Wave Particle Duality

1
Wave Particle Duality

• Advanced Higher Mechanics Topic 9
• By the Fantastic Four

2
Introduction

• Wave-Particle duality shows
• Light can act like a wave and like a particle.
• Other particles can act as waves
• Main experiment for showing light as particles is
  the photoelectric effect.

3
The Photoelectric Effect

• Cathode and anode in a vacuum.
• Quartz window to illuminate the cathode using an
  ultraviolet light.
• Sensitive ammeter shows photocurrent
• Potentiometer provides stopping potential to
  reduce photocurrent to zero.

4
The Photoelectric Effect cont

• Energy of photoelectrons depends on the frequency
  of the light. Below the threshold frequency, no
  electrons are emitted
• Hence, light cannot be considered as waves in
  this case but as a stream of particles, called
  photons (1905 Einsteins quantum theory of light)
• Energy E of a photon
  E hfWhere f frequency of
  beam of light h Plancks constant
  (6.63?1034 Js)
• This can also be written as E hc
  (vf ?) ?

5
The Photoelectric Effect cont

• When a photon is absorbed by the cathode, its
  energy is used in exciting an electron.
• Photoelectron is emitted when the energy is
  sufficient for an electron to escape from an
  atom 
• Conservation of energy relationship for the
  photoelectric effect
• hf hf? ½ mv²
• hf is the energy of incident photon
• hf? is the work function (min. energy
  required to produce photoelectron)
• ½ mv² is the kinetic energy of
  photoelectron

6
Compton Scattering

• Ehf

7
Compton Scattering

• Conservation of linear momentum

8
Wave-Particle Duality of particles

• We know light can behave as particles.
• The equation ? h/? links a property of waves
  (wavelength) with a property of particles
  (momentum).
• In 1924, Louis de Broglie suggested particles
  have a wavelength.
• Using the above equation, we can work out the de
  Broglie wavelength of particles.
• In most cases, this wavelength is VERY small.

9
Example

• Find the de broglie wavelength of an electron
  travelling at 4 x 105 ms-1.
• The momentum of the electron is ?e meve 9.11
  x 10-31 x 4 x 105 3.64 x 10-25 kgms-1
• The de Broglie wavelength is therefore ?e h /
  ?e 6.63 x 10-34 1.82 x 10-9 m
  3.64 x 10-25
• If the velocity is above about 0.1c, then
  relativistic calculations are needed to be done.
  This is not needed for this course.
• People like Jannik can also use this to work out
  the wavelength of a bowel of Shreddies.

10
Wave Properties

• Two properties of waves are
• Interference
• If you hit a ball in snooker, the balls dont
  combine to make one big ball, nor do they
  disappear altogether.
• Diffraction
• If a train travels through a tunnel, it does not
  spread out when it leaves the tunnel, it
  continues along the track.
• We have seen these effects before.

11
Electron Diffraction

• An object like a train has a wavelength many
  times smaller than the width of the tunnel.
• However, as shown before, electrons have a very
  small wavelength.
• This wavelength is about the same size as the
  spacing between atoms on a crystalline solid.
• Therefore, an electron can diffract when passing
  through a crystal.

12
Diffraction Pattern

• Here is a typical pattern from an electron
  diffracting through a crystalline solid.
• The different diffraction amounts is due to the
  atomic spacing in the solid and the wavelength of
  the incident beam.

13
Electron Microscope
14
What you NEED to know.

• The equations, E hf and ? h/?
• How to use the above equations.
• Describe and explain the photoelectric effect.
• Describe and explain electron diffraction.
• Know that a de Broglie wavelength of a particle
  is extremely small, other than on an atomic or
  sub-atomic level.