# 2.4.2 Threshold Frequency & Work Function

### Threshold Frequency

• 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

#### Exam 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 ### The 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   • 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, Vs, 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 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 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, Vs
• At this point, the energy needed to cross the gap is equal to the maximum kinetic energy KEmax of the electrons

KEmax = eVS ### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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