This mini-lesson covers Eduqas Component 3, Option B: X-rays (production, spectra, attenuation, CT), ultrasound (piezoelectric transducers, A- and B-scans, acoustic impedance, Doppler blood flow), MRI (precession, resonance, the Larmor frequency), radiation dose (gray and sievert) and nuclear medicine (Tc-99m tracers, the gamma camera, PET).
⚠️ This is an OPTION. Eduqas Component 3 Section B offers four options — A Alternating Currents, B Medical Physics, C The Physics of Sports, D Energy and the Environment. You study exactly ONE of them. Only work through this mini-lesson if Option B: Medical Physics is the one your school teaches. Everyone also needs the Component 3 core (Sections 1–10), which has its own mini-lesson.
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(a)–(c) X-rays
Producing and controlling an X-ray beam
Electrons are boiled off a heated filament, accelerated through a large p.d. and slammed into a metal target. Two processes make X-rays:
Bremsstrahlung ("braking radiation") — electrons decelerate in the target, producing a continuous spectrum with a sharp maximum photon energy (Emax = eV, when a single electron gives up all its energy in one go).
Characteristic lines — an incoming electron knocks out an inner-shell electron; an outer electron drops down and emits a photon of a definite energy, fixed by the target material.
The two dials: increasing the tube current (more electrons per second) increases the intensity but not the maximum photon energy. Increasing the accelerating p.d. increases the maximum photon energy (a "harder", more penetrating beam) and the intensity too.
Diagnosis vs therapy:low-energy X-rays are used for imaging (they are absorbed differently by bone and soft tissue, giving contrast). High-energy X-rays are used for therapy — deliberately depositing energy to destroy tumour cells, usually rotating the beam about the tumour so healthy tissue receives a much smaller dose.
(d)–(g) Attenuation and CT
Attenuation, half-value thickness and CT scanning
I = I₀e−µxµ is the attenuation coefficient (m⁻¹ or cm⁻¹), and it depends on the material and the photon energy. Bone (high Z) attenuates far more than soft tissue — which is precisely what gives an X-ray its contrast.
half-value thickness: x½ = ln 2 / µThe thickness that halves the intensity. Same mathematics as radioactive half-life — because it is the same exponential law.
Imaging soft tissue is hard, because soft tissues have similar attenuation coefficients. Solutions: a contrast medium (barium, iodine) with a high atomic number, and fluoroscopy — a continuous, low-dose real-time beam with an image intensifier to brighten the picture without raising the dose.
CT scanning: the X-ray tube rotates around the patient, taking hundreds of projections; a computer reconstructs a set of thin slices, which can be stacked into a 3-D image. Far better soft-tissue contrast and no superposition of structures — but a much higher radiation dose than a plain radiograph.
Calculate
Your turn — attenuation
1A beam of X-rays passes through 4.0 cm of tissue with attenuation coefficient µ = 0.25 cm⁻¹. What percentage of the incident intensity emerges?
%
Hint: I/I₀ = e^(−µx) = e^(−0.25 × 4.0) = e^(−1.0) = 0.368. Now express as a percentage.
Calculate
Your turn — half-value thickness
2Calculate the half-value thickness of that tissue (µ = 0.25 cm⁻¹).
cm
Hint: x½ = ln 2 / µ = 0.693 ÷ 0.25.
Quick check
Turning up the tube current
?The tube current in an X-ray machine is doubled, with the accelerating p.d. unchanged. What happens to the beam?
(h)–(k) Ultrasound
Ultrasound, acoustic impedance and Doppler
A piezoelectric crystal changes shape when a p.d. is applied and, conversely, produces a p.d. when it is squeezed. Drive it with an alternating p.d. at its resonant frequency and it generates ultrasound; the returning echoes squeeze it and it detects them. The same transducer does both.
Z = ρcAcoustic impedance (kg m⁻² s⁻¹): density × speed of sound in the medium. The fraction of intensity reflected at a boundary depends on the difference in Z between the two media.
The Z of air is minute compared with that of skin, so almost all the ultrasound would be reflected at an air gap and never enter the body. A coupling gel, with a Z close to that of skin, excludes the air and lets the beam through.
A-scan (amplitude): a single line of sight — a graph of echo amplitude against time. Depths are found from the time delays. Used to measure distances, e.g. in the eye.
B-scan (brightness): many A-scans from different directions, each echo displayed as a bright dot, building a 2-D image — the familiar fetal scan.
Δf / f = 2v cos θ / cDoppler ultrasound: the beam reflects off moving red blood cells, so the returning frequency is shifted. There is a factor of 2 because the cells act first as a moving receiver and then as a moving source.
Calculate
Your turn — acoustic impedance
3Soft tissue has a density of 1060 kg m⁻³ and a speed of sound of 1540 m s⁻¹. Calculate its acoustic impedance in units of 10⁶ kg m⁻² s⁻¹.
× 10⁶ kg m⁻² s⁻¹
Hint: Z = ρc = 1060 × 1540 = 1.632 × 10⁶ kg m⁻² s⁻¹. Enter just the number in front.
Calculate
Your turn — Doppler blood flow
4A 5.0 MHz ultrasound probe is aimed at 45° to a blood vessel in which the blood flows at 0.30 m s⁻¹. Take the speed of ultrasound in tissue as 1540 m s⁻¹. Calculate the Doppler frequency shift, in Hz.
