The Photoelectric Equation (Edexcel International A Level Physics)

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

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

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

Threshold Frequency

• The threshold frequency is defined as:

  The minimum frequency of incident electromagnetic radiation required to remove a photoelectron from the surface of a metal