The Photoelectric Effect | Physics for Grade 12 PDF Download

• The field of quantum mechanics is a relatively new field of research, compared to fields in classical mechanics (Newton’s laws, wave theory etc)
• Around 1900, discoveries, such as the electron and the gamma photon, began to conflict with the existing models scientists held about the nature of matter
• Soon after, new theories about the nature of matter began to emerge from Max Planck, Niels Bohr and Albert Einstein, who are seen as the pioneers of Quantum Theory

Timeline of the great advancements in quantum theory since 1900

Demonstrating the Photoelectric Effect

• The photoelectric effect can be observed on a gold leaf electroscope
• A plate of metal, usually zinc, is attached to a gold leaf, which initially has a negative charge, causing it to be repelled by a central negatively charged rod
  • This causes negative charge, or electrons, to build up on the zinc plate
• UV light is shone onto the metal plate, leading to the emission of photoelectrons
• This causes the extra electrons on the central rod and gold leaf to be removed, so, the gold leaf begins to fall back towards the central rod
  • This is because they become less negatively charged, and hence repel less

Observations of the Gold Leaf Experiment

Explaining the Observations

Observation:

• Placing the UV light source closer to the metal plate causes the gold leaf to fall more quickly

Explanation:

• Placing the UV source closer to the plate increases the intensity incident on the surface of the metal
• Increasing the intensity, or brightness, of the incident radiation increases the number of photoelectrons emitted per second
• Therefore, the gold leaf loses negative charge more rapidly

Observation:

• Using a higher frequency light source does not change how quickly the gold leaf falls

Explanation:

• The maximum kinetic energy of the emitted electrons increases with the frequency of the incident radiation
• In the case of the photoelectric effect, energy and frequency are independent of the intensity of the radiation
• So, the intensity of the incident radiation affects how quickly the gold leaf falls, not the frequency

• This provides important evidence that light is quantised or carried in discrete packets
• This also means the number of photoelectrons emitted is exactly equal to the number of photons incident on the surface in which the photoelectric effect is taking place
• Increasing the intensity of the electromagnetic radiation increases the number of photons per area incident on the surface
  • From the one-to-one interaction, this also means this increases the number of photoelectrons emitted from the surface

The Photoelectric Equation

Since energy is always conserved, the energy of an incident photon is equal to:
The work function + the maximum kinetic energy of the photoelectron

• The energy within a photon is equal to hf
• This energy is transferred to the electron to release it from a material (the work function) and the remaining amount is given as kinetic energy to the emitted photoelectron
• This equation is known as the photoelectric equation:

E = hf = Φ + ½ mv²max

Where:

• h = Planck's constant (J s)
• f = the frequency of the incident radiation (Hz)
• Φ = the work function of the material (J)
• ½ mv²_max= KE_max = the maximum kinetic energy of the photoelectrons (J)

This equation demonstrates:

• If the incident photons do not have a high enough frequency and energy to overcome the work function (Φ), then no electrons will be emitted
• hf₀ = Φ, where f₀ = threshold frequency, photoelectric emission only just occurs
• KEmax depends only on the frequency of the incident photon, and not the intensity of the radiation
• The majority of photoelectrons will have kinetic energies less than KE_max

Graphical Representation of Work Function

• The photoelectric equation can be rearranged into the straight line equation:
  y = mx + c
• Comparing this to the photoelectric equation:
  KE_max = hf - Φ
• A graph of maximum kinetic energy KE_max against frequency f can be obtained

The key elements of the graph:

• The work function Φ is the y-intercept
• The threshold frequency f₀ is the x-intercept
• The gradient is equal to Planck's constant h
• There are no electrons emitted below the threshold frequency f₀

Example: The graph below shows how the maximum kinetic energy E_k of electrons emitted from the surface of sodium metal varies with the frequency f of the incident radiation.

Calculate the work function of sodium in eV.

Threshold frequencies and wavelengths for different metals

Work Function

• The work function Φ, or threshold energy, of a material, is defined as:
  The minimum energy required to release a photoelectron from the surface of a metal
• Consider the electrons in a metal as trapped inside an ‘energy well’ where the energy between the surface and the top of the well is equal to the work function Φ
• A single electron absorbs one photon
• Therefore, an electron can only escape from the surface of the metal if it absorbs a photon which has an energy equal to Φ or higher

In the photoelectric effect, a single photon may cause a surface electron to be released if it has sufficient energy

• Different metals have different threshold frequencies and hence different work functions
• Using the well analogy:
  • A more tightly bound electron requires more energy to reach the top of the well
  • A less tightly bound electron requires less energy to reach the top of the well
• Alkali metals, such as sodium and potassium, have threshold frequencies in the visible light region
  • This is because the attractive forces between the surface electrons and positive metal ions are relatively weak
• Transition metals, such as zinc and iron, have threshold frequencies in the ultraviolet region
  • This is because the attractive forces between the surface electrons and positive metal ions are much stronger

The Maximum Kinetic Energy of Photoelectrons & Intensity