The shape of the lesson
By the end of the lesson, learners can
- Tune the wavelength: Slide through the spectrum and watch the energy, frequency and momentum move together.
- Three relations to know: Everything in this lesson comes from these.
- Photon: E = hf = hc/λ, momentum p = E/c = h/λ.
- Photoelectric: hf = Φ + KE_max; threshold f₀ = Φ/h; intensity sets rate, frequency sets KE_max.
- de Broglie: λ = h/p; for an electron through voltage V, p = √(2m₋eV).
- Energy levels: hf = E₁ − E₂ gives the wavelength of each spectral line.
One picture every idea returns to
A photon is a quantum of electromagnetic energy. Its energy is E = hf = hc/λ, often measured in electronvolts (1 eV = 1.60 × 10⁻¹⁹ J). Although a photon has no mass, it carries momentum p = E/c = h/λ. Higher frequency means more energy and more momentum.
Forty-five minutes, phase by phase
| Time | Phase | What happens in the room | Grouping |
|---|---|---|---|
| 0 to 5 min | Hook: predict | Open with the question in the title, Light arrives in packets.. Electromagnetic radiation is not a smooth stream of energy. Put the figure on the board: it is the one picture every idea in the lesson returns to. | Whole class, then pairs |
| 5 to 17 min | Teach and check: Tune the wavelength | Slide through the spectrum and watch the energy, frequency and momentum move together. Project tab 1 of the lab (The photon) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Three relations to know | Everything in this lesson comes from these. | Anticipation / Reaction Guide |
| 30 to 43 min | Check and plenary | The quick-check questions from the student lesson, answered on mini whiteboards one at a time; re-teach the one most get wrong, then a random call on the last. | Individual, then whole class |
| 43 to 45 min | Exit and homework | Set the worksheet below (4 questions, 35 marks) from the topic practice set. Learners self-assess against the objectives before they leave. | Individual |
Protect the parts that carry the learning
The sequence carries about fifty minutes of material, so the lab is driven by one student while the class predicts rather than explored freely. Times are a guide.
Protected: the check at 30 minutes. It is the only individual read on whether the key idea landed, and it is not cut.
Cut first if the build overruns: the last check in Three relations to know, never the check or the plenary.
In a 60 minute block: run worksheet questions 1 to 3 in class as a Rally Coach set and model both the hardest worked example and its check live.
Anticipation / Reaction Guide
Before the lesson, students mark five statements true or false. After the teaching they mark them again and justify any change of mind in one sentence each. The statements come from the examiner traps below.
The full structure, with its variations and the other twelve, is on the cooperative-learning page.
What to head off, and how
| Trap learners fall into | Teaching move that pre-empts it |
|---|---|
| A photon's energy is set by its frequency, not by the brightness of the light. | Making a beam brighter sends more photons per second, each still carrying the same hf. Keep wavelengths in metres when using E = hc/λ in joules, and convert to eV only at the end by dividing by 1.60 × 10⁻¹⁹. |
Energy and momentum of a photon: topic worksheet
4 questions, 35 marks. Written in the style of the papers; no past paper question is reproduced. These questions cover the whole topic, so sibling lessons share them.
Green light has a wavelength of 520 nm in a vacuum.
(a) Calculate the frequency of this light. [2]
(b) Calculate the energy of one photon, in joules. [2]
(c) Express this energy in electronvolts. [1]
(d) Calculate the momentum of one photon. [2]
(e) State how the photon energy would change if the wavelength were doubled. [1]
A helium-neon laser emits light of wavelength 633 nm with an output power of 2.0 mW.
(a) Calculate the energy of a single photon. [2]
(b) Calculate the number of photons emitted per second. [3]
(c) Calculate the momentum of one photon. [2]
Fig. 8.1 shows some of the electron energy levels of a hydrogen atom.
(a) Explain why the energy values are negative. [1]
(b) Calculate the energy of the photon emitted in the n = 3 to n = 2 transition, in eV and in joules. [2]
(c) Calculate the wavelength of this photon. [2]
(d) State the region of the spectrum in which this line appears. [1]
(e) Explain why the spectrum of hydrogen consists of discrete lines rather than a continuous band. [3]
Ultraviolet light of wavelength 254 nm falls on a zinc surface of work function 4.3 eV. This question follows the energy from photon to photoelectron.
