WAVE PROPERTIES OF PARTICLE

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UNIT 25 WAVE PROPERTIES OF PARTICLE (2 Hours)
25.1 The de Broglie wavelength 25.2 Electron
diffraction
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25.1 The de Broglie wavelength (1 Hour)

• At the end of this topic, students should be able
  to
• State wave-particle duality
• Use de Broglie wavelength,

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25.1 The de Broglie wavelength
Wave-Particle Duality is the phenomenon where
under certain circumstances a particle exhibits
wave properties, and under other conditions a
wave exhibits properties of a particle.

• From Quantum Theory, the energy of a photon is

.(1)

• From Einsteins Special Theory of Relativity,
  the energy of a particle is

.(2)
(1) (2)
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10.1 The de Broglie wavelength

• So, the momentum p of a photon with wavelength
  ?
• is given by

and
De broglie wavelength
property of wave
property of particle
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10.1 The de Broglie wavelength
Evidences to show duality of light
can behave as
PARTICLE WAVE
Photoelectric Effect Youngs Double Slit experiment
Compton effect Diffraction grating experiment
Particle behaves as a wave
Electron diffraction
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10.1 The de Broglie wavelength
Example 25.1.1
In a photoelectric effect experiment, a light
source of wavelength 5 x 10-7 m is incident on a
potassium surface. Calculate the momentum and
energy of the photon used. (Plancks constant, h
6.63 x 10-34 J s)
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Example 25.1.2
10.1 The de Broglie wavelength
An electron and a photon has the same wavelength
of 0.25 nm. Calculate the momentum and energy (in
eV) of the electron and the photon.
For an electron
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Solution 25.1.2
10.1 The de Broglie wavelength
For a photon
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Exercise

• 1. In a photoelectric effect experiment, a
  light source of wavelength 550 nm is incident
  on a sodium surface. Determine the momentum and
  the energy of a photon used.
• (Given the speed of light in the vacuum,
• c 3.00?108 m s?1 and Plancks constant, h
  6.63?10?34 J s)

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Exercise

• 2. An electron and a proton have the same speed.
• a. Which has the longer de Broglie wavelength?
  Explain.
• b. Calculate the ratio of ?e/ ?p.
• (Given c 3.00?108 m s?1, h 6.63?10?34 J s,
  me9.11?10?31 kg, mp1.67?10?27 kg and
  e1.60?10?19 C)

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25.2 Electron Diffraction(1 Hour)

• At the end of this topic, students should be able
  to
• Describe the observations of electron diffraction
  in Davisson-Germer experiment.
• Explain the wave behaviour of electron in an
  electron microscope.
• State the advantages of electron microscope
  compared to optical microscope.

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25.2 Electron diffraction
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25.2 Electron diffraction

• In 1927 , two physicists C.J Davission and L. H
• Germer carried out electron diffraction
  experiment
• to prove the de Broglie relationship.
• A graphite film is used as a target.
• A beam of electrons in a cathode-ray tube is
• accelerated by the applied voltage towards a
• graphite film.
• The beam of electrons is diffracted after
  passing
• through the graphite film.
• A diffraction pattern is observed on the
  fluorescence
• screen.
• This shows that a beam of fast moving particles
• (electrons) behaves as a wave, exhibiting
  diffraction
• a wave property.

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25.2 Electron diffraction

• Davisson and Germer discovered that if the
• velocity of electrons is increased, the rings
  are
• seen to become narrower showing that the
• wavelength of electrons decreases with
• increasing velocity as predicted by de Broglie
• relationship.

.(1)
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• The velocity of electrons can be determined
• from the accelerating voltage (voltage between
• anode and cathode) i.e

.(2)
(2) into (1) ,
V accelerating voltage
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Example 25.2.3
25.2 Electron diffraction
An electron is accelerated from rest through a
potential difference of 1200 V. Calculate its de
Broglie wavelength.
(me 9.11 x 10-31 kg)
or
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Example 25.2.4
25.2 Electron diffraction
An electron and a proton have the same kinetic
energy. Determine the ratio of the de Broglie
wavelength of the electron to that of the proton.
(me 9.11 x 10-31 kg, mp 1.67 x 10-27 kg)
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Exercise

• An electron and a photon has the same wavelength
  of 0.21 nm. Calculate the momentum and energy (in
  eV) of the electron and the photon.

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Electron Microscope

• A practical device that relies on the wave
• properties of electrons is electron microscope.

• It is similar to optical compound microscope in
  many
• aspects.

• The advantage of the electron microscope over
• the optical microscope is the resolving power
  of
• the electron microscope is much higher than
  that
• of an optical microscope.

The resolving power is inversely proportional
to the wavelength - a smaller wavelength
means greater resolving power, or the ability to
see details.
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Electron Microscope

• This is because the electrons can be accelerated
  
• to a very high kinetic energy giving them a
  very
• short wavelength ? typically 100 times shorter
• than those of visible light.

• As a result, electron microscopes are able to
• distinguish details about 100 times smaller.

• Two types of electron microscope

a) transmission electron microscope, which
produces a two-dimensional image. b) scanning
electron microscope , which produces a
three-dimensional image.
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Electron Microscope

• In the electron microscope, electrons are
  produced
• by the electron gun.
• Electrons are accelerated by voltages on the
  order of
• 105 V have wavelengths on the order of 0.004
  nm.
• Electrons are deflected by the magnetic lens
  to
• form a parallel beam which then incident on the
• object.
• The magnetic lens are actually magnetic fields
  that
• exert forces on the electrons to bring them to
  a
• focus.
• The fields are produced by carefully designed
• current-carrying coils of wire.

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Electron Microscope

• When the object is struck by the electrons, more
• penetrate in some parts than in others,
• depending on the thickness and density of the
  part.
• The image is formed on a fluorescent screen.
• The image is brightest where most electrons have
• been transmitted. The object must be very thin,
  
• otherwise too much electron scattering occurs
  and
• no image form.

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A mite maximum length 0.75 mm
Fig 40-18, p.1304
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Transmission Electron Microscope
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Scanning Electron Microscope
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Fig 40-17, p.1303
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Fig 41-12, p.1340