CIE AS/A Level Physics 24.3 PET scanning Study Notes- 2025-2027 Syllabus
CIE AS/A Level Physics 24.3 PET scanning Study Notes – New Syllabus
CIE AS/A Level Physics 24.3 PET scanning Study Notes at IITian Academy focus on specific topic and type of questions asked in actual exam. Study Notes focus on AS/A Level Physics latest syllabus with Candidates should be able to:
- understand that a tracer is a substance containing radioactive nuclei that can be introduced into the body and is then absorbed by the tissue being studied
- recall that a tracer that decays by \( \beta^+ \) decay is used in positron emission tomography (PET scanning)
- understand that annihilation occurs when a particle interacts with its antiparticle and that mass–energy and momentum are conserved in the process
- 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
- Calculate the energy of the gamma-ray photons emitted during the annihilation of an electron–positron pair
- understand that the gamma-ray photons from an annihilation event travel outside the body and can be detected, and an image of the tracer concentration in the tissue can be created by processing the arrival times of the gamma-ray photons
Radioactive Tracers in Medical Diagnosis
A tracer is a specially chosen substance that contains radioactive nuclei and is introduced into the body to study the function or condition of specific tissues or organs.
1. What Is a Radioactive Tracer?
A tracer is a chemical compound in which one or more atoms are replaced by radioactive isotopes. Once inside the body, the tracer behaves like the normal chemical and becomes absorbed by the target tissue.
Key idea: The tracer emits radiation (usually gamma rays), which can be detected from outside the body using a gamma camera.
2. Why Tracers Are Useful
- They allow doctors to study organ function, not just structure.
- They show blood flow, metabolic activity, and tissue uptake.
- They help detect abnormalities such as tumours, blockages, or organ failure.
Most tracers use gamma-emitting isotopes because gamma rays penetrate the body and can be detected externally.
3. Examples of Radioactive Tracers
- Technetium-99m (widely used for bone scans, kidney imaging)
- Iodine-131 (used for thyroid imaging and treatment)
- Fluorine-18 (used in PET scans to study glucose metabolism)
4. Properties Required for a Good Tracer
- Short half-life → minimises radiation exposure
- Emits penetrating gamma rays, not alpha or beta
- Absorbed selectively by the target tissue
- Non-toxic and chemically compatible with the body
Example
Why is a radioactive tracer able to show the function of a particular organ?
▶️ Answer / Explanation
The tracer is absorbed by the organ being studied, and the emitted gamma rays reveal how the organ takes up, processes, or passes the tracer.
Example
Explain why technetium-99m is commonly used as a tracer in medical imaging.
▶️ Answer / Explanation
- It emits gamma rays that can be detected outside the body.
- It has a short half-life (≈6 hours), reducing radiation dose.
- It can be chemically bonded to many compounds → absorbed by specific organs.
Example
A radioactive tracer is injected into the bloodstream to examine kidney function. Explain how the detector readings would differ between a healthy kidney and a damaged kidney.
▶️ Answer / Explanation
Healthy kidney:
- Tracer is rapidly absorbed and filtered from the blood.
- Gamma camera detects strong uptake followed by fast removal.
Damaged kidney:
- Slow or reduced uptake of tracer.
- Tracer remains in the bloodstream for longer.
- Gamma camera shows weaker, delayed, or abnormal patterns.
The difference in tracer movement reveals kidney function.
Tracer for PET Scanning and β⁺ Decay
Positron Emission Tomography (PET) is a powerful imaging technique that uses radioactive tracers which decay by β⁺ (positron) emission.
1. PET Uses β⁺-emitting Tracers
A PET tracer must decay by positron emission so that it releases a positron (the antimatter version of the electron).
Common PET tracers include:
- Fluorine-18 (¹⁸F) — used in FDG for imaging glucose metabolism
- Carbon-11
- Oxygen-15
- Nitrogen-13
These isotopes are often attached to biologically active molecules (like glucose) to track metabolic processes.
