22.2.1 Wave-Particle Duality

• Light waves can behave like particles, i.e. photons, and waves
• This phenomenon is called the wave-particle nature of light or wave-particle duality
• Light interacts with matter, such as electrons, as a particle
  • The evidence for this is provided by the photoelectric effect

• Light propagates through space as a wave
  • The evidence for this comes from the diffraction and interference of light in Young’s Double Slit experiment

Light as a Particle

• Einstein proposed that light can be described as a quanta of energy that behave as particles, called photons
• The photon model of light explains that:
  • Electromagnetic waves carry energy in discrete packets called photons
  • The energy of the photons are quantised according to the equation E = hf
  • In the photoelectric effect, each electron can absorb only a single photon - this means only the frequencies of light above the threshold frequency  will emit a photoelectron

• The wave theory of light does not support a threshold frequency
  • The wave theory suggests any frequency of light can give rise to photoelectric emission if the exposure time is long enough
  • This is because the wave theory suggests the energy absorbed by each electron will increase gradually with each wave
  • Furthermore, the kinetic energy of the emitted electrons should increase with radiation intensity
  • However, in the photoelectric effect none of this is observed

• If the frequency is above the threshold and the intensity of the light is increased, more photoelectrons are emitted per second
• Although the wave theory provided good explanations for phenomena such as interference and diffraction, it failed to explain the photoelectric effect

Compare wave theory and particulate nature of light

• Louis de Broglie discovered that matter, such as electrons, can behave as a wave
• He showed a diffraction pattern is produced when a beam of electrons is directed at a thin graphite film
• Diffraction is a property of waves, and cannot be explained by describing electrons as particles

When an electron beam is focused through a crystalline structure, a diffraction pattern can be observed

• In order to observe the diffraction of electrons, they must be focused through a gap similar to their size, such as an atomic lattice
• Graphite film is ideal for this purpose because of its crystalline structure
  • The gaps between neighbouring planes of the atoms in the crystals act as slits, allowing the electron waves to spread out and create a diffraction pattern

• The diffraction pattern is observed on the screen as a series of concentric rings
  • This phenomenon is similar to the diffraction pattern produced when light passes through a diffraction grating
  • If the electrons acted as particles, a pattern would not be observed, instead the particles would be distributed uniformly across the screen

• It is observed that a larger accelerating voltage reduces the diameter of a given ring, while a lower accelerating voltage increases the diameter of the rings

Investigating Electron Diffraction

• Electron diffraction tubes can be used to investigate wave properties of electrons
• The electrons are accelerated in an electron gun to a high potential, such as 5000 V, and are then directed through a thin film of graphite
• The electrons diffract from the gaps between carbon atoms and produce a circular pattern on a fluorescent screen made from phosphor

Electrons are accelerated from the cathode (negative terminal) to the anode (positive terminal) before they are diffracted through a graphite film

• Increasing the voltage between the anode and the cathode causes the energy, and hence speed, of the electrons to increase
• The kinetic energy of the electrons is proportional to the voltage across the anode-cathode:

E_k = ½ mv² = eV