Physics • Year 12 • Module 7 • Lesson 10
Synthesis — The Wave Model of Light
Lock in the key vocabulary, the wave evidence table, and the equations for the photoelectric effect before tackling harder questions.
1. Term–definition match
The definitions below are shuffled. Write the matching term from this list in the right-hand column: wave–particle duality, photoelectric effect, work function, threshold frequency, photon, ultraviolet catastrophe, Compton effect, photocurrent, threshold wavelength, polarisation. 10 marks (1 each)
| # | Definition | Matching term |
|---|---|---|
| 1.1 | The concept that light and matter exhibit both wave-like and particle-like properties depending on how they are observed. | |
| 1.2 | The emission of electrons from a metal surface when light of sufficient frequency strikes it. | |
| 1.3 | The minimum energy (φ) required to liberate one electron from the surface of a metal; measured in eV. | |
| 1.4 | The minimum frequency of light below which no electrons are ejected from a metal surface, no matter how intense the light. | |
| 1.5 | A discrete packet (quantum) of electromagnetic energy with energy E = hf; Einstein’s name for a quantum of light. | |
| 1.6 | The failure of classical wave theory to correctly predict the intensity of black-body radiation at short wavelengths; classical theory predicts infinite UV emission. | |
| 1.7 | The change in wavelength of X-rays scattered by electrons, explained by treating photons as particles with momentum p = h/λ. | |
| 1.8 | The electric current produced by electrons ejected from a metal surface in a photoelectric experiment; proportional to the intensity of incident light (above threshold frequency). | |
| 1.9 | The maximum wavelength of light that can eject electrons from a given metal surface; light with wavelength greater than this value cannot eject electrons regardless of intensity. Given by λ0 = hc/φ. | |
| 1.10 | A wave phenomenon in which transverse oscillations are restricted to a single plane; impossible for longitudinal waves, so its observation proves light is a transverse wave. |
2. True or false — with correction
Circle T or F for each statement. If the statement is false, write the corrected version on the line below it. 12 marks (1 T/F + 1 correction each)
2.1 According to the wave model, intense red light should eventually eject electrons from a metal surface, given enough time. T / F
2.2 In the photoelectric effect, the maximum kinetic energy of ejected electrons increases when the intensity of incident light is increased (frequency kept constant). T / F
2.3 Polarisation of light is direct evidence that light is a transverse wave. T / F
2.4 A photon of UV light carries less energy than a photon of red light. T / F
2.5 The threshold frequency for a metal depends on the intensity of the incident light. T / F
2.6 Young’s double slit experiment provides evidence for the wave model because it produces an interference pattern that a particle model cannot explain. T / F
3. Fill-in-the-blank paragraph
Use the word bank to complete the passage. Each word is used once. 8 marks (1 per blank)
Word bank:
frequency · instantaneous · intensity · photon · threshold · transverse · wave · work function
By 1900, the ___________ model of light had overwhelming support: interference, diffraction and polarisation all require ___________ waves. However, the photoelectric effect contradicted this model. Einstein proposed that light consists of quanta called ___________s, each with energy E = hf. There is a ___________ frequency below which no ejection occurs, regardless of how bright the light is. The maximum kinetic energy of ejected electrons depends on ___________, not on the ___________ of the light. Electrons are ejected ___________ — there is no time lag for energy to build up. The minimum energy needed to eject an electron is called the metal’s ___________.
4. Function recall
Answer each question in 1–2 sentences using precise terms from the lesson. 8 marks (2 each)
4.1 State what each symbol in Einstein’s photoelectric equation Kmax = hf − φ represents and give its SI unit.
4.2 Explain why polarisation is considered the strongest single piece of evidence that light is a transverse (rather than longitudinal) wave.
4.3 Describe how doubling the intensity of light (above the threshold frequency) affects: (a) the number of ejected electrons per second and (b) the maximum kinetic energy of each electron.
4.4 Explain what the Compton effect demonstrates about the nature of photons that the photoelectric effect alone could not fully prove.
5. Build a concept map
Draw labelled arrows between the six terms below to show how they connect. Each arrow must carry a linking phrase (e.g. “produces”, “determines”, “is evidence of”). Aim for at least 6 labelled arrows. 6 marks (1 per valid labelled arrow)
Supplied terms: photon · photoelectric effect · threshold frequency · work function · Kmax · intensity.
