Threshold Frequency (CIE A Level Physics)

Threshold Frequency

• The concept of a threshold frequency is required in order to explain why a low-frequency source, such as a filament lamp, was unable to liberate any electrons in the gold leaf experiment
• The threshold frequency is defined as:

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

Threshold Wavelength

• 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

Metal	Threshold Frequency (f0) / Hz	Threshold Wavelength (λ0) / nm
Sodium	4.40 × 1014	682
Potassium	5.56 × 1014	540
Zinc	1.02 × 1015	294
Iron	1.04 × 1015	289
Copper	1.13 × 1015	266
Gold	1.23 × 1015	244
Silver	9.71 × 1015	30.9

• 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 material

• It is therefore in units of J
• The higher the work function, the harder it is to release an electron from the surface of the 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 can absorb only one photon
  • Therefore, an electron can only escape the surface of the metal if it absorbs a photon which has an energy equal to Φ or higher

• 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

The work function as an energy well

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

• 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 manganese and iron, have threshold frequencies in the ultraviolet region
  • This frequency is much higher than light in the visible light region
  • This is because the attractive forces between the surface electrons and positive metal ions are much stronger