2.4.2 Threshold Frequency & Work Function

• The photoelectric effect is the phenomena in which electrons are emitted from the surface of a metal upon the absorption of electromagnetic radiation
• Electrons removed from a metal in this manner are known as photoelectrons
• 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

The photoelectric effect: photons of sufficient energy are able to liberate electrons from the surface of a metal

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

• The frequency and wavelength are related by the equation

• Since photons are particles of light, v = c (speed of light)

• Threshold frequency and wavelength are properties of a material, and vary from metal to metal

Threshold frequencies and wavelengths for different metals

• 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

Stopping Potential

• Stopping potential, V_s, is defined as:

The potential difference required to stop photoelectron emission from occurring

• The photons arriving at the metal plate cause photoelectrons to be emitted
  • This is called the emitter plate

• The electrons that cross the gap are collected at the other metal plate
  • This is called the collector plate

This set up can be used to determine the maximum kinetic energy of the emitted photoelectrons

• The flow of electrons across the gap results in an electromotive force (e.m.f.) between the plates that causes a current to flow around the rest of the circuit
  • Effectively, it becomes a photoelectric cell producing a photoelectric current

• If the e.m.f. of the variable power supply is initially zero, the circuit operates only on the photoelectric current
• As the supply is turned up, the emitter plate becomes more positive (because it is connected to the positive terminal of the supply)
• As a result, electrons leaving the emitter plate are attracted back towards it
  • This is because the potential difference (p.d.) across the tube opposes the motion of the electrons between the plates

• If any electrons escape with enough kinetic energy, they can overcome this attraction and cross to the collector plate
  • And if they don't have enough energy, they can't cross the gap

• By increasing the e.m.f. of the supply, eventually a p.d. will be reached at which no electrons are able to cross the gap – this is the stopping potential, V_s
• At this point, the energy needed to cross the gap is equal to the maximum kinetic energy KE_max of the electrons

KE_max = eV_S