6. Match the formula to its context
Four equations are listed in Column A. Match each to its correct description in Column B by writing the letter A–D. 4 marks (1 each)
| # | Column A — Equation | Column B — Description | Match |
|---|---|---|---|
| 6.1 | E = hf | A. Einstein’s photoelectric equation giving the maximum kinetic energy of ejected electrons | |
| 6.2 | Kmax = hf − φ | B. Photon momentum (used in Compton effect) | |
| 6.3 | p = h/λ | C. Planck’s quantisation: energy of one photon | |
| 6.4 | c = fλ | D. Wave equation valid for all EM radiation |
Q1 — Term–definition match
1.1 wave–particle duality • 1.2 photoelectric effect • 1.3 work function • 1.4 threshold frequency • 1.5 photon • 1.6 ultraviolet catastrophe • 1.7 Compton effect • 1.8 photocurrent • 1.9 threshold wavelength • 1.10 polarisation.
Marking notes. 1 mark per correct match. Accept minor wording variants.
Q2 — True / false with correction
2.1 True. This is exactly what the wave model predicts — that energy accumulates continuously, so given enough time even red light should eject electrons. The observation that it does not is what contradicts the wave model.
2.2 False. Increasing intensity (at fixed frequency) increases the number of ejected electrons (photocurrent), but does not increase their maximum kinetic energy. Each photon still has energy hf, so Kmax = hf − φ is unchanged.
2.3 True. Only transverse waves can be polarised. Longitudinal waves (like sound) cannot. The fact that light can be plane-polarised proves it is a transverse wave.
2.4 False. UV light has a higher frequency than red light. Since E = hf, a UV photon has more energy than a red photon.
2.5 False. The threshold frequency depends only on the work function of the metal, not on the intensity of the light. Changing intensity changes the number of photons but not their energy.
2.6 True. Classical particles travel in straight lines and would produce only two bright patches behind two slits. The observed alternating bright and dark fringe pattern is a property of wave superposition.
Q3 — Cloze paragraph
In order: wave / transverse / photon / threshold / frequency / intensity / instantaneous / work function.
Q4.1 — Photoelectric equation symbols
Kmax = maximum kinetic energy of ejected electrons (J or eV). h = Planck’s constant = 6.63 × 10−34 J·s (or 4.14 × 10−15 eV·s). f = frequency of incident light (Hz = s−1). φ = work function of the metal (J or eV).
Q4.2 — Why polarisation proves transverse
Polarisation restricts oscillations to a single plane. Only transverse waves (oscillations perpendicular to propagation direction) can be restricted this way. Longitudinal waves (oscillations parallel to propagation) have no plane of oscillation to restrict. Therefore, observable polarisation of light proves unambiguously that light is a transverse wave.
Q4.3 — Effect of doubling intensity
(a) The number of ejected electrons per second doubles. Higher intensity means twice as many photons per second arriving at the surface; each photon above the threshold frequency ejects one electron, so the photocurrent doubles. (b) The maximum kinetic energy of each electron stays the same. Each individual photon still has energy hf, so Kmax = hf − φ is unchanged.
Q4.4 — What the Compton effect adds
The photoelectric effect showed that light is absorbed in discrete quanta (photons) but did not directly demonstrate that photons carry momentum. The Compton effect showed that X-ray photons scatter off electrons and transfer momentum — with a measurable change in their wavelength — exactly as elastic particle collisions would. This proved photons have momentum p = h/λ, a fully particle-like property that the wave model cannot explain.
Q5 — Sample concept map
Correct maps should include arrows such as:
- photon — triggers → photoelectric effect
- threshold frequency — is set by → work function
- Kmax — is determined by → photon (frequency of)
- intensity — controls number of → photons per second
- work function — is subtracted from photon energy to give → Kmax
- intensity — does NOT determine → Kmax
Award 1 mark per valid labelled arrow.
Q6 — Formula matching
6.1 → C • 6.2 → A • 6.3 → B • 6.4 → D.
Note: Do not confuse E = hf (total photon energy) with Kmax = hf − φ (kinetic energy after overcoming the work function). The full photon energy is absorbed; only the excess above φ appears as kinetic energy.