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Year 12 Science

The Photoelectric Effect

Explore how light ejects electrons from metals, the concept of threshold frequency and work function, and how Einstein's equation provides evidence for the photon model of light.

What Is the Photoelectric Effect?

The photoelectric effect is the emission of electrons from a metal surface when light of sufficiently high frequency shines on it. These emitted electrons are called photoelectrons.

The Photoelectric Effect

hf

Photon

→

Metal Surface

e⁻
↑

A photon with energy E = hf strikes the metal. If hf ≥ φ, an electron is ejected.

Key Observations

  • • Below threshold frequency: no electrons emitted, regardless of intensity
  • • Above threshold: electrons emitted instantly
  • • Increasing intensity increases number of electrons, not their energy
  • • Increasing frequency increases maximum kinetic energy of electrons

Why Waves Cannot Explain This

  • • Wave theory predicts any frequency should eject electrons if bright enough
  • • Wave theory predicts a time delay for dim light
  • • Neither prediction matches experiment
  • • Only the photon model explains all observations

Einstein's Photoelectric Equation

Einstein explained the photoelectric effect by proposing that light consists of photons, each with energy E = hf. A photon transfers all its energy to one electron. Some energy is used to overcome the work function, and the rest becomes kinetic energy.

Ek(max) = hf - φ

Ek(max)

Maximum kinetic energy of ejected electron (J)

=

hf

Photon energy (J)
h = 6.63 × 10-34 J s

-

φ

Work function (J)
Minimum energy to free electron

Threshold frequency (f0): The minimum frequency needed to eject electrons. At threshold: hf0 = φ, so f0 = φ / h. Below this frequency, no photoelectrons are emitted.

Electron volts: Energy is often given in electron volts (eV). 1 eV = 1.6 × 10-19 J. To convert eV to J, multiply by 1.6 × 10-19.

Evidence for the Photon Model

The photoelectric effect provided compelling evidence that light has particle-like properties. Einstein received the Nobel Prize in Physics in 1921 for this explanation.

How the Photon Model Explains Each Observation

Threshold frequency: Each photon must have enough energy (hf ≥ φ) to free an electron. Lower frequency photons simply do not have enough energy, regardless of how many there are.

Instant emission: Energy transfer is one photon to one electron -- there is no need to accumulate energy over time.

Intensity and electron number: Higher intensity means more photons per second, so more electrons are ejected, but each photon still has the same energy.

Frequency and kinetic energy: Higher frequency photons carry more energy (E = hf), so after overcoming φ, more energy is left over as kinetic energy.

Key Vocabulary

Photon

A discrete packet (quantum) of electromagnetic energy with energy E = hf.

Work Function (φ)

The minimum energy required to liberate an electron from the surface of a metal.

Threshold Frequency (f0)

The minimum frequency of incident light required to eject photoelectrons. f0 = φ / h.

Photoelectron

An electron ejected from a metal surface as a result of absorbing a photon of sufficient energy.

Worked Examples

1

UV light of frequency 1.2 × 1015 Hz strikes a metal with work function 3.0 eV. Find Ek(max).

Step 1: Convert φ to joules: φ = 3.0 × 1.6 × 10-19 = 4.8 × 10-19 J

Step 2: Photon energy: E = hf = 6.63 × 10-34 × 1.2 × 1015 = 7.96 × 10-19 J

Step 3: Ek(max) = hf - φ = 7.96 × 10-19 - 4.8 × 10-19 = 3.16 × 10-19 J (or 1.97 eV)

2

A metal has a work function of 2.3 eV. Calculate the threshold frequency.

Step 1: Convert φ = 2.3 × 1.6 × 10-19 = 3.68 × 10-19 J

Step 2: At threshold: hf0 = φ, so f0 = φ / h

Step 3: f0 = 3.68 × 10-19 / 6.63 × 10-34 = 5.55 × 1014 Hz

3

Explain why increasing the intensity of light below the threshold frequency never ejects electrons.

Step 1: Increasing intensity increases the number of photons per second, but not the energy of each individual photon.

Step 2: Each photon interacts with one electron. If hf < φ, no single photon has enough energy to free an electron.

Step 3: Electrons cannot accumulate energy from multiple photons, so no photoelectrons are emitted regardless of intensity.

Knowledge Check

Select the correct answer for each question. Click "Check Answer" to see if you are right.

Question 1

In the photoelectric effect, increasing the frequency of incident light above the threshold will:

Question 2

The work function of a metal is 4.0 eV. What is the threshold frequency?

Question 3

Which observation of the photoelectric effect could NOT be explained by the wave model of light?

Question 4

A photon has energy 5.0 eV and strikes a metal with work function 2.0 eV. The maximum kinetic energy of the ejected electron is:

Question 5

Einstein received the Nobel Prize in Physics in 1921 for:

Key Concepts Summary

Year 12: Magnetic Fields Year 12: Wave-Particle Duality