The shape of the lesson
By the end of the lesson, learners can
- Absorbed by depth: Choose a material and a thickness and watch the transmitted intensity fall along I = I₀e⁻μᵛ.
- Production, attenuation, imaging: Four ideas carry the marks.
- 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
X-rays are made by accelerating electrons through a high p.d. and stopping them in a metal target; most of their energy becomes heat, but a little becomes X-ray photons of maximum energy hfₘₐₓ = eV. In the body the beam is attenuated, I = I₀e⁻μᵛ, and the image forms from the contrast between tissues with different μ. A CT scan combines many such views into a 3D image.
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, Shadows in hard light.. Slam fast electrons into a metal target and a few of them throw out X-ray photons. 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: Absorbed by depth | Choose a material and a thickness and watch the transmitted intensity fall along I = I₀e⁻μᵛ. Project tab 2 of the lab (X-rays) and let a student drive it while the class predicts. | Whole class, then pairs |
| 17 to 30 min | Teach and check: Production, attenuation, imaging | Four ideas carry the marks. | Mix-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 (4 questions, 31 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 Production, attenuation, imaging, 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.
Mix-Pair-Share
Students mix around the room until you call pair; they pair with the nearest classmate, discuss the prompt, then mix again. Three prompts of rising difficulty, three different partners.
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 |
|---|---|
| Only a small fraction of the electrons' energy becomes X-rays, the rest is heat, which is why the target must be cooled (often a rotating anode). | The maximum photon energy hfₘₐₓ = eV comes from an electron giving up all its kinetic energy in one go. Attenuation is exponential, so quoting a half-value thickness (ln2/μ) is often the quickest route in a calculation. |
Production and use of X-rays: topic worksheet
4 questions, 31 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 an X-ray tube, electrons are accelerated through a p.d. of 80 kV before striking the target.
(a) Calculate the maximum kinetic energy of an electron, in joules. [2]
(b) Hence state the maximum energy of an X-ray photon produced. [1]
(c) Calculate the minimum wavelength of the X-rays. [3]
(d) State what happens to most of the electrons' energy at the target. [2]
An X-ray beam passes through soft tissue of linear attenuation coefficient 0.20 cm⁻¹.
(a) Calculate the fraction of the beam transmitted through 10 cm of tissue. [2]
(b) Calculate the half-value thickness of the tissue. [2]
(c) Bone has a much larger attenuation coefficient. State and explain what this does to the image. [2]
(d) State one advantage and one disadvantage of a CT scan over a single X-ray image. [2]
A CT scanner builds an image from many X-ray exposures.
(a) Outline how a CT scan produces a three-dimensional image. [3]
(b) State why image contrast for soft tissue is better in CT than in a single X-ray. [2]
(c) State why the radiation dose is a concern. [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)E = eV = 1.60 × 10⁻¹⁹ × 80000 ✓ = 1.28 × 10⁻¹⁴ J (= 80 keV) ✓
- (b)hfₘₐₓ = eV = 1.28 × 10⁻¹⁴ J (80 keV) ✓
- (c)λₘₐₘ = hc/E = (6.63 × 10⁻³⁴ × 3.00 × 10⁸)/1.28 × 10⁻¹⁴ ✓✓ = 1.6 × 10⁻¹¹ m ✓
- (d)Most becomes heat in the target ✓, so it must be cooled (e.g. a rotating anode) ✓
- (a)I/I₀ = e⁻μᵛ = e⁻⁽⁰.²⁰ × ¹₀⁽ = e⁻² ✓ = 0.14 (14%) ✓
- (b)x½ = ln2/μ = 0.693/0.20 ✓ = 3.5 cm ✓
- (c)Bone transmits far less, so it casts a brighter shadow ✓; the difference in transmitted intensity gives contrast, making the bone visible ✓
- (d)Advantage: a 3D image with much better soft-tissue contrast ✓. Disadvantage: a much higher radiation dose ✓
- (a)X-ray images are taken from many angles around the body ✓; a computer combines these slices ✓ to reconstruct a 3D image that can be viewed from any direction ✓
- (b)Combining many views distinguishes small differences in attenuation ✓ that a single overlapping projection would hide ✓
- (c)X-rays are ionising, so a higher dose raises the risk of cell damage ✓
- (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.
X-rays are produced in an X-ray tube when:
- Afast-moving electrons are stopped by a metal target
- Ba metal is heated until it glows
- Ca radioactive source decays
- Dtwo nuclei fuse together
If electrons are accelerated through a p.d. V, the maximum energy of an X-ray photon produced is:
- AeV
- B½eV
- CeV²
- De/V
As an X-ray beam passes through a thickness x of material, its intensity:
- Adecreases exponentially as I = I₀e⁻μᵛ
- Bdecreases linearly with x
- Cstays constant
- Dincreases with x
Bone shows up clearly on an X-ray image because, compared with soft tissue, it has a:
- Amuch larger attenuation coefficient, so it absorbs more
- Bmuch smaller attenuation coefficient
- Chigher temperature
- Dstronger magnetic field
Quiz key
Electrons accelerated through a high p.d. are suddenly decelerated in the target; the lost kinetic energy is emitted as X-ray photons (most becomes heat).
hfₘₐₓ = eV: the most energetic photon is produced when an electron gives up all of its kinetic energy (= eV) in a single interaction.
Attenuation is exponential: I = I₀e⁻μᵛ, where μ is the linear attenuation coefficient of the material.
A larger μ means bone transmits far less of the beam, so it casts a brighter shadow; the difference in transmitted intensity is the image contrast.
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.