2. Why β⁺ Emission is Essential
When the tracer decays, it emits a positron:
\( \mathrm{p \rightarrow n + e^+ + \nu} \)
After travelling a short distance, the positron meets an electron and they annihilate.
Annihilation produces two gamma photons:
- Each has energy \( \mathrm{511\ keV} \)
- They travel in exactly opposite directions (180° apart)
These photon pairs are detected by the PET scanner, allowing precise location of tracer uptake.
3. Applications of PET
- Cancer detection (tumours use more glucose → brighter image)
- Brain activity mapping
- Heart perfusion studies
- Detecting metabolic abnormalities
Example
What type of radioactive decay must a tracer undergo for PET scanning?
▶️ Answer / Explanation
β⁺ (positron) decay, because PET imaging relies on detecting two gamma photons from positron–electron annihilation.
Example
Why is fluorine-18 suitable for PET imaging?
▶️ Answer / Explanation
- It decays by β⁺ emission → required for PET.
- It has a half-life of about 110 minutes → long enough for imaging but short enough to minimise dose.
- It can be incorporated into glucose-like molecules (FDG), allowing mapping of metabolic activity.
Example
A PET tracer emits a positron that annihilates with an electron, producing two photons. Explain how the PET scanner uses these photons to determine the point of annihilation.
▶️ Answer / Explanation
Key steps PET uses:
- The annihilation produces two gamma photons travelling in opposite directions (180° apart).
- The PET detector ring records both photons at the same time (coincidence detection).
- A straight line is drawn between the two detectors that registered the photons.
- The annihilation event must have occurred somewhere along that line.
Repeating this for millions of events allows the computer to reconstruct a detailed 3D map of tracer concentration.
Annihilation of Particles and Antiparticles
Annihilation is a fundamental particle-interaction process in which a particle meets its corresponding antiparticle and both are destroyed.
Their mass is converted into energy in the form of photons, and the process obeys the laws of mass–energy conservation and momentum conservation.
1. What Is Annihilation?
Annihilation occurs when a particle and its antiparticle collide. They disappear and are replaced by photons (usually gamma rays).
- Electron + positron → two gamma photons
- Proton + antiproton → multiple photons or mesons
In PET scanning, annihilation of an electron and positron emits two gamma photons.
2. Conservation of Mass–Energy
The total energy before the interaction equals the total energy after.
Initial energy = mass energy of particle + mass energy of antiparticle + any kinetic energies
Final energy = energy carried by photons
For electron–positron annihilation:
\( \mathrm{E_{photon\,total} = 2 m_e c^2 + KE_{e^+} + KE_{e^-}} \)
3. Conservation of Momentum
Momentum before and after the interaction must be equal.
Because the electron and positron usually meet with nearly equal and opposite momenta, the photons must be emitted in opposite directions (180° apart).
This ensures momentum is conserved.
4. Why Two Photons Are Produced
- One photon alone cannot conserve both energy and momentum in the annihilation of a stationary particle–antiparticle pair.
- Two photons emitted in opposite directions conserve both.
Example
What happens when an electron meets a positron?
▶️ Answer / Explanation
The electron and positron annihilate and produce two gamma photons travelling in opposite directions. Mass–energy and momentum are conserved.
Example
Explain why at least two photons must be produced when an electron and positron annihilate.
▶️ Answer / Explanation
If only one photon were emitted, momentum could not be conserved because a single photon carries momentum in one direction only.
Two photons emitted in opposite directions have equal and opposite momenta, ensuring total momentum remains zero before and after the collision.
Example
An electron and positron annihilate at rest. Calculate the energy of each gamma photon produced (electron rest mass = \( \mathrm{9.11\times10^{-31}\ kg} \)).
▶️ Answer / Explanation
Total rest energy available:
\( \mathrm{E = 2 m_e c^2} \)
Each photon gets half of this:
\( \mathrm{E_{photon} = m_e c^2} \)
Calculate:
\( \mathrm{E = (9.11\times10^{-31})(3.0\times10^8)^2} \)
\( \mathrm{E = 8.19\times10^{-14}\ J} \)
Convert to electronvolts:
\( \mathrm{1\ eV = 1.6\times10^{-19}\ J} \)
\( \mathrm{E = \dfrac{8.19\times10^{-14}}{1.6\times10^{-19}} = 5.12\times10^5\ eV = 511\ keV} \)
Each photon has energy 511 keV.
