Chapter 29 - Particles and Waves

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Chapter 29 - Particles and Waves
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• Who won the Nobel prize for his explanation of
  the photoelectric effect?
• Planck
• Bohr
• De Broglie
• Einstein
• The minimum amount of energy to free an electron
  from a piece of metal is called
• The electron volt
• The work function
• The threshold energy
• The quantum energy

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The Photon Model of Light

• The photon model of light consists of three basic
  postulates
• Light consists of discrete, massless units
  called
• photons. A photon travels in vacuum at the
  speed of light, 3.00 108 m/s.
• 2. Each photon has energy

• where f is the frequency of the light and h is a
  universal constant called Plancks constant. The
  value of Plancks constant is h 6.63 1034 J
  s.
• The superposition of a sufficiently large number
  of
• photons has the characteristics of a
  classical light wave.

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Photon Model of Light

• Although the ideas of the photon model of light
  are attributed to Einstein, the first work
  suggesting energy could be quantized was done by
  Max Planck, while studying blackbody radiation
  curves.

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13.3 Radiation
Radiation is the process in which energy is
transferred by means of electromagnetic waves. A
material that absorbs completely is called a
perfect blackbody. The absorbed energy is
emitted by vibrating atoms of the blackbody
object. At the beginning of the 20th century,
scientists, including Planck, studied the
spectrum of EM energy emitted by
blackbodies. The energy emitted did not agree
with theoretical models using classical physics.
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Photon Model of Light

• In 1900, Planck was able to solve the problem by
  constraining the energy of the vibrating atoms to
  be a series of discrete, or quantized values,
  such that

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Photon Model of Light

• Plancks conclusions implied that the lowest
  energy carried by EM waves was equal to hf.
• Einstein was the first to take Plancks idea
  seriously.

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The energy of a photon
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The energy of a photon
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The energy of a photon
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Compare the energy of a photon of red light with
that of a photon of blue light

1. The red photon has more energy because it has a
   greater wavelength
2. The blue photon has more energy because it has a
   greater frequency
3. All photons have the same energy, regardless of
   frequency
4. Photon energy depends on light intensity, not
   color.

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Compare the energy of a photon of red light with
that of a photon of blue light

1. The red photon has more energy because it has a
   greater wavelength
2. The blue photon has more energy because it has a
   greater frequency
3. All photons have the same energy, regardless of
   frequency
4. Photon energy depends on light intensity, not
   color.

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The electron volt

• The amount of energy, hf of a photon is a very
  small number in Joules
• It is time to introduce the electron volt, which
  is defined as the amount of potential energy an
  electron gains (or loses) when it moves through a
  potential difference of one volt

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The electron volt

• Electron volts are energy units, not voltage
  units (unfortunate choice of names if you ask me,
  but nobody did).
• In electron volt units, h 4.14 x 10-15 eVs

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29.3 Photons and the Photoelectric Effect
Experimental evidence that light consists of
photons comes from a phenomenon called the
photoelectric effect.
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The Photoelectric Effect

• In 1886 it was first discovered by Hertz, that a
  negatively charged electroscope could be
  discharged by shining ultraviolet light on it.
• In 1899, Thomson showed that the emitted charges
  were electrons. The emission of electrons from
  a substance due to light striking its surface
  came to be called the photoelectric effect.
• Around 1900, Lenard observed that the
  photoelectric effect was not dependent on light
  intensity, but rather on light frequency, which
  seemed to contradict classical physics.
• In 1905, Einstein used Plancks hypothesis of
  quantized energy to explain the contradiction.
  He won a Nobel Prize for his work.

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Einsteins Postulates

• Einstein framed three postulates about light
  quanta and their interaction with matter
• Light of frequency f consists of discrete quanta,
  each of energy E hf, where h is Plancks
  constant h 6.63 10-34 J s. Each photon
  travels at the speed of light c 3.00 108 m/s.
• Light quanta are emitted or absorbed on an
  all-or-nothing basis. A substance can emit 1 or 2
  or 3 quanta, but not 1.5. Similarly, an electron
  in a metal can absorb only an integer number of
  quanta.
• A light quantum, when absorbed by a metal,
  delivers its entire energy to one electron.

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29.3 Photons and the Photoelectric Effect
When light shines on a metal, a photon, with
energy hf, can give up its energy to an electron
in that metal. The minimum energy required to
remove the least strongly held electrons is
called the work function, W0. The value of W0 is
specific to the metal. The photon energy comes
in discrete packets called quanta, (plural for
quantum).
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29.3 Photons and the Photoelectric Effect
KEmax depends on the frequency of light incident
on the metal. The minimum frequency necessary
for an electron to leave the lattice structure of
the metal (with 0 KE) is the threshold frequency,
f0 . Electrons will not leave the metal at f lt
f0.
W0 hf0
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29.3 Photons and the Photoelectric Effect
Example 2 The Photoelectric Effect for a Silver
Surface The work function for a silver surface
is 4.73 eV. Find the minimum frequency that
light must have to eject electrons from the
surface. It is not necessary to change from
electron volts to Joules to solve this problem.
This is actually a frequency in the ultraviolet
spectrum, not visible.
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The speed of an electron

• Light of 300 nm is incident on sodium metal, W0
  2.75 eV. What is the maximum speed for an
  electron leaving the metal?
• Change wavelength to frequency
• f 1.00 x 1015 Hz, so hf 4.14 eV
• Kmax hf W0 using values given above
• Kmax 1.39 eV or 2.22 x 10-19 J

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The speed of an electron

• Light of 300 nm is incident on sodium metal, W0
  2.75 eV. What is the maximum speed for an
  electron leaving the metal?
• Kmax 2.22 x 10-19 J
• Now find speed, using ½ mv2 (m is mass of
  electron, not mass of Na atom)
• 3. v 6.99 x 105 m/s

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29.3 Photons and the Photoelectric Effect
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29.3 Photons and the Photoelectric Effect