The Photoelectric Equation (OCR A Level Physics)

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Interaction Between a Photon & Surface Electron

  • In the photoelectric effect, it is very important to note:

Each surface electron can only interact with a single photon

  • This provides important evidence that light is quantised or carried in discrete packets
  • This also means the number of photoelectrons emitted is exactly equal to the number of photons incident on the surface in which the photoelectric effect is taking place
  • Increasing the intensity of the electromagnetic radiation increases the number of photons per area incident on the surface
    • From the one-to-one interaction, this also means this increases the number of photoelectrons emitted from the surface

The Photoelectric Equation

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

The work function + the maximum 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 the remaining amount is given as kinetic energy to the emitted photoelectron
  • This equation is known as the photoelectric equation:

E = hf = Φ + ½ mv2max

  •  Where:
    • h = Planck's constant (J s)
    • f = the frequency of the incident radiation (Hz)
    • Φ = the work function of the material (J)
    • ½ mv2max= KEmax = the maximum kinetic energy of the photoelectrons (J)

  • This equation demonstrates:
    • If the incident photons do not have a high enough frequency and energy to overcome the work function (Φ), then no electrons will be emitted
    • hf0 = Φ, where f0 = threshold frequency, photoelectric emission only just occurs
    • KEmax 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 KEmax

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:

KEmax = hf - Φ

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

  • 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 + ½ mv2max         →    KEmax = 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

Examiner Tip

When using the photoelectric effect equation, hf, Φ and KEmax must all have the same units (joules). Therefore make sure to convert any values given in eV into Joules (× (1.6 × 10-19))

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Katie M

Author: Katie M

Expertise: Physics

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.