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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Introduction
Classical Physics - Deals with 2 categories of
phenomena (a) Particles -- tiny objects like
bullets, electron, proton, neutron. --
they have mass obey Newtons Laws. (b)
Waves -- travels through an opening or around
a barrier the wave diffracts different
parts of the wave interfere. -- both have
properties that are mutually exclusive.
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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. But we
cannot observe both aspect of its behavior
simultaneously,
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• According to the Quantum theory, a photon of
  electromagnetic radiation of wavelength ? has
  energy

.(1)
where h Planck constant c speed of light
in vacuum
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According to Einsteins Theory of special
relativity, the energy equivalent E of a mass m
is given by
Equating (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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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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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
Calculate the de- broglie wavelength for (a) A
car of mass 2x 103 kg moving at 50 ms -1. (b) An
electron of mass 9.11x10-31 kg moving at 1x108 m
s-1.
Solution
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Example 25.1.3
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 25.1.3
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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Solution

• From de Broglie relation,
• the de Broglie wavelength is inversely
  proportional to the mass of the particle. Since
  the electron lighter than the mass of the proton
  therefore the electron has the longer de Broglie
  wavelength.

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Solution
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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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The figure show the Davisson-Germer to discover
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
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
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)
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Example 25.2.4
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 (KE) 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.

- Thus, an electron microscope can distinguish
clearly 2 points separated by a distance which is
of the order of nanometer.
- But an compound microscope can only distinguish
clearly 2 points separated by a distance which is
of order of micrometer.
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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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Electron Microscope

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