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Learn7408Paper 3B · Option: Medical physicsRadionuclide imaging and therapyPET scanning
Radionuclide imaging and therapy · Subtopic 1 of 1

PET Scanning

In PET (positron emission tomography), a tracer containing a β⁺ emitter, often fluorine-18 in a glucose-like molecule, is absorbed by active tissue. Each emitted positron travels a millimetre or so and annihilates with an electron, producing two γ photons of 511511 keV each, travelling in opposite directions (conserving momentum). A ring of detectors records pairs arriving at the same time; the line joining them and the tiny difference in arrival times locate the event. Many events build a map of tracer concentration.

Cambridge 9702 Paper 4AQA 7408 Paper 3B≈ 35 minRevision 5 · updated 2026-10-27
Section 1 of 14

Learning objectives

  • Explain what a tracer is and why β⁺ emitters are used in PET.
  • Describe electron–positron annihilation using conservation laws.
  • Calculate the energy and wavelength of annihilation photons.
  • Explain how detected photon pairs produce an image.
Pause and think

When an electron and positron annihilate at rest, why must two photons be produced, not one?

Section 2 of 14

Core idea

Start hereAntimatter in a hospital

A PET scanner uses antimatter. A tracer emits positrons, each of which meets an electron within a millimetre and annihilates into two gamma rays flying apart. Detecting the pairs maps where the tracer gathered.

The big idea

Positron + electron → two γ photons, back to back, each 0.5110.511 MeV. Detector pairs locate the source.

1. Annihilation

Annihilation: two gamma photons back to back
γγring of detectors
Each event gives one line through the tracer's position. Thousands of lines cross where the tracer has collected (an active tumour, say).
Why two photons of equal energy
  1. pbefore≈0p_{\text{before}}\approx0
    Slow positron and electron.
  2. pafter=0⇒two photons, opposite directionsp_{\text{after}}=0\Rightarrow\text{two photons, opposite directions}
    One photon would carry momentum.
  3. 2mec2=2Eγ⇒Eγ=mec22m_ec^2=2E_\gamma\Rightarrow E_\gamma=m_ec^2
    Energy conservation; equal momenta mean equal energies.
Worked examplePhoton energy and wavelength

Electron rest energy.

Goal
EγE_\gamma; λ\lambda.
Strategy
mc2mc^2; λ=hc/E\lambda=hc/E.
  1. 9.11×10−31×(3.0×108)2=8.2×10−14 J9.11\times10^{-31}\times(3.0\times10^8)^2=8.2\times10^{-14}\text{ J}
    Rest energy.
  2. =0.511 MeV=0.511\text{ MeV}
    ÷ 1.6×10−131.6\times10^{-13}.
  3. λ=hcE=2.4×10−12 m\lambda=\frac{hc}E=2.4\times10^{-12}\text{ m}
    Gamma.
Answer0.5110.511 MeV each; 2.4×10−122.4\times10^{-12} m.
✓ CheckShorter than X-ray wavelengths ✓.
  • Tracer e.g. fluorine-18 in glucose (half-life 110 min).
  • Timing difference pinpoints the point along the line.
Common misconceptionOne photon One photon can't conserve momentum: always two.

Summary

  • e++e−→2γe^++e^-\to2\gamma, 0.5110.511 MeV each.
Key words
Annihilation
Particle and antiparticle become energy.
HistoryAntimatter predicted. Paul Dirac predicted the positron in 19281928 from his equation combining quantum mechanics and relativity. Carl Anderson spotted one in a cloud chamber in 19321932, its track curving the "wrong" way in a magnetic field. Within fifty years, antimatter was in routine hospital use.
Fun factYour banana emits positrons. Bananas contain potassium-40, which very occasionally decays by β⁺ emission. A typical banana produces a positron roughly every 7575 minutes. You are also a tiny source: potassium in your body emits a few thousand positrons a day.
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