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S6 Physics: Medical Physics – Ultrasound, X-ray and PET Basics (10 Questions)
S6 Physics: Medical Physics – Ultrasound, X-ray and PET Basics (10 Questions)
This paper starts from the three most common investigations: ultrasound, X-ray and PET. It drills the echo timing, half-value layer and annihilation photon calculations that appear every year, then adds lens power and the difference between gray and sievert, so the units and orders of magnitude are solid for the next two papers.
Quick answer An echo from 3.85 cm takes 50 microseconds over 7.7 cm; with a 1.5 cm half-value layer, 3 cm leaves 25 percent and 4.5 cm leaves 12.5 percent; the electron rest energy is 8.2 times 10 to the minus 14 J, about 511 keV, with two photons back to back; power is 1 over f, giving plus 4.0 D, and lenses in contact give 5.0 D, a focal length of 0.20 m; a coefficient of 0.20 per cm leaves 13.5 percent after 10 cm; 4 MHz at 0.60 m/s gives 3.1 kHz; 1.5 T gives 63.9 MHz and a wavelength near 4.7 m; the reflection is 38.7 percent at bone and 99.9 percent at air; 800 MBq over four half-lives leaves 50 MBq; and 0.030 Gy times 20 gives 0.60 Sv.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | about 20 minutes |
| Difficulty mix | Foundation 4 · Intermediate 3 · Challenge 2 · Error redo 1 |
| Chapter | Chapter: S6 Physics | Medical Physics: Imaging, Radiation Dose and Radiotherapy |
| Level | S6 |
02 Questions (10 items)
- FoundationAn obstetric ultrasound probe sends a pulse into the abdomen; the speed of sound in soft tissue is 1540 m/s. If the reflecting boundary is 3.85 cm deep, how many microseconds after emission does the echo return, and what total distance does the sound travel?
- FoundationA beam of X-rays has a half-value layer of 1.5 cm in tissue. What percentage of the intensity remains after 3.0 cm, and after 4.5 cm?
- FoundationWhen a positron annihilates with an electron each photon carries about 511 keV. Use E = mc squared with the electron mass 9.11 times 10 to the minus 31 kg to check this, and explain why two photons must leave in opposite directions.
- FoundationA patient needs a converging lens of focal length 0.25 m. What is its power in dioptres, and what is the combined focal length of a plus 2.0 D and a plus 3.0 D thin lens in contact?
- IntermediateThe linear attenuation coefficient of tissue for a beam of X-rays is 0.20 per cm. What percentage of the incident intensity survives 10 cm?
- IntermediateA Doppler ultrasound probe of 4.0 MHz measures blood flowing at 0.60 m/s parallel to the beam, with sound speed 1540 m/s. Find the frequency shift in Hz, and say what a negative shift means.
- IntermediateAn MRI scanner uses a 1.5 T main field and the proton gyromagnetic ratio is 42.58 MHz per tesla. Find the Larmor frequency and the wavelength of the corresponding radio wave in metres.
- ChallengeSoft tissue has Z equal to 1.63 times 10 to the 6, bone 7.0 times 10 to the 6 and air about 4.0 times 10 squared in SI units. Use R equals the square of the impedance difference over the sum to find the reflected intensity fraction for soft tissue against bone and against air, and explain why gel is used.
- ChallengeTechnetium-99m has a half-life of 6.0 hours. Starting from 800 MBq, find the activity after 24 hours and the time needed to fall to one eighth of the original activity.
- Error redoA patient absorbs 0.060 J of alpha particle energy in 2.0 kg of tissue; the radiation weighting factor for alpha particles is 20. Find the absorbed dose in Gy and the equivalent dose in Sv, and say what is wrong with the answer 0.030 Sv.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | The time is 2 times 0.0385 divided by 1540, which is 5.0 times 10 to the minus 5 s, or 50 microseconds; the total path is twice 3.85, namely 7.7 cm | The echo makes a return trip, so forgetting the factor of two halves the calculated depth. |
| 2 | 3.0 cm is two half-value layers, so the fraction is one half squared, which is 25 percent; 4.5 cm is three layers, so one half cubed, which is 12.5 percent | Each half-value layer halves the intensity, so the count is a power of two rather than a linear subtraction. |
| 3 | The energy is 9.11 times 10 to the minus 31 times the square of 3.00 times 10 to the 8, which is 8.2 times 10 to the minus 14 J, about 511 keV; the total momentum before annihilation is nearly zero, so the two photons must carry opposite momenta and leave back to back | The 511 keV is exactly the rest energy of an electron, and PET locates the event by detecting the pair arriving together. |
| 4 | The power is 1 divided by 0.25, which is plus 4.0 D; in contact the powers add to 5.0 D, so the focal length is 1 divided by 5.0, namely 0.20 m | Powers of thin lenses in contact add directly because power is the reciprocal of focal length. |
| 5 | The ratio is e to the power minus 0.20 times 10, which is e to the minus 2, about 0.135, that is 13.5 percent | Attenuation is exponential, not a fixed percentage lost per centimetre. |
| 6 | The shift is 2 times 0.60 times 4.0 times 10 to the 6 divided by 1540, about 3.1 kHz; a negative shift means the blood moves away from the probe | The factor of two comes from the blood first receiving then re-emitting the sound, so the Doppler effect acts twice. |
| 7 | The frequency is 42.58 times 1.5, which is 63.9 MHz, and the wavelength is 3.00 times 10 to the 8 divided by 6.39 times 10 to the 7, about 4.7 m | Frequency is proportional to field strength, so a 3 T scanner needs twice the radio frequency. |
| 8 | For bone the ratio is 5.37 over 8.63, squared, about 0.387, that is 38.7 percent; for air the ratio is about 0.9995, which squares to about 99.9 percent, so nearly everything is reflected at the skin and air boundary and gel with an impedance close to soft tissue replaces that boundary | The bigger the impedance mismatch the stronger the reflection, and air differs from soft tissue by several orders of magnitude. |
| 9 | 24 divided by 6 is four half-lives, so 800 divided by 16 gives 50 MBq, and one eighth corresponds to three half-lives, namely 18 hours | Count half-lives as powers of two, so four half-lives means dividing by sixteen. |
| 10 | The absorbed dose is 0.060 divided by 2.0, which is 0.030 Gy, and the equivalent dose is 0.030 times 20, which is 0.60 Sv; the error is treating absorbed dose as equivalent dose and omitting the weighting factor, a twentyfold underestimate | Gy is only energy per unit mass while Sv adds a factor for how damaging that kind of radiation is. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
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