Wave-Particle Duality (Cambridge International A-Level Physics)

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
  • Diffraction occurs when waves pass through a gap or around an obstacle and the waves spread out

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

Comparison of wave theory and particulate nature of light

Wave-Particle Duality: Electron Diffraction

Electron diffraction

• Louis de Broglie discovered that matter, such as electrons, can behave as a wave
• Experiments show that 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

Electron diffraction through a vacuum tube

Electrons accelerated through a high potential difference demonstrate wave-particle duality

• In order to observe the diffraction of electrons, they must be focused through a gap similar to their wavelength, 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
  • a lower accelerating voltage increases the diameter of the rings

Investigating electron diffraction

• Electron diffraction tubes can be used to investigate the 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 accelerated through a high potential

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:

$E_{k}=\frac{1}{2}mv^{2}=eV$

• Where:

  • E_k = kinetic energy (J)
  • m = mass (kg)
  • v = velocity (m s^–1)
  • e = charge of an electron (1.60 × 10^–19 C)
  • V = potential difference (V)