The Photoelectric Equation (OCR A Level Physics): Revision Note

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 each photoelectron is released by one photon, so the number of photoelectrons emitted per second is proportional to the number of photons incident per second on the surface in which the photoelectric effect is taking place

• Increasing the intensity of the electromagnetic radiation increases the number of photons per unit area per second incident on the surface

  • From the one-to-one interaction, this also increases the number of photoelectrons emitted per second 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 y-intercept is −Φ (minus the work function)

  • 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