Calculate PET photon energy and explain coincidence detection
Calculate the energy of each annihilation photon and explain how paired detections reveal tracer location.
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. Topic 24 was checked against Cambridge’s 2028–2030 syllabus; the other remaining syllabus-year changes are still being reconciled. Online study supports the theory but cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use exponential functions, wave speed, energy conservation and SI units; convert between joules and electronvolts when required.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
In the simplified symmetric case, what is the energy of each annihilation photon?
What you will learn
- Calculate the energy carried by each annihilation gamma photon
- Explain why the photons can be detected outside the body
- Describe how paired arrival times support PET image formation
Each photon carries the electron–positron rest-energy total
For a positron and electron that have slowed before annihilation, the energy from their rest masses is shared between two gamma photons. In the simplified symmetric case, each photon has energy Eγ = mec².
Use the electron mass and the speed of light to find joules. To convert joules to electronvolts, divide by the elementary charge. The result is about 511 keV for each photon.
Paired detections help locate the annihilation
The two gamma photons travel in nearly opposite directions and can leave the body. Detectors arranged around the patient register a pair that arrives within a short coincidence window.
A coincident pair identifies a line between the two detectors. Comparing their arrival times can indicate where along that line the event occurred. Processing many such pairs builds an image of tracer concentration.
Pause and explain
What does a coincident photon pair help identify?
Worked example
Calculate the energy of each photon using me = 9.11 × 10⁻³¹ kg, c = 3.00 × 10⁸ m s⁻¹ and e = 1.60 × 10⁻¹⁹ C.
Show the worked solution
- Energy per photon = mec².
- Eγ = 9.11 × 10⁻³¹ × (3.00 × 10⁸)² = 8.20 × 10⁻¹⁴ J.
- Convert to eV: Eγ/e = 8.20 × 10⁻¹⁴/(1.60 × 10⁻¹⁹) = 5.12 × 10⁵ eV = 512 keV.
Answer 8.20 × 10⁻¹⁴ J, approximately 512 keV per photon.
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Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
An annihilation photon has energy 8.19 × 10⁻¹⁴ J. Convert this to keV using e = 1.60 × 10⁻¹⁹ C.
Give me a hint
Divide by the joules per electronvolt, then convert eV to keV.
Compare my reasoning
- E/e = 8.19 × 10⁻¹⁴ / 1.60 × 10⁻¹⁹ eV.
- This is 5.12 × 10⁵ eV.
- Divide by 1000: 512 keV.
Approximately 512 keV.
Look for these in your work
- Uses J per eV
- Obtains eV before keV
- Converts by a factor of 1000
Two PET detectors register gamma photons from one annihilation within the coincidence window. What geometric information does this provide?
Give me a hint
Think of the path of two oppositely directed photons.
Compare my reasoning
- The photons travel in nearly opposite directions.
- The event lies along the line joining the two detector positions.
- Timing information can further estimate where on that line the event occurred.
The event is associated with the line joining the detectors; arrival-time difference can refine its position along the line.
Look for these in your work
- Uses the opposite photon directions
- Identifies the line of response
- Mentions timing for localisation along the line
A scanner records many coincident photon pairs from different detector positions. Explain how these detections produce an image of tracer concentration.
Give me a hint
Connect each event to a line constraint, then combine many events.
Compare my reasoning
- Each coincident pair supplies a line along which an annihilation occurred.
- Arrival times can add position information along the line.
- Combining many events from many directions estimates where tracer annihilations occur most often, creating a concentration image.
Processing many paired detections and their arrival times reconstructs the spatial distribution of tracer concentration.
Look for these in your work
- Explains what one pair contributes
- Includes timing information
- Connects many events to the final image
Common mistakes
- Using 2mec² as the energy of each photon instead of the pair total
- Forgetting that the pair’s rest energy is shared between two photons
- Assuming one coincidence pair alone creates a complete image
What can you explain now?
In the simplified symmetric case, what is the energy of each annihilation photon?
Compare with the explanation
mec²
The two photons share the pair’s total rest energy of 2mec².
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Make it stick
How does comparing the two photon arrival times help localise a PET event?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.