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X-rays were discovered in November 1895 by Wilhelm Röntgen, a German physicist working in Würzburg. Experimenting with Crookes tubes (evacuated glass tubes with a high voltage applied across two electrodes), he noticed that a fluorescent screen across the room was glowing, even though the tube was carefully shielded from visible light. Röntgen realised he had discovered an entirely new form of radiation — penetrating, invisible, and capable of passing through solid matter. He called it "X-ray" as a placeholder, and within weeks he had produced the first X-ray photograph in history: an image of his wife's hand, complete with wedding ring.
The medical applications were immediate and obvious. Within a year, hospitals around the world were using X-rays to image broken bones and locate foreign bodies. Today, well over a century later, X-ray radiography remains one of the most widely used diagnostic tools in medicine — and the physical principles of its operation are now the subject of Module 6.5 — Medical Imaging of the OCR A-Level Physics A specification (H556), a part of the syllabus that is unique to OCR and sets it apart from AQA and Edexcel Physics.
This lesson introduces the generation of X-rays, the attenuation law, half-value thickness, and the use of contrast media in clinical imaging.
X-rays are electromagnetic waves — the same kind of thing as visible light, just with much higher frequency and correspondingly higher photon energy. The X-ray region of the electromagnetic spectrum runs from about 10 nm down to 0.01 nm, corresponding to photon energies from about 100 eV to 100 keV. For medical imaging, energies in the range 20–150 keV are standard:
The higher the photon energy, the more penetrating the X-ray. Low-energy X-rays are absorbed in superficial tissues; high-energy X-rays pass through the whole body with little absorption. A clinical X-ray has to balance penetration against image contrast — both depend on photon energy.
X-rays are produced by accelerating electrons to high speed and then stopping them abruptly. An X-ray tube is the standard device:
flowchart LR
C["Cathode<br/>(heated filament)"]
E["Electrons<br/>accelerated"]
HV["High voltage<br/>~50-150 kV"]
A["Anode<br/>(tungsten target)"]
X["X-rays<br/>emerge"]
C --> E
HV --> A
E --> A
A --> X
The essential components are:
When an electron strikes the tungsten target, most of its kinetic energy is dissipated as heat (which is why the target must be actively cooled). But a small fraction (\sim 1\%) is converted into X-ray photons through two distinct physical processes.
As a fast electron passes near a tungsten nucleus, the intense Coulomb field deflects it and decelerates it. An accelerating charge always emits electromagnetic radiation; in this case the emitted radiation has X-ray energies. The German word Bremsstrahlung ("braking radiation") describes the process exactly.
The key feature of bremsstrahlung is that the emitted photon can have any energy from zero up to the maximum — which is reached when the electron gives up all its kinetic energy in a single photon. If the accelerating voltage is V, the maximum photon energy is:
E_max = eV
and the corresponding minimum wavelength is:
λ_min = hc/(eV)
This is the Duane-Hunt law. An X-ray tube operated at 100 kV has:
E_max = 100 keV
λ_min = hc / (eV) = (6.63 × 10⁻³⁴)(3 × 10⁸) / (1.60 × 10⁻¹⁹ × 10⁵)
≈ 1.24 × 10⁻¹¹ m = 12.4 pm
Photons of any energy less than eV can also be produced; the bremsstrahlung spectrum is continuous from 0 up to eV, falling off smoothly. Low-energy photons dominate in number but high-energy photons dominate in penetration.
In addition to the continuous bremsstrahlung spectrum, the X-ray tube produces characteristic X-rays at specific discrete energies, superimposed on the bremsstrahlung background as sharp peaks. These arise when a fast electron collides with an inner-shell electron of a tungsten atom, knocking it out. The resulting hole is then filled by a higher-shell electron dropping down, emitting a photon whose energy equals the difference between the two atomic levels.
Because atomic energy levels are quantised, the emitted photon energies are sharp and characteristic of the target element (hence "characteristic X-rays"). Tungsten's strong K-line at about 59 keV, and L-lines around 8–11 keV, are standard features of the X-ray spectrum.
The characteristic photon energies depend only on the atomic number of the target, not on the tube voltage — provided the tube voltage is high enough to knock out the inner-shell electron in the first place.
A typical medical X-ray spectrum therefore consists of:
eV.flowchart TB
G["Bremsstrahlung<br/>Continuous spectrum"]
K["K lines<br/>(~59 keV for W)"]
L["L lines<br/>(~10 keV for W)"]
F["Filter<br/>removes low energies"]
S["Clinical spectrum"]
G --> S
K --> S
L --> S
F --> S
As X-rays pass through matter, they are attenuated: some photons are absorbed (by the photoelectric effect or pair production), others are scattered (by Compton scattering). For a monoenergetic beam of intensity I_0 passing through a thickness x of a uniform material, the transmitted intensity is:
I = I₀ e^(-μx)
where \mu is the linear attenuation coefficient of the material, with units of m⁻¹ (or more commonly cm⁻¹). This is the analogue of the radioactive decay law we met in Lesson 2, but with distance rather than time as the independent variable.
The attenuation coefficient depends on:
Typical values at 100 keV:
| Material | \mu (cm⁻¹) |
|---|---|
| Air | \sim 2 \times 10^{-4} |
| Water (soft tissue) | \sim 0.17 |
| Muscle | \sim 0.18 |
| Fat | \sim 0.17 |
| Bone | \sim 0.4 |
| Lead | \sim 60 |
Notice how bone attenuates about 2–3 times more strongly than soft tissue — enough to make bones stand out clearly as white regions on a radiograph. Lead is enormously more attenuating still, which is why it is the shielding material of choice in X-ray rooms.
By analogy with half-life in radioactive decay, the half-value thickness x_{1/2} is the thickness of material that reduces the X-ray intensity to half its initial value. Setting I = I_0/2:
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