OCR A Level Physics A: Gamma camera, PET scanning and ultrasound (H556) – Revision Notes

These revision notes condense sections 6.5.2 (Diagnostic methods in medicine) and 6.5.3 (Using ultrasound) of the OCR Advanced GCE in Physics A (H556) specification, Version 3.0 (March 2026), for first assessment in 2017. Full explanations and worked examples are in the study guide; test yourself with the practice set. The course hub is OCR A Level Physics, the printable list is the checklist, and the free 10-minute diagnostics show where to focus. X-rays and CAT scanning (6.5.1) are covered separately.

Tracers, 6.5.2(a)

	Technetium-99m	Fluorine-18
Emission	Gamma only (about 140 keV)	Positron (β⁺), then two gamma photons from annihilation
Half-life	About 6 hours	About 110 minutes
Used with	Gamma camera	PET scanner
Carried by	Compound chosen for the organ	Fluorodeoxyglucose, a glucose-like molecule

A tracer is a radioactive substance attached to a molecule that goes where the doctor wants to look. A good one emits gamma rays (they leave the body), and has a half-life long enough to use and short enough to limit dose. The “m” in Tc-99m means metastable.

Activity after time t: A = A0 × (1/2)^(t / half-life).

Gamma camera, 6.5.2(b) and (c)

Component	Job
Collimator	Lead plate with parallel holes; only photons travelling along the holes pass, so the image is not blurred
Scintillator	Crystal that turns each absorbed gamma photon into a flash of light
Photomultiplier tubes	Light releases electrons from a photocathode; dynodes multiply them into a pulse
Computer and display	Compares pulses from tubes to find the position, adds a count, builds the image

Method for describing image formation, in steps:

1. Tracer in the organ emits gamma photons in all directions.
2. The collimator lets through only those travelling straight along its holes.
3. A photon in the crystal gives a flash of light.
4. The tubes nearest the flash give the biggest pulses.
5. The computer works out the position and builds up the counts into an image.

Diagnosis: shows function, not just structure. Hot spots (high uptake) and cold spots (low uptake) show disease; images taken over time show how fast the organ takes up and clears the tracer.

PET scanner, 6.5.2(d) and (e)

• Positron meets an electron and they annihilate: mass becomes two gamma photons.
• Momentum conservation: the photons go in opposite directions.
• Energy conservation: each carries the electron rest energy, mc² = 0.511 MeV (so 1.02 MeV in all).
• A ring of detectors records photons arriving together. Each pair defines a line through the annihilation. The computer finds where many lines cross.
• No collimator is used, so more of the radiation is detected than in a gamma camera.
• Resolution is limited because the positron travels a short distance before it annihilates.
• Diagnosis: fluorodeoxyglucose collects in tissue using much glucose, so tumours, the brain and the heart show brightly. Repeat scans show whether treatment has reduced activity.

Issues with an expensive scanner: purchase and running cost, a nearby supply of F-18 because of its short half-life, staff training, how many patients benefit, dose against benefit, and travel or waiting times without it.

Ultrasound, 6.5.3(a) to (c)

• Longitudinal wave, frequency above 20 kHz. Scanners use a few MHz.
• Higher frequency: shorter wavelength (λ = v/f), more detail, but more absorption, so less depth.
• Piezoelectric effect: a p.d. across the crystal changes its shape, and deforming it gives a p.d.
• A transducer is one crystal that emits pulses (alternating p.d. makes it vibrate) and receives echoes (vibration gives a p.d.).
• A-scan: echo strength against time from one direction. Depth d = ct/2.
• B-scan: many A-scans combined into a two-dimensional image; brightness shows echo strength.

Acoustic impedance and reflection, 6.5.3(d) to (f)

Quantity	Equation	Unit
Acoustic impedance	Z = ρc	kg m⁻² s⁻¹
Reflected fraction	Ir/I0 = (Z2 − Z1)² / (Z2 + Z1)²	none
Transmitted fraction	1 − Ir/I0	none

Method for a reflection question:

1. Find Z for each medium, using Z = ρc if only density and speed are given.
2. Subtract, add, then square the ratio.
3. Convert to intensity or percent if asked.
4. Comment: a big difference in Z means strong reflection and little transmission.

Gel: air has a tiny Z, skin a large one, so a bare air gap would reflect nearly everything. The gel removes air and has Z close to skin (impedance matching), so most ultrasound enters.

