Cambridge International AS & A Level · 24 · structured
Follow the physical chain in PET
Follow the physical chain in PET · Original GioPhysics question with a detailed, mark-by-mark answer guide.
- Demand
- demanding
- Marks
- 13
- Topics
- 6
- Answer
- Complete
Consider positron emission tomography as a physics model. A suitable tracer is taken up by the tissue being studied. A positron slows before annihilating with an electron, and assume their combined initial momentum is negligible. Use m_e=9.109×10⁻³¹ kg, c=2.998×10⁸ m s⁻¹ and 1 eV=1.602×10⁻¹⁹ J.
- (a)
Define a radioactive tracer, state the required decay type for PET and explain why tissue uptake matters to the resulting image.
3 marks - (b)
Explain what annihilation is and why the near-rest electron–positron event produces two equal-energy gamma photons in opposite directions.
4 marks - (c)
Calculate the energy of each photon in joules and keV. Explain why doubling m_ec² would give the pair's energy rather than each photon's energy.
3 marks - (d)
Explain how detectors outside the body use the photons and their arrival times to reconstruct an image.
3 marks
Ready to self-mark?Reveal the detailed answer guide
(a)
Define a radioactive tracer, state the required decay type for PET and explain why tissue uptake matters to the resulting image.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
A tracer is a substance containing radioactive nuclei that can be introduced into the body and taken up by tissue.
- 2
For PET it must provide positrons through β⁺ decay.
- 3
Its uptake/distribution makes the reconstructed concentration a marker of the tissue/process being investigated; this is not an anatomical photograph formed directly by the positrons.
(b)
Explain what annihilation is and why the near-rest electron–positron event produces two equal-energy gamma photons in opposite directions.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
An electron and its antiparticle, a positron, interact and cease to exist as that pair, with their energy transferred to radiation.
- 2
The event conserves total mass–energy and momentum.
- 3
Negligible initial momentum requires the two photon momenta to be equal and opposite.
- 4
Because photon p=E/c, their energies are equal, and the photons travel in opposite directions.
(c)
Calculate the energy of each photon in joules and keV. Explain why doubling m_ec² would give the pair's energy rather than each photon's energy.
List the given quantities with units, identify the required quantity, write the governing relationship before substituting, and keep extra digits until the final line so rounding does not distort the result.
- 1
Available rest energy is 2m_ec², shared equally by two photons in this approximation.
- 2
Each has E=m_ec²=9.109×10⁻³¹×(2.998×10⁸)²=8.19×10⁻¹⁴ J.
- 3
E/(1.602×10⁻¹⁶)=511 keV; using 2m_ec² for each would double-count the available energy.
(d)
Explain how detectors outside the body use the photons and their arrival times to reconstruct an image.
Identify what the question is testing, organise the response into distinct mark-earning points, and make every conclusion traceable to a physical principle or to the evidence supplied.
- 1
Some gamma photons leave the body and are detected by detectors arranged around it.
- 2
Pairs arriving within the appropriate coincidence window are associated with one annihilation; detector locations define a line on which it occurred.
- 3
Combining many such lines and timing information reconstructs the tracer concentration. Arrival times need not be identical when the event is not midway between detectors.
Complete marking guidance
Use these worked steps alongside the part-by-part answers. They explain the method and mark allocation; they do not add extra marks.
- (a) A tracer is a substance containing radioactive nuclei that can be introduced into the body and taken up by tissue.
- (a) For PET it must provide positrons through β⁺ decay.
- (a) Its uptake/distribution makes the reconstructed concentration a marker of the tissue/process being investigated; this is not an anatomical photograph formed directly by the positrons.
- (b) An electron and its antiparticle, a positron, interact and cease to exist as that pair, with their energy transferred to radiation.
- (b) The event conserves total mass–energy and momentum.
- (b) Negligible initial momentum requires the two photon momenta to be equal and opposite.
- (b) Because photon p=E/c, their energies are equal, and the photons travel in opposite directions.
- (c) Available rest energy is 2m_ec², shared equally by two photons in this approximation.
- (c) Each has E=m_ec²=9.109×10⁻³¹×(2.998×10⁸)²=8.19×10⁻¹⁴ J.
- (c) E/(1.602×10⁻¹⁶)=511 keV; using 2m_ec² for each would double-count the available energy.
- (d) Some gamma photons leave the body and are detected by detectors arranged around it.
- (d) Pairs arriving within the appropriate coincidence window are associated with one annihilation; detector locations define a line on which it occurred.
- (d) Combining many such lines and timing information reconstructs the tracer concentration. Arrival times need not be identical when the event is not midway between detectors.
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