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S6 Physics: Medical Physics – Error Correction Drill (10 Questions)
S6 Physics: Medical Physics – Error Correction Drill (10 Questions)
This paper targets the mistakes that recur in the previous three: forgetting the factor of two in echo timing, treating the half-value layer as linear, confusing absorbed with equivalent dose, swapping power and focal length, the factors in exponential attenuation and Doppler shift, Larmor scaling, the minimum wavelength, powers of two in half-lives, and a final item that clears up gray against sievert and the dose from ultrasound.
Quick answer An echo from 6.0 cm takes 78 microseconds over 12 cm; with a 2.0 cm half-value layer, 6.0 cm leaves 12.5 percent; 25 mGy of X-rays is 25 mSv while alpha particles give 0.50 Sv; a focal length of 0.50 m is plus 2.0 D, and lenses in contact give 4.0 D and 0.25 m; a coefficient of 0.15 per cm leaves 5.0 percent after 20 cm, with a half-value layer of 4.6 cm; 3.0 MHz at 0.50 m/s shifts by 1.9 kHz; 42.6 MHz per tesla gives 42.6 MHz at 1.0 T and 128 MHz at 3.0 T; 100 kV gives a minimum wavelength of 12.4 pm; 800 MBq falls to 50 MBq after four half-lives and 12.5 MBq after six; and 0.20 Gy of alpha particles is 4.0 Sv against 0.20 Sv for X-rays.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 questions |
| Suggested time | about 25 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)
- FoundationAbdominal ultrasound finds a boundary 6.0 cm deep in soft tissue where sound travels at 1540 m/s. About how many microseconds after emission does the echo return, and what total distance does the sound cover?
- FoundationA beam of X-rays has a half-value layer of 2.0 cm in tissue. What percentage of the original intensity remains after passing through 6.0 cm?
- FoundationA patient receives 25 mGy from X-rays with a radiation weighting factor of 1. What is the equivalent dose, and what would it be if the same 25 mGy came from alpha particles with a weighting factor of 20?
- FoundationA patient needs a converging lens of focal length 0.50 m; what is its power? If a plus 1.5 D and a plus 2.5 D thin lens are placed in contact, what are the combined power and focal length?
- IntermediateTissue has a linear attenuation coefficient of 0.15 per cm for 60 keV X-rays. What percentage of the incident intensity survives 20 cm, and what is the half-value layer of this tissue?
- IntermediateA Doppler ultrasound probe of 3.0 MHz insonates blood flowing at 0.50 m/s along the beam direction, where theta is zero and the speed of sound in soft tissue is 1540 m/s. What is the frequency shift in hertz?
- IntermediateThe Larmor frequency of protons in MRI is about 42.6 MHz per tesla. What are the proton resonance frequencies of 1.0 T and 3.0 T scanners?
- ChallengeAn X-ray tube runs at 100 kV. What is the largest energy a single photon can carry, and what is the corresponding minimum wavelength in picometres?
- ChallengeA radiotracer starts at 800 MBq with a half-life of 6.0 hours. What is the activity after 24 hours, and after a further 12 hours?
- Error redoA student writes that gray and sievert are identical because both are joules per kilogram, and that ultrasound also delivers a radiation dose, only less than X-rays. Identify both errors and work out the equivalent dose of 0.20 Gy of alpha particles with a weighting factor of 20 and of 0.20 Gy of X-rays with a weighting factor of 1.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | The time is twice 0.060 divided by 1540, which is 7.8 times 10 to the minus 5 s, about 78 microseconds, and the total path is twice 6.0, namely 12 cm | The echo makes a return trip, so dividing 1540 only once halves the calculated time. |
| 2 | Since 6.0 cm is three half-value layers, the fraction is one half cubed, which is 12.5 percent | Each half-value layer halves the intensity, so the calculation is a power of two, not a linear subtraction per centimetre. |
| 3 | For X-rays the equivalent dose is 25 times 1, which is 25 mSv; for alpha particles it is 25 times 20, which is 500 mSv, or 0.50 Sv | Equal absorbed dose does not mean equal risk, because the equivalent dose multiplies by the radiation weighting factor. |
| 4 | The power is 1 divided by 0.50, which is plus 2.0 D; in contact the powers add to 4.0 D, so the focal length is 1 divided by 4.0, namely 0.25 m | Power is the reciprocal of focal length, which is why powers of thin lenses in contact simply add. |
| 5 | The surviving fraction is e to the power of minus 0.15 times 20, which is e to the minus 3, about 0.050 or 5.0 percent; the half-value layer is ln 2 divided by 0.15, about 4.6 cm | Attenuation follows an exponential law, so a fixed percentage is not removed in every centimetre. |
| 6 | The shift is twice 3.0 times 10 to the 6 times 0.50 divided by 1540, about 1.9 times 10 to the 3 Hz | The blood both reflects and scatters the wave, so the receiver sees the shift twice, once on the way out and once on the way back. |
| 7 | At 1.0 T the frequency is 42.6 MHz, and at 3.0 T it is 42.6 times 3.0, about 128 MHz | The Larmor frequency is proportional to field strength, so doubling the field doubles the frequency. |
| 8 | The maximum photon energy is 100 keV; the minimum wavelength is h c divided by e V, which is 1.24 times 10 to the minus 6 electron-volt metres divided by 1.0 times 10 to the 5, about 1.24 times 10 to the minus 11 m, or 12.4 pm | The continuous spectrum has a short-wavelength cutoff because one photon can take at most the whole kinetic energy of one electron. |
| 9 | In 24 hours there are four half-lives, so the activity is 800 divided by 2 to the 4, which is 50 MBq; at 36 hours there are six half-lives, giving 800 divided by 2 to the 6, which is 12.5 MBq | Divide the elapsed time by the half-life to count the half-lives, then use a power of two rather than a linear proportion. |
| 10 | Gray is absorbed dose, the energy deposited per kilogram, while sievert is equivalent dose, equal to gray times the radiation and tissue weighting factors, so the units look alike but mean different things; ultrasound is a mechanical, non-ionising wave with zero radiation dose, not a smaller dose. Alpha particles give 0.20 times 20, which is 4.0 Sv, while X-rays give 0.20 times 1, which is 0.20 Sv | The same number of gray can mean very different risk, which is why risk assessment must use sievert. |
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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