AS LEVEL PHYSICS : ELECTRONS AND PHOTONS Quantum Physics : Wave Particle Duality

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AS LEVEL PHYSICS ELECTRONS AND PHOTONSQuantum
Physics Wave Particle Duality

• By the end of this presentation you should be
  able to
• Recall and use the de Broglie equation
• l h / mv ,
• Describe and interpret qualitatively the
  experimental evidence provided by electron
  diffraction for the wave nature of particles

Hyperlinks are indicated with h
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• Following the work on the particle nature of
  electromagnetic waves, Louis de Broglie suggested
  that particles (like electrons) could display
  wave like behaviour.
• He stated that the wavelength associated with a
  particle (the de Broglie wavelength) is inversely
  proportional to its momentum. Which leads to l
  h/ mv

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He arrived at this quite simply, by combining two
well known equations. E hf and E mc2
Can you use them to arrive at l h / mv ?
If Ehf and E mc2, then we can write hf
mc2, We need to get l into the equation, so
use f c / l, The equation then becomes . hc /
l mc2 Simplifying gives h / l mc or h / mc
l
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• When a fluorescent screen is placed behind the
  crystal, a diffraction pattern appears on the
  screen. The regularly spaced atoms in the crystal
  cause the diffraction.
• The pattern can be explained by associating with
  the electrons a wave of wavelength lambda, which
  changes with the momentum p of the electrons
  (according to a relation discovered by Louis de
  Broglie. )
• If the electrons are passed through a lattice of
  atoms with a separation similar to its de
  Broglie wavelength, then the electrons should
  diffract and interfere.
• See pg 136 in text

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• The idea that particles could behave as waves was
  subsequently confirmed by the diffraction pattern
  of crystals produced by electrons.

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• As with the photons, one electron travels through
  the lattice and hits the screen at one location.
  
• Where exactly the electron will hit the screen is
  not predictable, but the probability of where the
  electron will go is predictable. Where the image
  on the screen is bright in the above photograph,
  the probability is the highest. Where the image
  is dark, the probability is zero.
• The typical wavelength of the electron is very
  small. On the larger classical physics scale,
  the electron acts like a particle.
• A web-site to help

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Limitations of Electron Diffraction

• 1. - As the momentum of an object increases,
  its wavelength decreases.
• - Only because of an electrons very low
  mass, is the wavelength large enough to actually
  diffract and interfere as a wave with realistic
  size silts.
• 2. - Most electron diffraction is performed with
  high energy electrons whose wavelengths are
  orders of magnitude smaller than the interplanar
  spacings (distance between layers) in most
  crystals.
• - For this reason, along with the fact that
  electrons are charged, light particles their
  penetration into solids is very limited. To
  obtain a diffraction pattern by allowing
  electrons to pass through the target is then
  possible only if the target is less than 1 mm
  thick. This is how a transmission electron
  microscope (TEM) works.

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Question A tennis ball is a particle, can it
exhibit wave behaviour?

• (1) An electron produced by an electron gun has a
  velocity of 7 x 106 m/s. What is the de Broglie
  wavelength associated with it? (me 9.11 x
  10-31kg)
• ( 10-10 m)
• (2) What is the de Broglie wavelength of a tennis
  ball served with a velocity of 102 m/s? (its mass
  0.058kg)
• (10-34m)
• Use h 6.63 x 10 -34 Js

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• Find the wave length of matter waves associated
  with
• (i) An electron moving at 5 x 106 m/s, assume
  that electron at this speed is non relativistic.
  
• (ii) A tennis ball of mass 125 g moving at 120 km
  / hr.

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