CIE A Level Physics复习笔记22.1.4 Threshold Frequency

Threshold Frequency & Wavelength

  • 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

  • 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

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

Coconut Shy Photoelectric Effect, downloadable AS & A Level Physics revision notes

The Photoelectric Equation

  • Since energy is always conserved, the energy of an incident photon is equal to:

The threshold energy + the 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 gives the emitted photoelectron the remaining amount as kinetic energy
  • This equation is known as the photoelectric equation:

E = hf = Φ + ½mv2max

  • Symbols:
    • h = Planck's constant (J s)
    • f = the frequency of the incident radiation (Hz)
    • Φ = the work function of the material (J)
    • ½mv2max= the maximum kinetic energy of the photoelectrons (J)
  • This equation demonstrates:
    • If the incident photons do not have a high enough frequency (f) and energy to overcome the work function (Φ), then no electrons will be emitted
    • When hf0 = Φ, where f0 = threshold frequency, photoelectric emission only just occurs
    • Ekmax 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 Ekmax

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:

Ekmax = hf - Φ

  • A graph of maximum kinetic energy Ekmax against frequency f can be obtained

Graph of maximum kinetic energy of photoelectrons against photon frequency

  • 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

Worked Example

The graph below shows how the maximum kinetic energy Ek of electrons emitted from the surface of sodium metal varies with the frequency f of the incident radiation.

Calculate the work function of sodium in eV.

Step 1:            Write out the photoelectric equation and rearrange to fit the equation of a

straight line

E = hf = Φ + ½mv2max      →    Ekmax = hf - Φ

y = mx + c

 Step 2:            Identify the threshold frequency from the x-axis of the graph

When Ek = 0, f = f0

Therefore, the threshold frequency is f0 = 4 × 1014 Hz

Step 3:            Calculate the work function

From the graph at f0, ½ mvmax2 = 0

Φ = hf0 = (6.63 × 10-34) × (4 × 1014) = 2.652 × 10-19 J

Step 4:            Convert the work function into eV

1 eV = 1.6 × 10-19 J                 J → eV: divide by 1.6 × 10-19

The Photoelectric Equation Worked Example equation