Explain why the existence of a threshold frequency in the photoelectric effect cannot be accounted for by the classical wave model of light, and how the photon model successfully accounts for this observation.
Written & reviewed by James Millett — Biology (Imperial College London), PGCE Science (University of Cambridge).
When light is incident on a metal surface, electrons are emitted only if the frequency of the light exceeds a certain minimum value known as the threshold frequency. This is true regardless of the intensity of the incident light.
Model answer (4 marks)
In the classical wave model energy is delivered continuously to the metal surface. Therefore, even at low frequencies, a sufficiently intense or long‑duration beam should eventually give an electron enough energy to escape, which is not observed.
Because the classical model predicts electron emission at any frequency given enough time or intensity, it cannot explain the absence of emission below a certain frequency.
In the photon model light is quantised. Each photon carries energy E=hf. An electron can be emitted only if a single photon supplies at least the work function φ.
The threshold frequency f₀ is defined by hf₀=φ. Below f₀ no photon has enough energy to liberate an electron, regardless of the light intensity, which matches the experimental observation.
Because the classical model predicts electron emission at any frequency given enough time or intensity, it cannot explain the absence of emission below a certain frequency.
In the photon model light is quantised. Each photon carries energy E=hf. An electron can be emitted only if a single photon supplies at least the work function φ.
The threshold frequency f₀ is defined by hf₀=φ. Below f₀ no photon has enough energy to liberate an electron, regardless of the light intensity, which matches the experimental observation.
Examiner tips
- Use the key phrase ‘classical wave model predicts continuous energy delivery’ to justify the first two points.
- Show the photon energy equation E=hf and relate it to the work function to explain the threshold.
- Mention that intensity only increases the number of photons, not their energy.
- Keep the answer concise and use the exact terminology from the mark scheme.”]
Mark scheme (4 marks)
- In the classical wave model, energy is delivered continuously to the surface, so electrons should eventually be emitted at any frequency given sufficient time/intensity.
- The classical model therefore cannot explain why, at low frequencies, no electrons are emitted even with high-intensity illumination over long periods.
- In the photon model, light consists of discrete quanta (photons), each carrying energy E = hf, so a single photon must have sufficient energy to liberate one electron.
- The threshold frequency corresponds to the minimum photon energy equal to the work function (hf₀ = φ), so below this frequency no individual photon can supply enough energy to overcome the surface binding energy, regardless of intensity.
Key terms in this question
threshold frequency · photoelectric effect · photon · wave model · photon model
Related
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