Work Function & Threshold Frequency
- The photoelectric effect provides important evidence that light is quantised or carried in discrete packets
- This is shown by the fact each electron can absorb only a single photon
- This means only the frequencies of light above a threshold frequency will emit a photoelectron
Threshold Frequency & Wavelength
- The threshold frequency is defined as:
The minimum frequency of incident electromagnetic radiation required to remove a photoelectron from the surface of a metal
- The threshold wavelength, related to threshold frequency by the wave equation, is defined as:
The longest wavelength of incident electromagnetic radiation that would remove a photoelectron from the surface of a metal
- Threshold frequency and wavelength are properties of a material, and vary from metal to metal
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
Examiner Tip
A useful analogy for threshold frequency is a fairground coconut shy:
- One person is throwing table tennis balls at the coconuts, and another person has a pistol
- No matter how many of the table tennis balls are thrown at the coconut it will still stay firmly in place – this represents the low frequency quanta
- However, a single shot from the pistol will knock off the coconut immediately – this represents the high frequency quanta
