DavissonGermer experiment

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26.2 Electron Diffraction

• Davisson-Germer experiment
• A beam of accelerated electrons strikes on a
  layer of graphite which is extremely thin and a
  diffraction pattern is seen on the tube face as
  shown in figure 26.2a.

4000 V
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• This experiment made by Davisson and Germer
  proves the de Broglie relation was right where
  the wavelength of the electron is given by
• 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
  (eq. 26.2a).

where
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• The velocity of electrons are controlled by the
  
• applied voltage V across anode and cathode
• where

since
and
By substituting eq. (26.2b) into eq. (26.2a),
thus eq. (26.2a) can be written as
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• Electrons are not the only particles which behave
  as waves.
• The diffraction effects are less noticeable with
  more massive particles because their momenta are
  generally much higher and so the wavelength is
  correspondingly shorter.
• Diffraction of the particles are observed when
  the wavelength is of the same order as the
  spacing between plane of the atom.

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• Example 3
• a. An electron is accelerated from rest through
  a potential difference of 1200 V. Find its de
  Broglie wavelength.
• b. An electron and a photon has the same
  wavelength of 0.250 nm. Calculate the momentum
  and energy (in eV) of the electron and the
  photon.
• (Given c 3.00 x 108 m s-1, h 6.63 x 10-34 J
  s , 1 eV1.60 x 10-19 J, mass of electron, m
  9.11 x 10-31 kg, e 1.60 x 10-19 C )

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• Ans For electron
• a. ? 2.75 x 10-11 m
• b. p 3.16 x 10-24 kg m s-1
• K 34.3 eV

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• Example 4
• Compare the de Broglie wavelength of an electron
  and a proton if they have the same kinetic
  energy.
• (Given h 6.63 x 10-34 J s ,1 eV1.60 x 10-19
  J, me 9.11 x 10-31 kg, mp 1.67 x 10-27 kg )

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• Ans 42.8

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26.3 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.
• 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. Therefore the
  diffraction effect of electrons as a wave is much
  less than that of light.
• As a result, electron microscopes are able to
  distinguish details about 100 times smaller.

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• In operation, a beam of electrons falls on a thin
  slice of sample.
• The sample (specimen) to be examined must be very
  thin (a few micrometres) to minimize the effects
  such as absorption or scattering of the
  electrons.
• The electron beam is controlled by electrostatic
  or magnetic lenses to focus the beam to an image.
• The image is formed on a fluorescent screen.
• There are two types of electron microscopes
• Transmission produces a two-dimensional image.
• Scanning produces images with a
  three-dimensional quality.

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• Figures 26.3a and 26.3b are diagram of the
  transmission electron microscope and the scanning
  electron microscope.

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