The shape of the lesson
By the end of the lesson, learners can
- Make electrons diffract: Fire electrons through a thin graphite film and they form diffraction rings.
- Which evidence shows which nature: Examiners want you to match the behaviour to the right model.
- 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
Light and matter both show wave and particle behaviour. Interference and diffraction reveal the wave nature; the photoelectric effect reveals the particle nature. Any moving object has a de Broglie wavelength λ = h/p = h/mv. Electron diffraction is the direct evidence that particles have a wave nature.
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, Everything is both.. Light diffracts like a wave yet ejects electrons like a particle. 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: Make electrons diffract | Fire electrons through a thin graphite film and they form diffraction rings. Project tab 3 of the lab (Wave-particle duality) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Which evidence shows which nature | Examiners want you to match the behaviour to the right model. | Think-Pair-Share |
| 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 (3 questions, 27 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 Which evidence shows which nature, 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.
Think-Pair-Share
Pose the question, give thirty seconds of silent thinking, then a minute to compare with a partner before a few pairs share with the class. The silent minute is the part that cannot be cut.
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 |
|---|---|
| Everyday objects also have a de Broglie wavelength, but it is fantastically small (because their momentum is huge), so they never show diffraction. | Diffraction is only observable when λ is comparable to the spacing of the gaps, which for electrons means atomic spacings, hence a crystal. Use p = mv for slow electrons, or p = √(2m₃eV) when given an accelerating voltage. |
Wave-particle duality: topic worksheet
3 questions, 27 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.
An electron moves with a speed of 2.0 × 10⁶ m s⁻¹.
(a) Calculate the momentum of the electron. [2]
(b) Calculate its de Broglie wavelength. [2]
(c) State why a beam of these electrons can be diffracted by a crystal but not by a wide slit. [2]
(d) A cricket ball of mass 0.16 kg moves at 30 m s⁻¹. State, with a reason, whether its wave nature could be observed. [2]
Electrons are accelerated from rest through a potential difference of 2500 V.
(a) Calculate the kinetic energy of an electron, in joules. [2]
(b) Show that the momentum of an electron is about 2.7 × 10⁻²³ N s. [2]
(c) Calculate the de Broglie wavelength of the electrons. [2]
(d) State and explain the effect on the wavelength of doubling the accelerating voltage. [2]
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)p = mv = 9.11 × 10⁻³¹ × 2.0 × 10⁶ ✓ = 1.8 × 10⁻²⁴ N s ✓
- (b)λ = h/p = 6.63 × 10⁻³⁴ / 1.8 × 10⁻²⁴ ✓ = 3.6 × 10⁻¹⁰ m (0.36 nm) ✓
- (c)Diffraction is strong only when the gap is comparable to λ ✓; this λ matches atomic spacings in a crystal but is far smaller than a slit width ✓
- (d)No ✓; p = 4.8 N s gives λ ≈ 1.4 × 10⁻³⁴ m, far too small to diffract through any gap ✓
- (a)KE = eV = 1.60 × 10⁻¹⁹ × 2500 ✓ = 4.0 × 10⁻¹⁶ J ✓
- (b)p = √(2m₋KE) = √(2 × 9.11 × 10⁻³¹ × 4.0 × 10⁻¹⁶) ✓ = 2.7 × 10⁻²³ N s ✓
- (c)λ = h/p = 6.63 × 10⁻³⁴ / 2.7 × 10⁻²³ ✓ = 2.5 × 10⁻¹¹ m (25 pm) ✓
- (d)λ ∝ 1/√V ✓, so doubling V multiplies λ by 1/√2 ≈ 0.71 (the wavelength falls to about 18 pm) ✓
- (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 de Broglie wavelength of a moving particle is given by:
- Aλ = h / p
- Bλ = hp
- Cλ = p / h
- Dλ = hf
Electron diffraction is direct evidence that electrons:
- Ahave a wave nature
- Bhave no momentum
- Ctravel faster than light
- Dcarry no charge
If the speed of an electron increases, its de Broglie wavelength:
- Adecreases
- Bincreases
- Cstays the same
- Dbecomes zero
Which observation is evidence for the particle nature of light?
- Athe photoelectric effect
- Bdiffraction through a grating
- Ctwo-source interference
- Drefraction at a glass block
Quiz key
The de Broglie relation is λ = h/p, where p is the momentum. A larger momentum means a shorter wavelength.
Diffraction is a wave phenomenon. Electrons forming a diffraction pattern shows that particles also behave as waves.
λ = h/mv, so a larger speed gives a larger momentum and a shorter wavelength. The diffraction rings shrink.
The photoelectric effect needs discrete photons to explain the threshold frequency and instantaneous emission. Diffraction and interference are wave behaviours.
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.