Positron Annihilation and Gamma-Ray Production in PET Scanning
Positron Emission Tomography (PET) relies on the annihilation of positrons inside the body to produce detectable gamma-ray photons.
1. Emission of Positrons from the Tracer
The radioactive tracer used in PET decays by β⁺ (positron) emission.
A positron (\( \mathrm{e^+} \)) is the antimatter counterpart of the electron.
2. Interaction of the Positron with Tissue
- After emission, the positron travels a very short distance (a few millimetres).
- It gradually loses kinetic energy as it interacts with electrons in the tissue.
- Eventually, a slow-moving positron encounters an electron (\( \mathrm{e^-} \)).
3. Annihilation of Positron and Electron
When the positron meets an electron, they annihilate each other.
Their mass is converted into electromagnetic energy:
\( \mathrm{e^+ + e^- \rightarrow 2\gamma} \)
- Two gamma-ray photons are produced.
- Each photon has energy \( \mathrm{511\ keV} \).
- They travel in opposite directions (at 180° to each other).
This 180° emission ensures momentum conservation.
4. Detection by the PET Scanner
The PET scanner is a ring of gamma detectors surrounding the patient.
- Both photons arrive at opposite sides of the ring at the same instant.
- This coincidence detection identifies the line along which annihilation occurred.
- Repeating this for millions of events reconstructs a detailed 3D image of tracer distribution.
The brighter the area → the more tracer uptake → higher metabolic activity.
Example
Why do two gamma rays travel in opposite directions when a positron annihilates with an electron in PET scanning?
▶️ Answer / Explanation
To conserve momentum. Two photons emitted 180° apart have equal and opposite momenta, keeping total momentum zero before and after the event.
Example
Explain how the annihilation photons allow the PET scanner to determine where the decay occurred inside the body.
▶️ Answer / Explanation
The two 511 keV photons reach detectors on opposite sides of the ring simultaneously. The scanner draws a “line of response” between these detectors. The annihilation event occurred somewhere on that line. Combining many such lines builds a 3D map of tracer concentration.
Example
A positron travels a few millimetres before annihilating with an electron. Explain how this affects the spatial resolution of PET images.
▶️ Answer / Explanation
The annihilation does not occur exactly where the positron was emitted, but slightly away due to the positron’s short travel distance.
- This introduces uncertainty in the exact emission point.
- The line of response is accurate, but the true origin lies a few millimetres from the detected path.
- This limits spatial resolution in PET imaging.
Modern PET systems compensate for this using reconstruction algorithms and higher detector sensitivity.
Energy of Gamma-Ray Photons from Electron–Positron Annihilation
When an electron and a positron annihilate, their entire rest mass is converted into electromagnetic energy.
Typically, two identical gamma-ray photons are produced.
1. Rest Energy of an Electron (or Positron)
\( \mathrm{E = m c^2} \)
- Electron mass: \( \mathrm{m = 9.11\times10^{-31}\ kg} \)
- Speed of light: \( \mathrm{c = 3.0\times10^8\ m/s} \)
So:
\( \mathrm{E = (9.11\times10^{-31})(3.0\times10^8)^2} \)
\( \mathrm{E = 8.19\times10^{-14}\ J} \)
Convert to electronvolts:
\( \mathrm{1\ eV = 1.6\times10^{-19}\ J} \)
\( \mathrm{E = \dfrac{8.19\times10^{-14}}{1.6\times10^{-19}} = 5.12\times10^5\ eV = 511\ keV} \)
2. Energy of Gamma Photons in Annihilation
In most cases (annihilation at rest):
- Total mass energy = \( \mathrm{2m_e c^2} = 2 \times 511\ keV = 1022\ keV} \)
- This energy is equally shared between the two gamma photons.
