explain that, in PET scanning, positrons emitted by the decay of the tracer annihilate when they interact with electrons in the tissue, producing a pair of gamma-ray photons travelling in opposite directions

Production and Use of X‑rays – PET Scanning

Objective

Explain that, in PET scanning, positrons emitted by the decay of the tracer annihilate when they interact with electrons in the tissue, producing a pair of gamma‑ray photons travelling in opposite directions.

What is a PET Scan? 🔬

A Positron Emission Tomography (PET) scan is a medical imaging technique that shows how tissues and organs are functioning. It uses a radioactive tracer that emits positrons.

How Positrons Are Produced ⚛️

  • The tracer (e.g., \$^{18}\$F) undergoes beta-plus decay: \$^{18}\$F → \$^{18}\$O + \$e^+ + \nu_e\$.
  • The emitted positron (\$e^+\$) is a light, positively charged particle.
  • It travels a short distance (a few millimetres) before it meets an electron.

Annihilation Process – The Fireworks Analogy 🎆

When the positron meets an electron, they annihilate each other. Think of it like two dancers (positron and electron) performing a perfect pirouette and then releasing two fireworks that shoot straight out in opposite directions.

Mathematically, the annihilation can be written as:

\$e^+ + e^- \rightarrow \gamma + \gamma\$

Each gamma photon has an energy of 511 keV.

Why Do the Photons Go in Opposite Directions? 🧭

  1. Conservation of momentum: The total momentum before annihilation is zero (positron + electron). After annihilation, the two photons must balance each other’s momentum, so they travel back‑to‑back.
  2. Conservation of energy: The combined energy of the two photons equals the rest mass energy of the positron and electron (2 × 511 keV).

Detection of Gamma Photons

In a PET scanner, detectors are arranged in a ring around the patient. When a pair of opposite photons hits the detectors simultaneously, a coincidence event is recorded.

Using the line of response (the straight line connecting the two detectors), the scanner reconstructs the location of the annihilation event. By collecting many such events, a 3‑D image of tracer concentration is produced.

Exam Tip Box

Remember:

Key terms: positron, electron, annihilation, gamma photon, coincidence detection.

Formula to cite: \$e^+ + e^- \rightarrow \gamma + \gamma\$

Why opposite directions matter: Conservation of momentum & energy.

Visual aid: Draw a simple diagram with two arrows pointing opposite each other to illustrate the back‑to‑back photons.

Practice question: “Explain how the conservation laws lead to the detection principle in PET.”

Summary Table

StepProcessKey Point
1Tracer decays (β⁺)Produces positron (\$e^+\$)
2Positron meets electron (\$e^-\$)Annihilation → two γ photons
3Photons detected in coincidenceReconstruct annihilation location