Question

In a PET scanner, the positron combines with:

• A. Neutron and emits one gamma ray
• B. Electron and emits photon
• C. Electron and emits high-energy photo
• D. Electron and emits two gamma rays

Hint:

The Physics of PET Annihilation: - Antimatter Positron ($e^+$) + Matter Electron ($e^-$) $\rightarrow$ Annihilation. - This event produces exactly two $511\text{ keV}$ gamma rays that fly away from each other in opposite directions along a $180^\circ$ line. - PET scanners use coincidence timing windows to detect these simultaneous, opposing photon hits, allowing the system to map metabolic activity inside the body.

Answer 1

The Correct Option is D

Concept: Positron Emission Tomography (PET) is a highly sensitive nuclear medicine functional imaging method. The process begins by injecting a patient with a radiotracer labeled with a positron-emitting radionuclide (such as Fluorine-18 in FDG). This unstable nucleus decays over time, releasing a positron ($e^+$), which is the antimatter counterpart of an electron.

Step 1: Understanding the Annihilation Event.
Once emitted, the positron travels a very short distance through the surrounding tissue (typically less than $1\text{ mm}$), losing kinetic energy through collisions with nearby atoms. Once it slows down, the positron interacts with a standard electron ($e^-$) from a neighboring tissue molecule. Because matter and antimatter cannot coexist peacefully, the two particles instantly destroy one another in a process called a matter-antimatter annihilation event.

Step 2: Calculating mass-to-energy conversion and emission products.
According to Einstein's mass-energy equivalence equation ($E = mc^2$), the combined rest mass of the electron and positron is converted entirely into pure electromagnetic energy. To satisfy the Law of Conservation of Linear Momentum, this energy cannot be released as a single photon. Instead, the annihilation event splits the energy evenly, emitting exactly two gamma-ray photons that travel in opposite directions along a straight line (forming a $180^\circ \pm 0.5^\circ$ angle). Each of these gamma photons carries an identical energy of $511\text{ keV}$. \[ e^+ + e^- \longrightarrow \gamma \, (511\text{ keV}) + \gamma \, (511\text{ keV}) \quad \text{at } 180^\circ \] The surrounding PET detector ring tracks these pairs using coincidence detection circuits, creating a line of response (LOR) to pinpoint the source of the radiotracer. This mechanism matches Option (D).