Each gamma photon has energy \( \mathrm{511\ keV} \)
Final Result:
Energy of each annihilation photon = \( \mathrm{511\ keV} \)
Two photons → total energy = \( \mathrm{1022\ keV} \)
Example
What is the energy of each gamma photon produced when an electron and a positron annihilate at rest?
▶️ Answer / Explanation
Each has energy equal to the rest energy of the electron: \( \mathrm{511\ keV} \).
Example
Calculate the wavelength of the gamma photon produced during electron–positron annihilation. (Each photon has energy \( \mathrm{511\ keV} \).)
▶️ Answer / Explanation
Convert energy to joules:
\( \mathrm{511\ keV = 511\times10^3\times1.6\times10^{-19} = 8.18\times10^{-14}\ J} \)
Use \( \mathrm{E = \frac{hc}{\lambda}} \):
\( \mathrm{\lambda = \frac{hc}{E} = \frac{6.63\times10^{-34} \times 3.0\times10^8}{8.18\times10^{-14}} } \)
\( \mathrm{\lambda = 2.43\times10^{-12}\ m} \)
Wavelength ≈ \( \mathrm{2.4\ pm} \)
Example
An electron and positron annihilate while moving, and the total energy converted to photons is \( \mathrm{1.5\ MeV} \). If two identical photons are produced, calculate the energy of each.
▶️ Answer / Explanation
Total energy shared equally:
\( \mathrm{E_{photon} = \dfrac{1.5\ MeV}{2} = 0.75\ MeV} \)
Each photon has energy \( \mathrm{750\ keV} \).
This is higher than the rest-energy-only case because the particles had kinetic energy.
Detection of Gamma Photons in PET and Image Formation
In PET scanning, the gamma-ray photons produced during positron–electron annihilation leave the body and are detected by a ring of external sensors. Using the arrival times and detection positions of these photons, a detailed image of tracer concentration inside the body is constructed.
1. Gamma Photons Escape the Body
Each annihilation event produces two gamma photons of energy \( \mathrm{511\ keV} \), travelling in opposite directions (180° apart).
Because gamma rays are highly penetrating:
- They can pass through tissue with little attenuation.
- They exit the body and reach the PET detectors.
2. Detection by the PET Scanner
The scanner consists of a circular ring of gamma-ray detectors around the patient.
When an annihilation occurs:
- Two photons are detected almost simultaneously
- At two detectors directly opposite each other
- This is called coincidence detection
This pair of detections tells the scanner that the annihilation occurred somewhere along the straight line joining the two detectors.
3. Using Arrival Times to Locate the Source
The PET computer compares the exact arrival times of the two photons.
- If they arrive at exactly the same time → event is at the midpoint.
- If one arrives slightly earlier → event is closer to that detector.
This technique is called time-of-flight PET, which improves image clarity.
4. Reconstructing the Image
The process is repeated for millions of annihilation events.
The computer:
- collects millions of “lines of response”
- uses them to map where annihilations (and therefore tracer molecules) are most concentrated
- creates a high-resolution 3D image of the tracer distribution
This image shows metabolic activity, blood flow, and abnormal tissue function.
Example
Why can the gamma photons produced by annihilation events be detected outside the body?
▶️ Answer / Explanation
They have high energy (511 keV) and therefore can pass through bodily tissue with little absorption, allowing them to reach the detectors.
Example
Explain how coincidence detection helps locate the point of annihilation in PET.
▶️ Answer / Explanation
Both photons produced from an annihilation hit opposite detectors at nearly the same moment. This pair of detections (a coincidence) indicates that the event occurred somewhere along the straight line between the two detectors.
Example
Describe how PET uses the arrival time difference of the two gamma photons to improve image resolution.
▶️ Answer / Explanation
If one photon reaches its detector slightly earlier than the other, the annihilation event must have occurred closer to that detector.
This small timing difference (on the order of picoseconds) allows the scanner to narrow down the location of the event along the line of response.
This technique, known as time-of-flight PET, reduces uncertainty and sharpens the final reconstructed image.