The Photoelectric Equation (OCR A Level Physics)

Interaction Between a Photon & Surface Electron

• In the photoelectric effect, it is very important to note:

  Each surface electron can only interact with a single photon

• 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 mv²_max

•  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

  • KE_max 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