Advance Notice article (written for this paper): Seeing inside the body with antimatter
(1) Positron emission tomography (PET) builds a three-dimensional map of where a radioactive tracer collects in the body. The most common tracer is a sugar labelled with fluorine-18, which decays by β⁺ emission with a half-life of 110 minutes.
(2) Because fluorine-18 decays so quickly, it is made in a cyclotron close to the hospital. A typical dose leaves the cyclotron at 08:00 with an activity of 2.0 GBq and is injected about two hours later.
(3) Each positron travels about a millimetre through tissue before it meets an electron. The pair annihilates, producing two gamma photons, each of energy 511 keV, which travel in almost exactly opposite directions.
(4) A ring of detectors surrounds the patient. When two detectors on opposite sides register photons within a few nanoseconds of each other, the annihilation must have happened somewhere on the line joining them. Modern scanners also measure the tiny difference in arrival times to locate the event along that line.
(5) A scan typically collects about 4 × 10⁸ such coincidences in 20 minutes. Like all counting experiments, the image is noisy: the uncertainty in N counts is about √N.
(6) A PET scan gives the patient an effective dose of about 7 mSv, compared with an average background dose in the UK of 2.7 mSv per year. The commonly used risk estimate is a 5% chance of a fatal cancer per sievert.
(7) PET shows what tissues are doing (for example, fast-growing tumours take up more sugar), while X-ray CT shows their structure. Many scanners combine the two.
1(a)4 marks
Explain how a transformer changes the size of an alternating voltage, and why its core is made of laminated iron.
1(b)4 marks
A 500-turn coil of area 2.0 × 10⁻³ m² rotates at 25 revolutions per second in a 0.15 T field. Calculate the maximum flux linkage and the peak emf.
1(c)3 marks
Explain why motors and transformers use iron cores with short, wide magnetic paths.
2(a)4 marks
Calculate the electric potential and field strength 0.20 m from a point charge of +5.0 nC, and state the relationship between field and potential.
2(b)4 marks
An electron at 3.0 × 10⁷ m s⁻¹ enters, at right angles, a uniform field of 2.0 × 10⁴ V m⁻¹ between plates 0.050 m long. Calculate its deflection on leaving the plates.
2(c)3 marks
Compare the electric field around a point charge with the gravitational field around a point mass.
3(a)4 marks
An electron is modelled as a standing wave in a box of length 0.10 nm. Calculate the energy of the lowest level, in eV, and explain why the energy is quantised. (E = h²/8mL² for n = 1)
3(b)4 marks
Calculate the closest distance a 5.0 MeV alpha particle can get to a gold nucleus (Z = 79) in a head-on collision.
3(c)4 marks
Show that p + p → p + n + π⁺ conserves charge and baryon number, and explain why electrons of about 20 GeV are needed to probe the structure inside protons.
4(a)4 marks
Tissue receives an absorbed dose of 0.50 mGy from alpha radiation (weighting factor 20). Calculate the equivalent dose and the risk of a fatal cancer, using 5% per sievert.
4(b)4 marks
Use the binding energy per nucleon curve to explain why both fission of heavy nuclei and fusion of light nuclei release energy.
4(c)3 marks
Each fission of uranium-235 releases about 200 MeV. Calculate the energy released by fission of 1.0 kg of U-235.
5(a)4 marks
A GPS satellite is 2.0 × 10⁷ m from a receiver. Calculate the signal travel time, the position error caused by a 1.0 μs timing error, and explain why satellites carry atomic clocks.
5(b)3 marks
In a microwave oven, hot spots (antinodes) are 6.1 cm apart. Calculate the frequency of the microwaves.
6(a)4 marks
The top of a tall building sways with SHM of frequency 0.20 Hz and amplitude 0.30 m. Calculate the maximum speed and maximum acceleration.
6(b)4 marks
Explain why wind gusts can make the building resonate, and how a tuned mass damper reduces the motion.
75 marks
Each water molecule needs about 0.42 eV to escape from the liquid. Calculate the Boltzmann factor at 300 K and the ratio of the factors at 310 K and 300 K. Explain why evaporation cools the remaining liquid.
Advance Notice article (written for this paper): Seeing inside the body with antimatter
(1) Positron emission tomography (PET) builds a three-dimensional map of where a radioactive tracer collects in the body. The most common tracer is a sugar labelled with fluorine-18, which decays by β⁺ emission with a half-life of 110 minutes.
(2) Because fluorine-18 decays so quickly, it is made in a cyclotron close to the hospital. A typical dose leaves the cyclotron at 08:00 with an activity of 2.0 GBq and is injected about two hours later.
(3) Each positron travels about a millimetre through tissue before it meets an electron. The pair annihilates, producing two gamma photons, each of energy 511 keV, which travel in almost exactly opposite directions.
(4) A ring of detectors surrounds the patient. When two detectors on opposite sides register photons within a few nanoseconds of each other, the annihilation must have happened somewhere on the line joining them. Modern scanners also measure the tiny difference in arrival times to locate the event along that line.
(5) A scan typically collects about 4 × 10⁸ such coincidences in 20 minutes. Like all counting experiments, the image is noisy: the uncertainty in N counts is about √N.
(6) A PET scan gives the patient an effective dose of about 7 mSv, compared with an average background dose in the UK of 2.7 mSv per year. The commonly used risk estimate is a 5% chance of a fatal cancer per sievert.
(7) PET shows what tissues are doing (for example, fast-growing tumours take up more sugar), while X-ray CT shows their structure. Many scanners combine the two.
8(a)3 marks
Write the decay equation for fluorine-18 (Z = 9) and state what happens to the quarks (paragraph 1).
8(b)4 marks
Explain why the two photons in paragraph 3 travel in opposite directions and each have energy 511 keV, and calculate their wavelength.
8(c)4 marks
Calculate the activity of the dose in paragraph 2 when it is injected at 10:00.
8(d)4 marks
Two photons from one annihilation arrive at opposite detectors with a time difference of 0.40 ns (paragraph 4). Calculate how far the annihilation was from the midpoint between the detectors.
8(e)4 marks
Use paragraph 6 to calculate the risk of a fatal cancer from one PET scan and compare the dose with background radiation.
8(f)*6 marks
Discuss the benefits and risks of PET scanning for a patient who may have a tumour, using information from the article.
8(g)4 marks
Explain two physical factors that limit how sharp a PET image can be.
8(h)6 marks
Paragraph 5 says the uncertainty in N counts is about √N.
(i) Calculate the percentage uncertainty for a region recording 2500 counts.
(ii) How long would the scan need to be to halve this uncertainty?
(iii) Explain why doubling the injected activity is not a good alternative.
Finished?
Answer every question to finish (25 left), or finish when the time’s up.
Score 0 / 100 · 0 of 25 marked
This paper is written by Plasmo in the style of the OCR A-Level Physics exam. It is not a past paper and is not produced or endorsed by the exam board.
OCR A-Level Physics Mock Exam: Paper 2: Scientific literacy in physics | Plasmo