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X-rays and CT scanning
Slam fast electrons into metal and X-rays come out; send those through a body and the shadows betray what is inside. One tube, one exponential law, and a century of refinement ending in the CT scanner, which turns hundreds of shadows into slices.
Builds on The photoelectric effect and The time constant and exponential decay.
IN THIS TOPIC
- Describe how an X-ray tube produces X-rays, and find the maximum photon energy from the tube pd.
- Use I = I₀e−μx for attenuation, and explain image contrast including contrast media.
- Explain how a CT scanner builds cross-sectional images, and weigh it against a plain X-ray.
WHAT YOU PROBABLY THINK
A CT scanner is just a sharper X-ray photograph.
Making X-rays
An X-ray tube is an electron gun aimed at a metal target. Electrons boil off a heated cathode, accelerate through a pd of tens of kilovolts, and decelerate violently in the target metal. Rapid deceleration of charge radiates, and at these energies the radiation is X-rays. Most of the beam energy becomes heat in the target, which is why the anode spins and is made of tungsten.
The photons come out with a spread of energies, but there is a hard ceiling: no photon can carry more than one electron brought in. An electron accelerated through pd V arrives with energy eV, so
and the shortest wavelength in the beam follows from E = hc/λ. Raising the tube voltage hardens the beam; raising the current brightens it. The two dials do different jobs.
Attenuation and contrast
Passing through matter, X-rays are absorbed and scattered, and the surviving intensity falls exponentially with thickness:
where μ is the attenuation coefficient of the material. The same mathematics as capacitor discharge and radioactive decay, now applied to X-rays in tissue.
The attenuation has named mechanisms, and OCR asks for them: simple scatter at low photon energies, the photoelectric effect (dominant at diagnostic energies, and the source of bone contrast, since its strength climbs steeply with atomic number), Compton scattering at higher energies, and pair production only above 1.02 MeV, twice the electron rest energy.
An image is only as good as its contrast: bone absorbs far more strongly than soft tissue, so bones throw crisp shadows. Two soft tissues with similar μ are nearly indistinguishable, which is why a patient drinks a contrast medium such as a barium compound before a gut X-ray. Barium's high atomic number means it attenuates strongly, painting the gut's outline into the image.
Catching the transmitted beam matters as much as shaping it. Film has given way to digital flat-panel detectors, in which a scintillator layer converts each X-ray to light read out by photodiodes; an image intensifier does the same job for live fluoroscopy screening. Both need far less exposure than film, which is a dose saving, and digital images can be enhanced and shared at once.
WORKED EXAMPLE
Halving thickness for bone
The attenuation coefficient of bone for one diagnostic beam is μ = 0.60 cm−1. What thickness of bone halves the intensity?
Half means e−μx = 0.5, so x = ln 2 / μ = 0.693/0.60 = 1.2 cm.
The half-value thickness plays exactly the role half-life plays in decay: the exponential's own natural yardstick.
From shadows to slices
A plain X-ray flattens the body into one shadow: everything along each ray is stacked into a single darkness. A CT scanner refuses the flattening. Its tube and detectors rotate around the patient, recording attenuation along thousands of directions, and a computer solves the inverse problem: what map of μ across this slice would produce all of these shadows at once?
The answer is a cross-sectional image on which soft tissues are distinguishable, and stacking slices gives a three-dimensional reconstruction. The costs are dose and money: many exposures mean a far larger radiation dose than a single plain film, so the sharper picture must justify itself clinically. That trade, detail against dose, is the recurring theme of every ionising technique.
THE EXAM BIT
- Tube questions score on the energy chain: electrons gain eV crossing the tube, and the maximum photon energy equals it. Emax = eV, then λmin = hc/Emax if asked.
- State what most of the electron energy becomes: heat in the target. It explains the rotating tungsten anode and is a routine mark.
- Attenuation working mirrors decay working: identify μ, use I = I₀e−μx, and take logs when the thickness is wanted.
- Contrast answers name the mechanism: materials with different attenuation coefficients transmit different intensities, and a contrast medium adds a strong absorber where the anatomy alone offers none.
- CT against plain film: cross-sectional detail without superposition, but a much larger dose. Give both halves.
CHECK YOURSELF
An X-ray tube runs at 80 kV. Find the maximum photon energy in joules, and state why photons of lower energy are also present.
Show a hint
One electron's energy after the pd caps one photon's energy.
Show the answer
Emax = eV = 1.60 × 10−19 × 80 000 = 1.3 × 10−14 J.
Most electrons lose their energy in several stages rather than one, each stage radiating a photon with only part of the total, so the spectrum fills in below the maximum.
The tube pd caps the photon energy: E max equals eV.
Attenuation is exponential, and contrast is a difference in μ.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
CHECK YOUR PROGRESS
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- Describe how an X-ray tube produces X-rays, and find the maximum photon energy from the tube pd.
- Use I = I₀e−μx for attenuation, and explain image contrast including contrast media.
- Explain how a CT scanner builds cross-sectional images, and weigh it against a plain X-ray.
Open the full revision checklist to track your progress across the whole unit.
No animated video for this topic yet; these notes stand alone. InkPhysics on YouTube.