Doppler, 6.5.3(g)

Δf / f = 2v cos θ / c

• θ is the angle between the beam and the blood flow; at 90° there is no shift.
• The 2 arises because the moving blood acts as a receiver and then a source.
• Rearranged: v = c Δf / (2 f cos θ).
• Check the units: f and Δf in Hz (not MHz and kHz mixed).
• Blood speed comes out in m s⁻¹ because c is in m s⁻¹.

Worked reminders

Decay. A Tc-99m source of 300 MBq is used 12 h later. That is 2 half-lives, so A = 300 × (1/2)² = 75 MBq.

Reflection. A beam of intensity 8.0 mW m⁻² crosses a boundary between tissues of Z = 1.38 × 10⁶ and 1.62 × 10⁶ kg m⁻² s⁻¹.

Ir/I0 = (0.24 × 10⁶ / 3.00 × 10⁶)² = 0.0064
Ir = 0.0064 × 8.0 = 0.051 mW m⁻²;  transmitted = 7.95 mW m⁻²

Doppler. A 6.0 MHz beam meets blood at 0.80 m s⁻¹, at 30° to the flow (c = 1540 m s⁻¹).

Δf = 2 × 6.0×10⁶ × 0.80 × cos 30° / 1540 = 5.4 × 10³ Hz

Image description. For any “describe how the image is formed” question, name each component in order and say what it does to the signal. For PET the order is: positron emitted, annihilation, two photons in opposite directions, detectors in a ring, coincidence, lines of response, computer.

Must-know distinctions

• Gamma camera: single gamma photons, collimator needed. PET: pair of photons from annihilation, no collimator.
• Tc-99m is a gamma emitter. F-18 is a positron emitter.
• A-scan: a graph for one line. B-scan: a two-dimensional image.
• Z is a property of the medium. Reflection depends on the difference between two Z values.
• Gamma camera: shows where single photons came from by blocking the rest. PET: shows where pairs came from by timing.
• Ultrasound intensity reflected and transmitted add up to the incident intensity at a boundary.

Quick self-test

1. A Tc-99m source of 400 MBq is used 3.5 h later. Half-life 6.0 h. Find the activity.
2. F-18 of 250 MBq is used 120 min later. Half-life 110 min. Find the activity.
3. A gel has density 1030 kg m⁻³ and speed 1480 m s⁻¹. Find Z.
4. Two media have Z = 1.50 × 10⁶ and 2.25 × 10⁶ kg m⁻² s⁻¹. Find Ir/I0.
5. An echo arrives 52 μs after the pulse, with speed 1540 m s⁻¹. Find the depth.
6. A 3.5 MHz beam at 40° gives a shift of 1.8 kHz (c = 1540 m s⁻¹). Find v.
7. State the energy of one annihilation photon in MeV and the number of photons produced.
8. Why does the gamma camera need a collimator?
9. Why is F-18 made near the PET scanner?
10. By what factor is the Doppler shift changed if the angle goes from 40° to 70°, other things equal?

Answers

1. 400 × (1/2)^(3.5/6.0) = 267 MBq.
2. 250 × (1/2)^(120/110) = 117 MBq.
3. 1030 × 1480 = 1.52 × 10⁶ kg m⁻² s⁻¹.
4. (0.75/3.75)² = 0.040.
5. d = 1540 × 52 × 10⁻⁶ / 2 = 0.040 m (4.0 cm).
6. v = 1540 × 1.8 × 10³ / (2 × 3.5 × 10⁶ × cos 40°) = 0.52 m s⁻¹.
7. 0.511 MeV; two photons.
8. It allows only photons travelling along the holes to reach the crystal, so each point in the image corresponds to a line through the patient.
9. Its half-life of about 110 minutes means the activity falls quickly in transit.
10. cos 70° / cos 40° = 0.45, so the shift falls to 45% of its value.

Where marks are usually lost

• Giving the gel as a lubricant, with no mention of impedance or air.
• Using d = ct rather than d = ct/2.
• Dropping the 2 or cos θ in the Doppler equation, or mixing MHz and Hz.
• Saying PET photons travel the same way: they go in opposite directions.
• Saying the gamma camera detects positrons.
• Writing the reflection fraction without squaring, or giving a negative answer.
• Describing the collimator, scintillator and tubes without saying what each does to the signal.
• Giving a one-sided answer when asked to discuss a scanner’s cost and benefit.

Official syllabus

OCR Advanced GCE in Physics A (H556), specification Version 3.0 (March 2026), for first assessment in 2017, published by OCR: sections 6.5.2 and 6.5.3.