catastrophe At short wavelengths,
there was a major disagreement between the
Rayleigh-Jeans law and experiment.
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Max Planck (1900) assumed that the cavity
radiation came from atomic oscillations in the
cavity walls. He made two assumptions about the
nature of the oscillators
1) The energy of an oscillator can have only
certain discrete values
i) The energy is quantized. ii) Each energy value
corresponds to a quantum state.
2) The oscillators emit or absorb energy when
making a transition from one quantum state to
another, E h f.
The average energy of a wave is the energy
difference between levels of the oscillator,
weighted according to the probability of the wave
being emitted exp(-En /kBT).
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Energy-level diagram A diagram that shows the
quantized energy levels and the allowed
transitions.
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Planck generated a theoretical expression for the
wavelength distribution
Plancks constant h 6.626 10-34 Js is a
fundamental constant of nature.
Conclusions from Plancks equation
1) At long wavelengths, Plancks equation reduces
to the Rayleigh-Jeans expression (using
ex?1x) 2) At short wavelengths, it predicts
an exponential decrease in intensity with
decreasing wavelength. This is in agreement with
the experimental results. 3) Total power radiated
(P40.61)
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4) Peak of the distribution (most probable
wavelength, P40.62)
Wiens displacement law
Question fpeak1/lpeak?
Example 40.1
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Read Ch40 1 Homework Ch40 6(a-c),7,10,13 Due
March 13
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March 13 Photoelectric effect 40.2 The
photoelectric effect Photoelectric effect When
light is incident on certain metallic surfaces,
electrons are emitted. The emitted electrons are
called photoelectrons.
Apparatus Photoelectrons are emitted from the
negative plate and collected at the positive
plate. The current is measured by an ammeter.

• At large positive DV, the current reaches a
  maximum value (all the electrons emitted are
  collected).
• The maximum current increases as the intensity of
  the incident light increases.
• When DV is negative, the current drops.
• When DV is equal to or more negative than -DVs,
  the current is zero. DVs is the stopping
  potential.
• The Maximum kinetic energy of the photoelectrons
• Kmax eDVs.

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Classical predictions and the experimental
results

• 1) Dependence of photoelectron kinetic energy on
  light intensity
• Classical prediction As the light intensity is
  increased, the electrons should be ejected with
  more kinetic energy.
• Experimental result The maximum kinetic energy
  is independent of light intensity.
• 2) Time interval between incidence of light and
  ejection of photoelectrons
• Classical prediction At low light intensities,
  a measurable time interval is required for the
  electron to absorb the incident radiation.
• Experimental result Electrons are emitted
  almost instantaneously, even at very low light
  intensities.
• Dependence of the ejection of electrons on light
  frequency
• Classical prediction Electrons should be
  ejected at any frequency as long as the light
  intensity is high enough.
• Experimental result No electrons are emitted if
  the incident light falls below some cutoff
  frequency c, regardless of the light intensity.
• Dependence of photoelectron kinetic energy on
  light frequency
• Classical prediction There should be no
  relationship between the frequency of the light
  and the photoelectron kinetic energy.
• Experimental result The maximum kinetic energy
  of the photoelectrons increases with increasing
  light frequency.

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• Einstein (1905) extended Plancks concept of
  quantization to electromagnetic waves
• All electromagnetic radiation can be considered
  as a stream of quanta (photons). Each photon has
  an energy of E h.
• A photon of incident light gives all its energy
  hf to a single electron in the metal.
• Electrons ejected from the surface of the metal
  without collision with other metal atoms before
  escaping have the maximum kinetic energy Kmax

Kmax h f
Work function (f) The minimum energy with which
an electron is bound in the metal. It is on the
order of a few electron volts.
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Photon model explanation of the photoelectric
effect
Kmax h f

• 1) Dependence of photoelectron kinetic energy on
  light intensity
• Kmax depends on the light frequency and the work
  function, and is independent of light intensity.
• 2) Time interval between incidence of light and
  ejection of photoelectrons
• Each photon can have enough energy to eject an
  electron immediately.
• Dependence of the ejection of electrons on light
  frequency
• There are no photoelectrons ejected below a
  certain cutoff light frequency, regardless of the
  light intensity. The photon must have more energy
  than the work function in order to eject an
  electron.
• Dependence of photoelectron kinetic energy on
  light frequency
• As the frequency increases, the kinetic energy
  will increase linearly once the photon energy
  exceeds the work function.

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Measurement of the cutoff frequency fc, the
Plancks constant h, and the work function f
fc The intersect on the x axis. h The slope. f
The intersect on the y axis. f h fc. Cutoff
wavelength
Quiz 40.3 Example 40.3
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Applications of the photoelectric effect
CCD Camera
Photomultiplier tube
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Read Ch40 2 Homework Ch40 14,16,17 Due March
27
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• March 23 Compton scattering
• 40.3 The Compton effect
• Arthur Holly Compton (1892 1962)
• Nobel Prizer in Physics (1927) for the discovery
  of the Compton effect.
• Met Lab at the University of Chicago.
• Chancellor of Washington University at St. Louis
  (1946-1953).

