10 GCSE Physics questions about the X-ray and CT scanner, from Foundation to Higher, each with a full worked solution.
An X-ray machine fires a beam of high-frequency X-rays through the body onto a detector. Bone absorbs X-rays strongly, while soft tissue lets most of them through, so bones show up white. A CT scanner spins the X-ray tube all the way round the patient and a computer combines hundreds of images into detailed 3D slices – much more information, but a bigger radiation dose.
Course: Combined Science + Separate Physics | Tier: Foundation + Higher | Topics: Waves · Atomic Structure
📌 KEY DEFINITIONS – learn them word for word
X-rays: high-frequency, short-wavelength electromagnetic waves. They are ionising. They pass easily through soft tissue but are absorbed by bone.
Ionising radiation: radiation with enough energy to knock electrons off atoms, turning them into ions. It can damage cells and DNA and cause mutations and cancer.
Radiation dose: a measure of the risk of harm resulting from an exposure of the body to radiation. It is measured in sieverts (Sv). 1000 millisieverts (mSv) = 1 sievert (Sv).
Equations you’ll use
| Quantity | Symbol | Unit |
|---|---|---|
| wave speed | v | metres per second (m/s) |
| frequency | f | hertz (Hz) |
| wavelength | λ | metres (m) |
| power | P | watts (W) |
| potential difference | V | volts (V) |
| current | I | amps (A) |
| energy transferred | E | joules (J) |
| time | t | seconds (s) |
| efficiency | – | no unit (decimal or %) |
| radiation dose | – | sieverts (Sv) |
Equations: v = f λ | P = V I | E = P t | efficiency = useful output energy ÷ total input energy | 1 kV = 1000 V, 1 mA = 0.001 A
Use FIFA for every calculation
- F – Formula: write the equation as it appears on the sheet.
- I – Insert: put in the numbers (convert to standard units first).
- F – Fix: rearrange to make the unknown the subject.
- A – Answer: calculate and always give the unit.
Foundation: aim for Q1–8. Higher: aim for Q4–10.
Questions
Q1 (F) X-rays used in a hospital have a wavelength of 1.0 × 10−10 m. They travel at 3.0 × 108 m/s. Calculate their frequency.
Show solution
F: v = f λ
I: 3.0 × 108 = f × 1.0 × 10−10
F: f = 3.0 × 108 ÷ 1.0 × 10−10
A: 3.0 × 1018 Hz
Q2 (F) Explain why bones show up clearly on an X-ray image. [2 marks]
Show answer
• X-rays are absorbed by bone (it is dense) …
• … but are transmitted through soft tissue, so they reach the detector except where bone blocks them. The bone appears as a white “shadow”.
Q3 (F) A chest X-ray gives a dose of about 0.02 mSv. A CT scan of the abdomen gives about 10 mSv. How many chest X-rays give the same dose as one abdominal CT scan?
Show solution
A: number = 10 ÷ 0.02 = 500 chest X-rays
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Q4 (F) The X-ray tube in a CT scanner works at a potential difference of 120 kV with a current of 400 mA. Calculate the power of the tube in kW.
Show solution
Convert first: 120 kV = 120 000 V; 400 mA = 0.40 A
F: P = V I
I: P = 120 000 × 0.40
F: P is already the subject
A: 48 000 W = 48 kW
Q5 (F/H) The 48 kW tube is switched on for 5.0 s during a scan. Calculate the energy transferred to the tube, in kJ.
Show solution
F: E = P t
I: E = 48 000 × 5.0
F: E is already the subject
A: 240 000 J = 240 kJ
Q6 (F/H) Only 1.0% of the energy supplied to an X-ray tube is carried away by X-rays. Calculate the energy carried by X-rays in Q5, and state what happens to the rest.
Show solution
F: efficiency = useful output energy ÷ total input energy
I: 0.010 = useful output ÷ 240 000
F: useful output = 0.010 × 240 000
A: 2400 J carried by X-rays
The other 237 600 J is dissipated, heating up the tube’s metal target (its thermal energy store) – which is why X-ray tubes need cooling.
Q7 (F/H · S only) The average UK background radiation dose is about 2.7 mSv per year. How many years of background radiation give the same dose as one 10 mSv CT scan? Give your answer to 2 significant figures.
Show solution
A: years = 10 ÷ 2.7 = 3.70… = 3.7 years (2 s.f.)
Q8 (F/H) A radiographer stands behind a lead screen or leaves the room while the X-ray is taken, but the patient does not. Explain why. [3 marks]
Show answer
• The radiographer takes many X-rays every day, so without protection their dose would build up and their risk of cancer would increase.
• Lead absorbs X-rays, so the screen reduces the radiographer’s dose.
• The patient has only one (or a few) X-rays, and the benefit of a diagnosis is greater than the small risk.
Q9 (H) One estimate is that the risk of developing a fatal cancer increases by about 5% for every 1 Sv of dose. Calculate the extra risk from a 10 mSv CT scan, as a percentage and as “1 in …”.
Show solution
Convert first: 10 mSv = 0.010 Sv
Step 1: extra risk = 0.010 × 5% = 0.05%
Step 2: 0.05% = 0.0005, and 1 ÷ 0.0005 = 2000
A: about 1 in 2000
Q10 (H) A patient has been in a car crash and may have internal bleeding. Evaluate whether the doctor should order a CT scan. [6 marks]
Show answer
Model answer – points for and against, then a conclusion:
• Benefit: a CT scan gives detailed 3D images of soft tissue and organs, so bleeding or damage can be found quickly and accurately.
• Finding internal bleeding quickly could save the patient’s life – this benefit is large and immediate.
• Risk: X-rays are ionising – they can damage DNA and may cause cancer later.
• A CT scan gives a much larger dose (about 10 mSv) than a normal X-ray (about 0.02 mSv) – similar to several years of background radiation.
• But the extra risk is small – about 1 in 2000 – and the harm (if any) happens many years later.
• Conclusion: the benefit of finding a life-threatening injury far outweighs the small increase in risk, so the doctor should order the scan (but should avoid repeating it unnecessarily).
⚠️ Where students lose marks
- Mixing up mSv and Sv – 1 Sv = 1000 mSv, so 10 mSv = 0.010 Sv.
- Saying X-rays make the patient radioactive – they irradiate the patient but do not contaminate them.
- Writing that X-rays “bounce off” bone – bone absorbs X-rays.
- In risk-vs-benefit questions, only giving the risks – you must weigh both sides and reach a conclusion.
More devices: all 40 everyday devices · Waves · Atomic Structure
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