PET scanning Cambridge International AS & A Level Physics revision
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In plain words
A PET scan shows what the body is doing, not just what it looks like. The patient is given a slightly radioactive form of something the body uses, such as sugar. It gathers where cells are busiest, and gives itself away with pairs of gamma rays that fly off in exactly opposite directions.
5 things to know
- A tracer is a substance containing radioactive nuclei that is put into the body and absorbed by the tissue being studied.
- PET uses a tracer that decays by β⁺ emission, giving out positrons.
- Annihilation: each positron travels only a very short way before it meets an electron. The two annihilate, and their mass becomes the energy of two gamma-ray photons. Mass–energy and momentum are both conserved, so the two photons travel in opposite directions.
- Each photon carries the rest energy of one electron: E = mc² = 8.2 × 10⁻¹⁴ J, which is 0.51 MeV.
- The photons leave the body and are picked up by a ring of detectors. From the arrival times of each pair, a computer works out where the annihilation happened and builds an image showing where the tracer has gathered.
Worked example
Find the energy and the wavelength of each gamma-ray photon produced when an electron and a positron annihilate. (Mass of an electron = 9.11 × 10⁻³¹ kg.)
- Each photon gets the rest energy of one particle: E = mc² = 9.11 × 10⁻³¹ × (3.00 × 10⁸)² = 8.2 × 10⁻¹⁴ J.
- λ = hc ÷ E = 6.63 × 10⁻³⁴ × 3.00 × 10⁸ ÷ 8.2 × 10⁻¹⁴.
- = 2.4 × 10⁻¹² m.
Tips and tricks
- Two photons in opposite directions: the total momentum was almost zero before, so it must be zero afterwards.
- The positron and the electron have the same mass, so the two photons have the same energy.
It lands in your notebook with its questions as flashcards.
PET scanning: 5 questions and answers
These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.
By which kind of decay does the tracer used in a PET scan decay?
It has to give out positrons.
What is annihilation?
Their mass becomes the photons' energy.
How many gamma-ray photons are produced when a positron and an electron annihilate in a PET scan?
One photon alone could not conserve momentum.
Why do the two photons travel in opposite directions?
The total momentum before was nearly zero.
What is detected outside the body in a PET scan?
The positrons never get out: they annihilate within about a millimetre.
Quiz
5 questions
Tap an answer and you’ll see straight away whether it’s right, and why.
Worksheet
4 questions, 9 marks. Write your answers on paper, then check them.
PET scanning
Cambridge International AS & A Level Physics 9702 · 9 marks · papermunch.org
Name ______________________________ Date ______________
State what is meant by a tracer.[2]
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A substance containing radioactive nuclei that is introduced into the body and is absorbed by the tissue being studied.
Explain how the gamma-ray photons are produced in a PET scan, and why they travel in opposite directions.[3]
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The tracer emits a positron, which meets an electron in the tissue. They annihilate: their mass is converted into the energy of two gamma-ray photons. Momentum is conserved, and the total momentum beforehand was close to zero, so the photons must move in opposite directions.
Each photon has an energy of 8.2 × 10⁻¹⁴ J. Find its frequency.[2]
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1.2 × 10²⁰ Hz.
Describe how the detected photons are used to make an image.[2]
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Detectors round the body record the pair of photons from each annihilation and their arrival times. A computer uses these to locate each annihilation, and so builds an image of the concentration of tracer in the tissue.
Answers: PET scanning
- 1. A substance containing radioactive nuclei that is introduced into the body and is absorbed by the tissue being studied.
- 2. The tracer emits a positron, which meets an electron in the tissue. They annihilate: their mass is converted into the energy of two gamma-ray photons. Momentum is conserved, and the total momentum beforehand was close to zero, so the photons must move in opposite directions.
- 3. 1.2 × 10²⁰ Hz.
- 4. Detectors round the body record the pair of photons from each annihilation and their arrival times. A computer uses these to locate each annihilation, and so builds an image of the concentration of tracer in the tissue.