(a) Calculate the energy of each photon, in eV. [2]
(b) Calculate the maximum kinetic energy of the photoelectrons, in eV and in joules. [2]
(c) Calculate the momentum of one of these photoelectrons. [2]
(d) Calculate the de Broglie wavelength of such a photoelectron. [2]
(e) Calculate the momentum of one incident photon, and comment on how it compares with the photoelectron's momentum. [3]
Answer key and marking notes
- (a)f = c/λ = 3.00 × 10⁸ / 520 × 10⁻⁹ ✓ = 5.77 × 10¹⁴ Hz ✓
- (b)E = hf = 6.63 × 10⁻³⁴ × 5.77 × 10¹⁴ ✓ = 3.83 × 10⁻¹⁹ J ✓
- (c)E = 3.83 × 10⁻¹⁹ / 1.60 × 10⁻¹⁹ = 2.39 eV ✓
- (d)p = h/λ = 6.63 × 10⁻³⁴ / 520 × 10⁻⁹ ✓ = 1.28 × 10⁻²⁷ N s ✓
- (e)E = hc/λ, so doubling λ halves the energy ✓
- (a)E = hc/λ = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / 633 × 10⁻⁹ ✓ = 3.14 × 10⁻¹⁹ J (≈ 1.96 eV) ✓
- (b)number per second = P/E = 2.0 × 10⁻³ / 3.14 × 10⁻¹⁹ ✓✓ = 6.4 × 10¹⁵ s⁻¹ ✓
- (c)p = h/λ = 6.63 × 10⁻³⁴ / 633 × 10⁻⁹ ✓ = 1.05 × 10⁻²⁷ N s ✓
- (a)Energy must be supplied to free the electron from the atom; the zero is taken at infinity, so bound states are negative ✓
- (b)ΔE = −1.51 − (−3.40) = 1.89 eV ✓ = 1.89 × 1.60 × 10⁻¹⁹ = 3.02 × 10⁻¹⁹ J ✓
- (c)λ = hc/ΔE = 1240/1.89 ✓ = 656 nm ✓
- (d)Visible (red) ✓
- (e)The energy levels are discrete ✓; only certain transition energies are possible ✓; each gives one fixed photon energy and wavelength, so the spectrum is a set of lines ✓
- (a)E = 1240/254 ✓ = 4.88 eV ✓
- (b)KE_max = 4.88 − 4.3 = 0.58 eV ✓ = 0.58 × 1.60 × 10⁻¹⁹ = 9.3 × 10⁻²⁰ J ✓
- (c)p = √(2m₋KE) = √(2 × 9.11 × 10⁻³¹ × 9.3 × 10⁻²⁰) ✓ = 4.1 × 10⁻²⁵ N s ✓
- (d)λ = h/p = 6.63 × 10⁻³⁴ / 4.1 × 10⁻²⁵ ✓ = 1.6 × 10⁻⁹ m (1.6 nm) ✓
- (e)pₙₘₒₜₒₙ = h/λ = 6.63 × 10⁻³⁴ / 254 × 10⁻⁹ = 2.6 × 10⁻²⁷ N s ✓; this is far smaller than the photoelectron's momentum (4.1 × 10⁻²⁵ N s) ✓, about 160 times smaller ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
The energy of a photon is directly proportional to its:
- Afrequency
- Bwavelength
- Camplitude
- Dspeed
One electronvolt is equal to:
- A1.60 × 10⁻¹⁹ J
- B6.63 × 10⁻³⁴ J
- C3.00 × 10⁸ J
- D1.60 × 10⁻¹⁶ J
A photon of wavelength λ has momentum:
- Ah / λ
- Bhλ
- Chc / λ
- Dλ / h
If the wavelength of a photon is doubled, its energy is:
- Ahalved
- Bdoubled
- Cunchanged
- Dquadrupled
Quiz key
E = hf, so the energy is proportional to the frequency. Amplitude (brightness) sets the number of photons, not the energy of each one.
An electronvolt is the energy gained by an electron accelerated through 1 V: 1 eV = e × 1 V = 1.60 × 10⁻¹⁹ J.
p = E/c = hf/c = h/λ. The momentum is inversely proportional to wavelength.
E = hc/λ, so energy is inversely proportional to wavelength. Doubling λ halves the energy (and halves the momentum).
What to project
The student lesson embeds these tabs. Open them full screen on the projector; every slider has a drag handle on the stage.
Slides for this lesson
A projectable deck for every pack is on the way. Until then, present the student lesson full screen: its sections, figure and lab tabs follow the same order as the plan above.