Trace PET tracers and positron–electron annihilation
Follow a radioactive tracer through β⁺ decay and explain the creation of two oppositely directed gamma photons.
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
What particle is emitted by β⁺ decay?
What you will learn
- Describe the role of a radioactive tracer in PET
- Identify a β⁺ tracer
- Explain positron–electron annihilation using conservation of mass–energy and momentum
- Describe the two-photon outcome
A tracer highlights tissue activity
A tracer contains radioactive nuclei. It is introduced into the body and absorbed by the tissue being studied, so its distribution indicates where that tissue is active.
PET uses a tracer that decays by β⁺ decay, emitting a positron. The positron travels a short distance through tissue and can then interact with an electron.
Annihilation converts mass–energy into photons
When a particle meets its antiparticle, annihilation can occur. A positron and an electron annihilate, and mass–energy and momentum are conserved in the interaction.
For a positron and electron that have slowed before annihilation, the pair produces two gamma-ray photons travelling in opposite directions. Opposite directions allow momentum to balance. The photons can escape the body and be detected by the scanner.
Pause and explain
Why do the two annihilation gamma photons travel in opposite directions in the simplified model?
Worked example
A PET tracer decays by β⁺ emission. Describe the sequence from tracer uptake to photons that leave the body.
Show the worked solution
- The tracer is absorbed by the tissue being studied.
- Its β⁺ decay emits a positron, which encounters an electron in the tissue.
- The positron and electron annihilate, producing two gamma photons travelling in opposite directions; the photons can escape and be detected.
Answer Tracer uptake is followed by β⁺ decay, positron–electron annihilation and emission of two oppositely directed gamma photons.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
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.
State what is introduced into a patient for a PET scan and why it concentrates in the tissue being studied.
Give me a hint
Distinguish the radioactive nuclei from the tissue uptake they mark.
Compare my reasoning
- The introduced substance is a tracer containing radioactive nuclei.
- It is absorbed by the tissue being studied.
- Its distribution provides a signal associated with that tissue.
A radioactive tracer is introduced and absorbed by the target tissue, marking its distribution for imaging.
Look for these in your work
- Identifies a radioactive tracer
- States that tissue absorbs it
- Explains its imaging role
A tracer emits a β⁺ particle. Identify the particle and describe what can happen when it encounters an electron.
Give me a hint
Name both particles before describing their interaction.
Compare my reasoning
- β⁺ emission produces a positron.
- A positron is the antiparticle of an electron.
- When they interact, they can annihilate, converting their mass–energy into radiation while conserving momentum.
The emitted positron can annihilate with an electron, converting mass–energy into radiation.
Look for these in your work
- Identifies a positron
- Recognises the antiparticle pair
- Mentions conservation in the conversion
Explain why a simplified PET annihilation event produces a pair of gamma photons in opposite directions rather than a single photon.
Give me a hint
Use momentum conservation for a pair initially at rest or moving slowly.
Compare my reasoning
- Before annihilation, the positron–electron pair has approximately zero total momentum in the simplified model.
- A single photon would carry non-zero momentum, so momentum would not balance.
- Two photons with equal and opposite momenta can conserve momentum while carrying the released energy.
Two oppositely directed photons allow both the released energy and the initial momentum to be conserved.
Look for these in your work
- States the initial momentum condition
- Explains why one photon would not balance momentum
- Connects opposite photon directions to conservation
Common mistakes
- Calling the β⁺ particle an electron
- Saying annihilation destroys mass–energy rather than converting it
- Describing only one gamma photon for a near-rest positron–electron pair
What can you explain now?
What particle is emitted by β⁺ decay?
Compare with the explanation
A positron
β⁺ means a positively charged electron antiparticle.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Which conservation principle explains the opposite directions of the two annihilation photons?
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.