Hz
Hint: Δf = 2f v cos θ / c = (2 × 5.0 × 10⁶ × 0.30 × cos 45°) ÷ 1540 = (2.12 × 10⁶) ÷ 1540.
Quick check
Why the gel?
?Why must a coupling gel be applied between an ultrasound probe and the skin?
Sort it
X-ray, ultrasound or MRI?
Tap a feature, then tap the imaging technique it belongs to.
☢️ X-ray / CT
🔊 Ultrasound
🧲 MRI
(l)–(n) MRI
Magnetic resonance imaging
Hydrogen nuclei (single protons — abundant in the water and fat of the body) behave like tiny magnets. Placed in a strong magnetic field they precess about the field direction, like a spinning top, at the Larmor frequency:
f = 42.6 × 10⁶ × Bf in Hz when B is in tesla. For B = 1.5 T this gives about 64 MHz — a radio frequency.
A radio pulse at exactly that frequency is absorbed resonantly, flipping the protons. When the pulse stops they relax back, re-emitting radio waves that are picked up by the receiver coils. The relaxation times differ between tissue types (and between healthy and diseased tissue), which is what generates the contrast. Superimposed gradient fields make the Larmor frequency depend on position, so the signal can be located in 3-D.
Choosing the modality:X-ray/CT — fast, cheap, superb for bone, but ionising. Ultrasound — cheap, portable, real-time, non-ionising (safe in pregnancy), but poor through bone and gas. MRI — outstanding soft-tissue contrast and no ionising radiation, but expensive, slow, noisy, claustrophobic, and impossible for patients with some metal implants.
Calculate
Your turn — Larmor frequency
5An MRI scanner has a magnetic flux density of 1.5 T. Calculate the Larmor frequency of hydrogen nuclei, in MHz.
MHz
Hint: f = 42.6 × 10⁶ × B = 42.6 × 10⁶ × 1.5 = 6.39 × 10⁷ Hz. Convert to MHz.
(o)–(q) Radiation dose
Absorbed, equivalent and effective dose
Ionising radiation damages living tissue by ionising molecules — breaking DNA strands directly, or producing free radicals that do the damage. Three quantities, each more refined than the last:
absorbed dose D = energy ÷ massUnit: the gray (Gy) = 1 J kg⁻¹. It counts the energy deposited, but not how harmful it is.
equivalent dose H = D × WRUnit: the sievert (Sv). WR is the radiation weighting factor: about 1 for beta, gamma and X-rays, but about 20 for alpha — because alpha particles are so densely ionising.
effective dose E = H × WTAlso in sieverts. WT is the tissue weighting factor — some organs (e.g. bone marrow, lung) are far more radiosensitive than others (e.g. skin, bone surface).
Calculate
Your turn — equivalent dose
6A tissue of mass 2.0 kg absorbs 5.0 mJ of energy from alpha radiation, for which the radiation weighting factor is 20. Calculate the equivalent dose, in mSv.
mSv
Hint: Absorbed dose D = E/m = 5.0 × 10⁻³ ÷ 2.0 = 2.5 × 10⁻³ Gy = 2.5 mGy. H = D × W(R) = 2.5 × 20.
(r)–(t) Nuclear medicine
Tracers, the gamma camera and PET
A radionuclide tracer is attached to a molecule the body handles in a known way, injected, and then tracked from outside. This images function, not just anatomy.
Technetium-99m is the workhorse: it emits a gamma photon of convenient energy (so it escapes the body but is easily detected), emits no alpha or beta (which would only add dose), and has a half-life of about 6 hours — long enough for the scan, short enough that the activity soon decays away.
Gamma camera: a collimator (a lead honeycomb) only lets through photons travelling perpendicular to the crystal, so each detected photon can be traced back to a point in the patient. A scintillator converts each gamma photon into a flash of light, and a photomultiplier (or CCD) turns that flash into a measurable electrical pulse.
PET (positron emission tomography): a positron-emitting tracer (often fluorine-18 in a glucose analogue) is injected. Each emitted positron travels a few mm, meets an electron and annihilates, producing two 511 keV gamma photons travelling in almost exactly opposite directions. Detecting both in coincidence pins down the line the annihilation occurred on. Because tumours consume glucose greedily, they light up.
Quick check
Why two photons in PET?
?In a PET scan, why are two gamma photons detected travelling in opposite directions?
Quick check
Why technetium-99m?
?Why is technetium-99m so widely used as a medical tracer?
Quick check
Choosing a modality
?A pregnant patient needs an image of the fetus. Which modality is chosen, and why?
Match it
Match each equation to its quantity
Tap an item on the left, then its partner on the right.
Equation
Quantity
Recap
Option B — the big ideas
X-rays: tube current → intensity; accelerating p.d. → maximum photon energy; low energy = diagnosis, high = therapy
Attenuation: I = I₀e^(−µx); x½ = ln2/µ; contrast media and fluoroscopy; CT = rotating beam, slices, higher dose
Ultrasound: piezoelectric transducer; Z = ρc; coupling gel; A-scan vs B-scan
Doppler: Δf/f = 2v cos θ / c — blood flow
MRI: f = 42.6 × 10⁶ B; precession, resonance, relaxation times; no ionising radiation
Dose: D (gray) → H = D W(R) (sievert) → E = H W(T); alpha W(R) ≈ 20
Nuclear medicine: Tc-99m (gamma only, ~6 h); gamma camera (collimator, scintillator, photomultiplier); PET (two 511 keV photons back-to-back)
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