Medical Physics

This guide covers Topic 24, Medical physics, in full — subtopics 24.1 Production and use of ultrasound, 24.2 Production and use of X-rays and 24.3 PET scanning — from Cambridge International AS & A Level Physics 9702, 2025–2027 series. This is A Level content, applying wave and nuclear physics to medical imaging techniques. Note that this syllabus series no longer names A-scan/B-scan terminology or “sharpness” as examinable outcomes — the current requirement is that pulse-echo reflection at tissue boundaries yields diagnostic information, and that image quality is discussed in terms of contrast; A-scan and B-scan are mentioned below only as background context for how that diagnostic information is actually displayed.

Before studying this

This resource assumes wave properties from Waves: Progressive Waves, the Doppler Effect and Polarisation, and photon and nuclear concepts from Quantum Physics and Nuclear Physics.

Syllabus coverage

CAMBRIDGE INTERNATIONAL AS & A LEVEL PHYSICS 9702 — A Level, Topic 24

24.1 Production and use of ultrasound — understanding how ultrasound waves are generated and detected using piezo-electric transducers; recalling and using the specific acoustic impedance Z = ρc; recalling and using the intensity reflection coefficient equation I_r/I_i = (Z₂ − Z₁)²/(Z₂ + Z₁)²; recalling and using I = I₀e^(−μx) for the attenuation of ultrasound intensity in matter; understanding that pulse-echo reflection at boundaries between tissues of different acoustic impedance provides diagnostic information about internal body structures.

24.2 Production and use of X-rays — describing the principles of the production of X-rays by electron bombardment of a metal target; recalling and using λ_min = hc/(eV) for the minimum wavelength (maximum photon energy) produced for a given accelerating potential difference; describing the use of X-rays in imaging internal body structures, including a simple treatment of the contrast of X-ray images; recalling and using the equation I = I₀e^(−μx) for the attenuation of X-rays in matter; outlining the principles of computed tomography (CT) scanning and its advantages and disadvantages compared with a simple X-ray image.

24.3 PET scanning — outlining the principles of positron emission tomography (PET scanning), including the production of positron-emitting isotopes, positron-electron annihilation and the emission of two identical gamma-ray photons, and how the resulting data is used to obtain diagnostic information about internal body structures; calculating the energy of each annihilation photon from the rest mass of the electron and positron using E = mc².

Production and detection of ultrasound

Ultrasound waves (sound waves above the range of human hearing) are generated and detected using piezo-electric transducers: crystals that change shape when a voltage is applied (producing ultrasound) and generate a voltage when mechanically deformed (detecting reflected ultrasound).

Ultrasound imaging

Every tissue in the body has a specific acoustic impedance:

Z = ρc

where ρ is the density of the tissue and c is the speed of ultrasound through it. When ultrasound reaches a boundary between two tissues of different acoustic impedance, part of the wave reflects and part transmits through. The proportion of intensity reflected is given by the intensity reflection coefficient:

I_r / I_i = (Z₂ − Z₁)² / (Z₂ + Z₁)²

A larger impedance mismatch produces a stronger reflection. It is exactly this pulse-echo reflection at tissue boundaries — sending a pulse and timing/measuring the strength of the echoes reflected from boundaries inside the body — that provides the diagnostic information ultrasound scanning is based on; older terminology described the resulting display as an A-scan (a single line of amplitude against depth) or a B-scan (many such lines combined into a two-dimensional image), and either remains a reasonable way to picture how the reflected pulses are actually displayed.

Worked example. Soft tissue has Z = 1.63 × 10⁶ kg m⁻² s⁻¹ and bone has Z = 6.40 × 10⁶ kg m⁻² s⁻¹. The intensity reflection coefficient at the boundary:

I_r/I_i = (6.40 − 1.63)² / (6.40 + 1.63)² = 22.75 / 64.48 ≈ 0.353

so about 35% of the incident intensity is reflected at a soft tissue–bone boundary — which is also why structures lying behind bone are poorly imaged by ultrasound.

Attenuation of ultrasound

As with X-rays, ultrasound intensity decreases exponentially as it travels through tissue, due to absorption and scattering:

I = I₀ e^(−μx)

where μ is the (ultrasound) attenuation coefficient of the tissue and x is the distance travelled. Greater attenuation, alongside reflection at boundaries, limits how deep into the body a useful ultrasound image can be obtained.

Production of X-rays

X-rays are produced by accelerating electrons through a large potential difference and firing them at a metal target. On impact, the rapid deceleration of the electrons converts their kinetic energy into electromagnetic radiation (X-ray photons), a process sometimes described as bremsstrahlung (“braking radiation”). The maximum photon energy possible equals the kinetic energy gained by an electron accelerated through the full potential difference V, eV, which sets the minimum wavelength produced:

λ_min = hc / (eV)

A photon can carry at most all of an electron’s kinetic energy, so no photon of shorter wavelength (higher energy) than this can be produced — λ_min depends only on the accelerating p.d., not on the target material.

