PET scanning

Physics A2 · Medical physics. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

A tracer is a substance containing radioactive nuclei. It is put into the body and is absorbed by the tissue being studied. For PET scanning the tracer decays by β+ decay, so it emits positrons.

A positron is the antiparticle of the electron. It travels a very short distance in the tissue, meets an electron, and the two undergo annihilation: their mass becomes the energy of two gamma-ray photons. Momentum is conserved, so the two photons travel in opposite directions.

The photons leave the body and reach a ring of detectors. From the difference in their arrival times, a computer finds where on the line between the two detectors each annihilation happened. Many events build up an image of the tracer concentration.

Rules to remember

Common mistake

Students say the tracer emits the gamma rays directly, or use 2mec2 for one photon. The tracer emits positrons; each of the two photons gets mec2.

Worked example

An electron and a positron, both almost at rest, annihilate. What is the frequency of each gamma-ray photon? (me = 9.11 × 10−31 kg)

  1. Energy of each photon = mec2 = 9.11 × 10−31 × (3.00 × 108)2 = 8.20 × 10−14 J.
  2. f = E/h = (8.20 × 10−14) ÷ (6.63 × 10−34).
  3. f = 1.24 × 1020 Hz.

Answer: About 1.2 × 1020 Hz.

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