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24.3.2Medical physics and astronomy (A Level)

Annihilation in PET Scanning

5 min read 8 parts Lesson 12 of 22 1 quiz

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Lesson summary

24.3.2 Annihilation in PET Scanning — AS PHYSICS 9702 notes: Explain annihilation of a positron and an electron, the energy and momentum of the two gamma-ray photons and why they suit PET imaging.Positron — The antiparticle of the electron, with the same mass (9.11 × 10−31 kg) bu…

  • Conservation
  • Total energy
  • Each photon
  • Same for all tracers
  • Frequency and wavelength
  • Approximation

Section 1 of 8Positron emission and annihilation

1Positron
  • The antiparticle of the electron, with the same mass (9.11 × 10−31 kg) but charge +e.
2Range
  • After β+ decay it travels less than a millimetre, losing energy by collisions, before meeting an electron.
3Annihilation
Annihilation when a particle meets its equivalent antiparticle they are both destroyed and their mass is converted into energy.
4Process
  • Process e+ + e− → 2γ, which is the opposite of pair production.
5General
  • Annihilation occurs between any particle and its antimatter counterpart.
6Conservation
  • Mass-energy, momentum and charge are conserved.

Section 2 of 8Energy of the photons

Total energy
  • The converted mass is 2me, so Etotal = 2mec2 = 1.64 × 10−13 J = 1.02 MeV.
Each photon
  • The energy is shared equally, so each photon has E = hf = mec2 = 8.2 × 10−14 J = 0.511 MeV.
Same for all tracers
  • Every annihilation photon in a PET scan has 511 keV.
Frequency and wavelength
  • Frequency and wavelength f = E/h and λ = hc/E, about 2.4 × 10−12 m.
Momentum
  • Each photon has momentum p = E/c.
Approximation
  • The small kinetic energy of the positron at annihilation is neglected.

Section 3 of 8Why two photons in opposite directions

Initial momentum
  • The electron and positron are nearly at rest, so total momentum is about zero.
One photon
  • A single photon has momentum E/c, which cannot be zero, so it would violate conservation of momentum.
Two photons
  • Photons moving in exactly opposite directions have equal and opposite momenta and total zero.
Equal energies
  • The photons have equal energies, so equal momentum magnitudes.
Angle
  • They are 180 degrees apart, within a very small angle caused by residual motion.
Charge
  • The total charge is zero before and after.

Section 4 of 8Why gamma rays suit imaging

Penetration
  • The 511 keV photons are energetic enough to pass through the body and escape to a detector.
Straight lines
  • They are not deflected by electric or magnetic fields and travel in straight lines.
Line of annihilation
  • Each pair defines a line along which the annihilation occurred.
Coincidence
  • Two simultaneous detections on opposite sides of the body identify one event.
Alpha and beta
  • These would be stopped inside the body and could not form an image.

Section 5 of 8Chain of events for FDG

1
FDG is taken up by active cells.
2
Fluorine-18 decays by β+ emission.
3
The positron slows over about a millimetre and annihilates with an electron.
4
Two 511 keV gamma photons leave in opposite directions.
Resolution limit
  • The positron range blurs the image slightly, since the tracer atom and the annihilation site differ, setting a limit to PET resolution.
Attenuation
  • Some photons are absorbed in tissue, so data are corrected for attenuation and deeper activity is recorded with lower sensitivity.

Section 6 of 8More from the specification

1Positron emission and annihilation mechanism
  • Radiotracers administered to a patient emit positrons;
  • when a positron collides with an orbital electron, annihilation produces two collinear 511 keV gamma photons.
2Ring detector and coincidence detection
  • A circular array of scintillation crystals detects arrival of paired annihilation photons, enabling computer algorithms to reconstruct high-resolution 3D metabolic activity images.
3Short half-life radiotracers
  • Medical radiotracers such as fluorine-18 have short half-lives, delivering diagnostic data while minimising ionizing radiation dose to patients.
4Radioactive
  • Describes a nucleus that decays spontaneously and randomly.
5Half-life
  • Time for half the nuclei of an isotope to decay.
6Radiation
  • Transfer by electromagnetic waves, requiring no medium
7Radioactive tracer
  • A substance containing radioactive nuclei introduced into the body and absorbed by tissue to study the structure and function of organs.
8Nuclear equation
  • Equation in which nucleon number and charge are conserved.

Section 7 of 8Key terms

TermMeaning
PositronThe antiparticle of the electron, with the same mass and charge +e.
AntiparticleA particle with the same mass as another but opposite charge and other quantum properties.
AnnihilationThe process in which a particle and its antiparticle meet and their mass is converted into the energy of gamma photons.
Gamma-ray photonA high-energy photon from a nuclear process or annihilation, 0.511 MeV for annihilation of an electron and positron.
Pair productionThe creation of a particle and its antiparticle from a high-energy photon.

Section 8 of 8Exam technique

1
Saying only the positron's mass is converted — the electron's mass is also converted, giving 1.02 MeV in total.
2
Saying each photon carries 1.02 MeV — that is the total and each photon has 0.511 MeV.
3
Forgetting that two photons are needed to conserve momentum — one photon cannot give zero total momentum.
4
Thinking annihilation occurs at the nucleus that emitted the positron — the positron travels a short distance first.
5
Describing annihilation as destroying energy — energy, momentum and charge are conserved.
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