X-ray imaging and attenuation

As X-rays pass through the body, different tissues absorb (attenuate) them by different amounts — denser tissue such as bone absorbs more than soft tissue, which is what creates image contrast on an X-ray photograph. This attenuation follows an exponential law:

I = I₀ e^(−μx)

where I₀ is the initial intensity, x is the thickness of the material, and μ is the attenuation (absorption) coefficient, which depends on the material and the X-ray energy.

Worked example. X-rays of initial intensity I₀ pass through 5.0 cm of tissue with attenuation coefficient 0.20 cm⁻¹. The transmitted intensity as a fraction of I₀:

I/I₀ = e^(−μx) = e^(−0.20 × 5.0) = e^(−1.0) ≈ 0.37

Worked example. X-rays are produced using an accelerating p.d. of 80 kV. The minimum wavelength produced:

λ_min = hc/(eV) = (6.63 × 10⁻³⁴ × 3.00 × 10⁸) / (1.60 × 10⁻¹⁹ × 80 000)
      ≈ 1.55 × 10⁻¹¹ m

Computed tomography (CT)

A CT scanner rotates an X-ray tube (and detectors) around the patient, taking many two-dimensional X-ray images from different angles. A computer combines this whole set of images to reconstruct a three-dimensional image of internal structures, which can then be viewed as any chosen slice. Compared with a single plain X-ray image, CT gives far better soft-tissue contrast and full 3-D information, but at the cost of a substantially higher radiation dose, longer scan time and higher expense.

PET scanning

Positron emission tomography (PET) uses a radioactive tracer that emits positrons (the antiparticle of the electron). Each emitted positron travels a very short distance before meeting an electron in the body tissue, and the two particles undergo annihilation — their combined mass is converted entirely into energy, emitted as two identical gamma-ray photons travelling in opposite directions. Detectors surrounding the body record these paired gamma-ray emissions; because the two photons travel in exactly opposite directions, the location of each annihilation event (and hence the tracer’s concentration) can be reconstructed, building up a detailed image of metabolic activity inside the body.

Annihilation photon energy

Because momentum is conserved and the total momentum before annihilation is approximately zero, the two photons share the total energy released equally. That total energy comes from the combined rest mass of the electron and positron converting entirely into radiation, via E = mc². For an electron (or positron) of rest mass 9.11 × 10⁻³¹ kg, the energy of each photon is:

E = mc² = 9.11 × 10⁻³¹ × (3.00 × 10⁸)² ≈ 8.19 × 10⁻¹⁴ J ≈ 0.511 MeV

so each annihilation produces two photons of 0.511 MeV, not one photon of 1.022 MeV — the energy is shared between the pair, one mass’s worth of energy per photon.

Common mistakes

• Forgetting X-ray (or ultrasound) attenuation is exponential, not linear — I = I₀e^(−μx) must be used, not a simple proportional reduction.
• Assuming PET scanning detects the positron itself — it detects the pair of gamma-ray photons produced by positron-electron annihilation, not the positron directly.
• Mixing up acoustic impedance mismatch (relevant to ultrasound reflection) with X-ray attenuation coefficient (relevant to X-ray absorption) — these are distinct physical quantities relevant to different imaging techniques.
• Saying λ_min depends on the target material — it depends only on the accelerating p.d.; the target material instead determines the characteristic line spectrum superimposed on the continuous background.
• Giving 1.022 MeV as the energy of one annihilation photon — that is the total energy released; each of the two photons carries half of it, 0.511 MeV.
• Claiming CT delivers a lower radiation dose than a plain X-ray image — CT’s much richer 3-D information comes at the cost of a substantially higher dose.

Quick revision checklist

• Piezo-electric transducers generating and detecting ultrasound
• Z = ρc for specific acoustic impedance, and I_r/I_i = (Z₂−Z₁)²/(Z₂+Z₁)² for the intensity reflection coefficient
• I = I₀e^(−μx) for the attenuation of ultrasound as well as X-rays
• X-ray production by electron bombardment, and λ_min = hc/(eV) for the minimum wavelength
• I = I₀e^(−μx) for X-ray attenuation, and contrast from differential absorption between tissues
• Computed tomography: rotating the X-ray source/detectors to build a 3-D image, at the cost of a higher dose
• PET scanning: positron emission, annihilation, and paired 0.511 MeV gamma-ray detection, from E = mc²

Related resources

• Nuclear Physics — the previous A Level topic
• Astronomy and Cosmology — the final A Level topic
• Cambridge AS & A Level Physics hub

Written against Cambridge International AS & A Level Physics 9702, 2025–2027 series. Always check the current syllabus for your examination year.