The shape of the lesson
By the end of the lesson, learners can
- Lines that cross: Each annihilation sends two gamma photons to opposite detectors; the line joining them runs through the tracer.
- Tracer, annihilation, coincidence: Four linked ideas.
- Ultrasound: Z = ρc; Iᵣ/I₀ = (Z₁ − Z₂)²/(Z₁ + Z₂)²; depth d = ½ct.
- X-rays: hfₘₐₓ = eV; attenuation I = I₀e⁻μᵛ; half-value thickness ln2/μ.
- PET: β⁺ tracer; e⁻ + e⁺ → 2γ of 0.511 MeV, opposite directions; coincidence gives a line of response.
One picture every idea returns to
A positron-emitting tracer is taken up by the tissue under study. Each positron annihilates with an electron, producing two gamma photons of 0.511 MeV that travel in opposite directions. A ring of detectors records the pair in coincidence; the line joining the two detectors that fire passes through the annihilation site, and many such lines reconstruct an image of the tracer's distribution.
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, Two photons, one line.. Feed the body a tracer that emits positrons. 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: Lines that cross | Each annihilation sends two gamma photons to opposite detectors; the line joining them runs through the tracer. Project tab 3 of the lab (PET scanning) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Tracer, annihilation, coincidence | Four linked ideas. | Jigsaw |
| 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, 32 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 Tracer, annihilation, coincidence, 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.
Jigsaw
Split the content into expert pieces. Expert groups master one piece each, then regroup so every home team has one expert per piece, and each expert teaches their piece to the team.
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 |
|---|---|
| The 0.511 MeV photon energy is exactly the rest energy of an electron, m₋c²; two are produced so the total comes from the electron and the positron. | The photons go in opposite directions for momentum conservation, which is what makes the line of response work. PET shows physiological function (e.g. metabolic activity), complementing the structural detail of CT or MRI. |
PET scanning: topic worksheet
4 questions, 32 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.
In PET, a positron from the tracer annihilates with an electron.
(a) Show that the energy of each gamma photon produced is about 0.51 MeV. [3]
(b) State the directions in which the two photons travel, and why. [2]
(c) Explain how detecting the pair locates a line of response. [2]
(d) State what a PET scan shows that a CT scan does not. [1]
Describe how a PET scan is carried out and how the image is formed.
(a) State the type of tracer used and how it reaches the region of interest. [2]
(b) Describe what happens to the emitted positrons. [2]
(c) Explain how many lines of response build up an image. [2]
(d) State why the tracer must have a short half-life. [1]
A common PET tracer is fluorine-18, which has a half-life of 110 minutes. (ln2 = 0.693)
(a) Calculate the decay constant of fluorine-18, in min⁻¹. [2]
(b) A sample is prepared with activity 8.0 × 10⁸ Bq. State its activity after 220 minutes. [2]
(c) Calculate the activity after 60 minutes. [3]
(d) State why the short half-life is both useful and inconvenient. [1]
A clinic must choose an imaging method for three cases.
(a) State which of the three techniques use ionising radiation, and which does not. [2]
(b) Suggest the best method to monitor a developing fetus, with a reason. [2]
(c) Suggest the best method to check for a bone fracture, with a reason. [2]
(d) Suggest the best method to find an area of unusually high metabolic activity, with a reason. [3]
Answer key and marking notes
- (a)Each photon carries the electron rest energy: E = m₋c² = 9.11 × 10⁻³¹ × (3.0 × 10⁸)² ✓ = 8.2 × 10⁻¹⁴ J ✓ = 0.51 MeV ✓
- (b)In opposite directions (180° apart) ✓, so that momentum is conserved ✓
- (c)Two detectors firing at the same instant (in coincidence) ✓ fix the straight line the photons travelled, which passes through the annihilation point ✓
- (d)Physiological function (e.g. metabolic activity), not just structure ✓
- (a)A positron-emitting (β⁺) isotope attached to a molecule such as glucose ✓; it is taken up by the tissue that uses that molecule ✓
- (b)Each positron travels a short distance, then annihilates with an electron ✓, producing two 0.511 MeV gamma photons in opposite directions ✓
- (c)Each coincidence gives one line of response through the tracer ✓; many lines cross where the tracer concentrated, reconstructing the image ✓
- (d)To limit the radiation dose to the patient ✓
- (a)λ = 0.693/110 ✓ = 6.3 × 10⁻³ min⁻¹ ✓
- (b)220 min = 2 half-lives, so A = 8.0 × 10⁸/4 ✓ = 2.0 × 10⁸ Bq ✓
- (c)A = A₀e⁻λᵗ = 8.0 × 10⁸ × e⁻⁶.³⁸₋⡊⠿ × ⁶₀ ✓ = 8.0 × 10⁸ × e⁻⁰.³⁸ ✓ = 5.5 × 10⁸ Bq ✓
- (d)Useful: the dose falls quickly; inconvenient: it must be made near the scanner and used at once ✓
- (a)X-rays/CT and PET use ionising radiation ✓; ultrasound does not ✓
- (b)Ultrasound ✓; it is non-ionising and so safe for the fetus, and gives real-time soft-tissue images ✓
- (c)X-ray ✓; bone has a high attenuation coefficient, giving strong contrast against soft tissue ✓
- (d)PET ✓; a tracer that follows metabolism concentrates in active tissue ✓, and the annihilation gamma pairs map where it gathers ✓
The lesson's own checks as a quiz
The quick-check and exam-style questions from the student lesson, printable with the key.
The tracer used in a PET scan is a substance that emits:
- Apositrons (β⁺ emitter)
- Balpha particles
- Cultrasound
- DX-rays directly
When a positron annihilates with an electron, the result is:
- Atwo gamma photons travelling in opposite directions
- Ba single gamma photon
- Ctwo photons in the same direction
- Dan alpha particle
Each gamma photon from the annihilation has an energy of about:
- A0.511 MeV (the electron rest energy)
- B931 MeV
- C13.6 eV
- D0 (photons are massless)
Two detectors on the ring registering photons at the same instant define:
- Aa line of response passing through the annihilation point
- Bthe exact energy of the tracer
- Cthe patient's temperature
- Dthe half-life of the tracer
Quiz key
PET uses a positron-emitting (β⁺) isotope; the positrons annihilate inside the body to produce the detected gamma photons.
Two gamma photons are produced, travelling back to back so that momentum is conserved.
Each photon carries the rest energy of one electron, m₋c² = 0.511 MeV, supplied by the annihilating electron and positron.
A coincidence fixes the straight line the two photons travelled along; that line passes through the annihilation site, and many lines locate the tracer.
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.