Wave Particle Duality

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Wave Particle Duality

• Quantum Physics Lesson 3

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Todays Objectives

• Explain what is meant by wave-particle duality.
• Describe the main points of de Broglies
  hypothesis that matter particles also have a
  wave-like nature.
• State and use the equation ? h/p h/mv
• Describe evidence for de Broglies hypothesis.

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Wave particle duality

• We have seen..

Photons Quanta (particles) of light
Electrons Being diffracted. A property of waves
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Prince Louis de Broglie1892-1987

• Electrons should not be considered simply as
  particles, but that frequency must be assigned to
  them also.
• (1929, Nobel Prize Speech)

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De Broglie (1924)

• Suggested that particles such as electrons might
  show wave properties.
• He summised that the de Broglie wavelength, ? was
  given by

m mass v velocity of the particle
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• Note that-
• This is a matter wave equation not
  electromagnetic wave
• The de Broglie wavelength can be altered by
  changing the velocity of the particle.

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In words...
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The diffraction tube
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Summary of Experiment

• Beam of electrons directed at a thin metal foil.
• Rows of atoms cause the electron beam to be
  diffracted in certain directions only.
• We observe rings due to electrons being
  diffracted by the same amount from grains of
  different orientations, at the same angle to the
  incident beam.

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What we should see
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Electron diffraction

• 1927 Davisson Gerner confirmed this prediction
  with experiments using electron beams.
• They actually used a nickel target instead of a
  carbon one (we used)
• The wavelength they measured agreed with de
  Broglie
• There is a relationship between the accelerating
  voltage V and the k.e. of the particles

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• Diffraction effects have been shown for
• Hydrogen atoms
• Helium atoms
• Neutrons
• Neutron diffraction is an excellent way of
  studying crystal structures.

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De Broglie Wavelength

• In 1932, De Broglie discovered that all particles
  with momentum have an associated wavelength.

What is the wavelength of a human being, assuming
he/she weighs 70 kg, and is running at 25 m/s?
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Practice Questions

• 1.Find the wavelength of an electron of mass 9.00
  10-31 kg moving at 3.00 107 m s-1
• 2.  Find the wavelength of a cricket ball of mass
  0.15 kg moving at 30 m s-1.
• 3.  It is also desirable to be able to calculate
  the wavelength associated with an electron when
  the accelerating voltage is known. There are 3
  steps in the calculation. Calculate the
  wavelength of an electron accelerated through a
  potential difference of 10 kV.

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• Step 1 Kinetic energy
• EK eV 1.6 10-19 10000 1.6 10-15 J
• Step 2
• EK ½ mv2 ½m (mv) 2 p2 / 2m,
• so momentum
• p v2mEk v2 9.1 10-31 1.6 10-15
• 5.4 10-23 kg m s-1
• Step 3 Wavelength
• ? h / p 6.63 10-34 / 5.4 10-23 1.2
  10-11 m
• 0.012 nm.

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Slit spacing, d Wavelength, ? Distance to screen,
L Fringe spacing, x

d2
Laser
d1
L1
Slits
Screen 1
Screen 2
L2
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End