Compton effect The decrease in energy (increase
in wavelength) of an x-ray or gamma ray photon
when interacting with matter.
Compton (1922) The classical wave theory of
light cannot explain the scattering of x-rays
from electrons. Classical model 1) Radiation
pressure should cause the electrons to accelerate
in the direction of the wave propagation. 2)
Electrons oscillate at the apparent frequency.
Depending on the energy absorbed, at a given
angle the scattered wave should have a frequency
distribution resulted from the Doppler effect.
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Experimental results 1) The electrons are
scattered through an angle f (billiard ball
collision). 2) At a given angle, only one
frequency of radiation (beside the incident
frequency) is observed.
Comptons explanation 1) The photons can be
thought as point-like particles having energy h
and momentum h/l. 2) The total energy and
momentum of the isolated system of the colliding
photon-electron pair are conserved.
Apparatus
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Compton shift equation
Experiment Spectra of scattered x-ray at various
angles
The shifted peak (l') is caused by the scattering
of x-rays from free electrons
Compton wavelength of the electron
The unshifted wavelength (l0) is caused by x-rays
scattered from the electrons that are tightly
bound to the atoms. (me? mnucleus)
Quiz 40.5 Example 40.4
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Derivation of the Compton shift equation
Energy conservation
Momentum conservation
Three equations, three unknowns (l', v and f) ?
eliminating v and f ? relation between l', l0 and
q
Questions 1) Can Dl be negative? 2) What is the
largest Dl?
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Read Ch40 3 Homework Ch40 24,26,28 Due April
3
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March 25 Wave properties of particles 40.4
Photons and electromagnetic waves

• Depending on the phenomenon being observed, some
  experiments are best explained by the photon
  model, while others are best explained by the
  wave model.
• We must accept both models and admit that the
  true nature of light is not describable in terms
  of any single classical model.
• The particle model and the wave model of light
  complement each other.

40.5 The wave properties of particles

• Louis de Broglie (1892 1987)
• French physicist.
• Nobel Prizer in Physics (1929) for his prediction
  of the wave nature of electrons.
• Originally studied history.

• Broglie hypothesis
• All forms of matter have both wave and particle
  characteristics.
• The de Broglie wavelength of a particle is
  .
• The frequency of a particle is .

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• Broglie hypothesis ? The dual nature of matter
• Particle nature p and E.
• Wave nature ? and .

• Davisson-Germer experiment (1926)
• Scattering of low-energy electrons from a nickel
  target exhibited maxima and minima at specific
  angles.
• They measured the wavelength of electrons and
  confirmed the de Broglie relationship
• p h /l.

• Principle of complementarity
• The wave and particle models of either matter or
  radiation complement each other.
• Neither model can be used exclusively to describe
  matter or radiation adequately.

Quiz 40.6 Example 40.5
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Application the electron microscope

• The electron microscope depends on the wave
  characteristics of electrons.
• The electron microscope has a high resolving
  power because the electrons have a very short
  wavelength
• lelectron (1/ 100) lphoton.

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Read Ch40 4-5 Homework Ch4036,39,41 Due
April 3
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March 27 Quantum particle 40.6 The quantum
particle

• Quantum particle A model that is a result of
  the recognition of the dual nature of matter.
• Entities have both particle and wave
  characteristics.
• We must choose one appropriate behavior in order
  to understand a particular phenomenon.
• Model From waves we can construct an entity that
  exhibits properties of a particle.

Ideal particle zero size, localized in
space. Ideal wave single frequency, infinitely
long, unlocalized in space. However, a localized
entity can be built by summing up infinitely long
waves.
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Summing up a large number of waves produces a
wave packet.
The envelope travels through space with a
different speed than the individual waves.
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Group velocity in terms of energy and momentum
?The group velocity of a wave packet is identical
to the speed of the particle that it represents.
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Read Ch40 6 Homework Ch4045 Due April 3
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March 30 Uncertainty principle 40.7 The
double-slit experiment revisited

• Electron diffraction experiment
• Parallel mono-energetic electron beams are used.
• Small slit widths compared to the electron
  wavelength.
• A typical wave interference pattern is observed.

A minimum occurs at
Closing one slit alternatively no interference
pattern can be observed.

• Conclusions
• An electron interacts with both slits
  simultaneously. It passes trough both slits.
• If an attempt is made to determine experimentally
  which slit the electron goes through, the act of
  measuring destroys the interference pattern.

Closing one slit
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40.8 The uncertainty principle
Quantum theory predicts that it is physically
impossible to measure simultaneously the exact
position and exact momentum of a particle.
Heisenberg uncertainty principle If a
measurement of the position of a particle has an
uncertainty Dx, and a simultaneous measurement of
its x component of momentum has an uncertainty
Dpx, then
Werner Heisenberg (1901-1976) Nobel Prizer in
Physics (1932) for the creation of quantum
mechanics. University of Munich.
The uncertainties arise from the quantum
structure of matter, rather than instrumental
reasons.
Uncertainty principle in terms of energy and time
Example 40.6, 40.7
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Read Ch40 7-8 Homework Ch40 46,49,60,65 Due
April 10