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S6 Physics: Medical Physics – CT, Dose and Therapy (10 Questions)
S6 Physics: Medical Physics – CT, Dose and Therapy (10 Questions)
The second paper moves into everyday hospital work: the definition of the CT number, working back from echo time to depth, correcting short sight, aluminium filtration, then PET energy and mass, Doppler at an angle, dose conversion, MRI slice selection, and a comparison of surface dose in photon and proton therapy.
Quick answer A coefficient of 0.0190 against water at 0.0200 gives minus 50 HU and air gives minus 1000; 26 microseconds gives 2.0 cm; a far point of 0.40 m gives minus 2.5 D; one eighth needs three half-value layers, 6.0 mm of aluminium; two 511 keV photons total 1.022 MeV, about 1.64 times 10 to the minus 13 J and 1.82 times 10 to the minus 30 kg; 5 MHz at 60 degrees and 0.40 m/s gives 1.3 kHz; 0.040 Gy is 40 mGy and 40 mSv; 0.010 T gives 426 kHz; a tumour dose of 2.0 Gy needs 6.7 Gy at the photon surface but only 0.40 Gy with protons, a factor of 17; and a 1064 nm photon carries 1.17 eV, far from ionising.
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)
- FoundationCT numbers are defined as 1000 times the difference of the linear attenuation coefficient from water divided by that of water. A tissue has 0.0190 per cm while water has 0.0200 per cm; find its CT number, and that of air where the coefficient is nearly zero.
- FoundationA probe receives an echo 26 microseconds after emitting a pulse, and the speed of sound in tissue is 1540 m/s. How deep is the reflecting boundary?
- FoundationA short-sighted patient has a far point of 0.40 m. What power of contact lens lets this eye focus on an object at infinity, and is the lens converging or diverging?
- FoundationA beam of X-rays has a half-value layer of 2.0 mm of aluminium. What thickness of aluminium reduces the intensity to one eighth?
- IntermediateOne positron annihilation in PET emits two 511 keV photons. Find the total energy in MeV and in joules, and the equivalent rest mass.
- IntermediateA 5.0 MHz probe makes an angle of 60 degrees with a blood vessel, the blood speed is 0.40 m/s and the speed of sound is 1540 m/s. Find the Doppler shift.
- IntermediateA patient absorbs 0.020 J in 0.50 kg of tissue from X-rays, for which the weighting factor is 1. Find the absorbed dose in mGy and the equivalent dose in mSv.
- ChallengeA 1.5 T MRI scanner uses gradient coils to create a field difference of 0.010 T, and the proton gyromagnetic ratio is 42.58 MHz per tesla. Find the frequency difference in kHz and explain how this selects a slice.
- ChallengeA photon beam delivers only 30 percent of its surface dose at the tumour depth, while a proton beam gives 100 percent at the Bragg peak and 20 percent at the entrance. To give the tumour 2.0 Gy, find the surface dose for each method and the ratio.
- Error redoA surgical Nd:YAG laser has wavelength 1064 nm and power 10 W. Find the energy of one photon in eV and decide whether it is ionising radiation; explain why saying it ionises cells like X-rays is wrong.
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | The CT number is 1000 times minus 0.0010 over 0.0200, which is minus 50, and air with almost zero attenuation gives about minus 1000 | Water is fixed at zero and air at minus one thousand, so fat-like tissue gives a negative number. |
| 2 | The depth is 1540 times 26 times 10 to the minus 6, divided by 2, which is 0.020 m, or 2.0 cm | Divide the time by two for the one-way trip before multiplying by the speed, or the answer is out by a factor of two. |
| 3 | The image of an object at infinity must fall 0.40 m in front of the eye, so the focal length is minus 0.40 m and the power is minus 2.5 D, a diverging lens | Short sight is corrected with a negative power that diverges the incoming light so the far point is pushed back onto the retina. |
| 4 | One eighth is one half cubed, so three half-value layers are needed, and three times 2.0 gives 6.0 mm of aluminium | Convert the remaining fraction into a number of half-value layers first, then multiply by the layer thickness. |
| 5 | The total is 1.022 MeV, about 1.64 times 10 to the minus 13 J, and dividing by the square of the speed of light gives about 1.82 times 10 to the minus 30 kg, the mass of two electrons | The rest mass of two electrons becomes two photons, so the total energy is exactly 1.022 MeV. |
| 6 | The cosine of 60 degrees is 0.50, so the shift is 2 times 0.40 times 5.0 times 10 to the 6 times 0.50 divided by 1540, about 1.3 kHz | A larger angle gives a smaller cosine, so the probe should be aligned as closely as possible with the flow. |
| 7 | The absorbed dose is 0.020 divided by 0.50, which is 0.040 Gy or 40 mGy, and the equivalent dose is also 40 mSv because the weighting factor is one | For X-rays the weighting factor is one, so the numbers coincide although the quantities differ. |
| 8 | The difference is 42.58 times 0.010, which is 0.426 MHz, about 426 kHz; only the thin layer whose resonance matches the radio pulse is excited, so the body is imaged slice by slice | A field gradient turns position into frequency, and that is the basis of spatial encoding in MRI. |
| 9 | For photons the surface dose is 2.0 divided by 0.30, about 6.7 Gy; for protons it is 2.0 times 0.20, which is 0.40 Gy; the ratio is about 17 | Protons deposit most of their energy at the Bragg peak, so the entrance and exit doses are much lower and normal tissue is spared. |
| 10 | The energy is h c over the wavelength, 6.63 times 10 to the minus 34 times 3.00 times 10 to the 8 divided by 1.064 times 10 to the minus 6, about 1.87 times 10 to the minus 19 J, that is 1.17 eV; ionising an atom needs roughly 10 eV or more, so the laser is non-ionising and cuts by heating rather than by breaking bonds | Whether radiation is ionising depends on the energy of a single photon, not on the total power. |
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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