Lecture 21 Quantum Physics I

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Lecture 21Quantum Physics I
Chapter 27.1 ? 27.5
Outline

• Blackbody Radiation
• The Photoelectric Effect
• X-Rays
• The Compton Effect

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Blackbody Radiation
Objects at any temperature emit EM radiation that
is often referred to as thermal radiation. A good
representation of a blackbody is a cavity, which
light enters through a small hole and which
absorbs the entire incident radiation. The total
amount of radiation, emitted by a blackbody, is
proportional to its temperature and depends only
on its temperature.
Blackbody Spectrum
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Properties of Blackbody Radiation
The peak of the intensity distribution shifts to
shorter wavelengths as the temperature
increases. Wiens displacement ?max T 0.2898
10?2 m K.
Classic theory predicts that the amount of energy
radiated by a BB should increase as ? approaches
0 and go to infinity (ultraviolet catastrophe).
The issue was resolved by Max Planck in
1900. Planck proposed a theory that individual
particles in a BB emit only certain discrete
energies (quanta). E h f, h 6.626 10?34 J s ?
Plancks constant
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The Photoelectric Effect

• Experiments showed that light directed onto a
  metal surface causes the surface to emit
  electrons.
• This phenomenon is called photoelectric effect.

• 3 features of photoelectric effect
• The electron is always emitted at once even under
  a faint light.
• A bright light causes more electrons to be
  emitted than the faint light, but the average
  kinetic energy of the electrons is the same.
• The higher the light frequency, the more kinetic
  energy the electrons have.

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Explanation of the Photoelectric Effect
Einstein suggested that some minimum energy (?)
is needed to pull an electron away from a
metal. ? is called the work function of the metal.
If the quantum energy E lt ?, no electron comes
out.
cutoff frequency
E h f
hf KEmax ?
fc ? /h c/?c
Photons have properties of particles localized
in a small region of space, have energy and
momentum, and interact with other particles (like
billiard balls).
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Electronvolt
Energy unit evectronvolt (eV)
1 eV is the energy an electron gets after passing
through a potential difference of 1 V.
1 eV 1.6 10?19 J
Stopping potential for the photoelectric effect
is the potential difference required to reduce
the current from the photoelectrons to zero.
eV0 KEmax
eV0 h f ? ? ch/? ? ?
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Sample Problem
A light beam is shining on a metal target that
has a work function of 2.2 eV. If a stopping
potential of 1.3 V is required, what is the
wavelength of the incoming monochromatic light?
e ?Vs h f ? ?
? 2.2 eV ?Vs 1.3 V h 6.63 10?34 J s c 3
108 m/s 1 eV 1.6 10?19 J 1 nm 10?9 m
ch/? e ?Vs ?
? c/ f

• ch m J s
• ???? ??
• e ?Vs ? s J

3.55 10?7 m
355 nm
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X-rays
The wave theory of light and the quantum theory
of light complement each other.
In 1895 Wilhelm Roentgen discovered the inverse
photoelectric effect by observing a glow of a
fluorescent screen under bombardment by
electrons. The discovered radiation was very
penetrating and was called X-rays. X-rays are
produced whenever fast electrons are suddenly
stopped. They turned out to be electromagnetic
waves of extremely high frequency.
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X-Rays
X-rays have very short wavelengths (? 10?10 m
or 0.1 nm), much shorter than those of the
visible light. They can show diffraction only on
very closely spaced structures (for example,
crystals).
Crystal lattice structure
The condition for constructive interference of
X-rays is known as Braggs law.
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The Compton Effect
The Compton effect deals with scattering of
X-rays off a material and an accompanied change
of their wavelengths.
The photon may transfer some energy and momentum
to the electron that it collided with, decrease
its energy, and increase its wavelength.

• ?0 ? wavelength of the incident photon
• ? wavelength of the scattered photon
• ? ? scattering angle

h ?? ???0 ? (1 ? cos
?) mec
Compton wavelength 0.00243 nm
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Summary

• Blackbody (thermal) radiation is emitted by an
  object at any temperature and can be explained
  only under an assumption about energy emission in
  discrete values (quanta).
• The photoelectric effect demonstrates the
  particle nature of light.