X-rays and CT Scanning

Producing X-rays — electrons are accelerated through a large potential difference, typically tens of kilovolts, and slammed into a metal target. Their sudden deceleration converts kinetic energy into X-ray photons.

Maximum photon energy — a photon can carry at most all the electron's kinetic energy:

E_max = e V so λ_min = h c / (e V)

Raising the tube voltage produces more energetic, more penetrating X-rays.

Efficiency is very poor — around 1% of the electron energy becomes X-rays and the rest becomes heat, which is why the target is a rotating disc of tungsten: a high melting point, and the heat spread over a large area rather than a single spot.

Attenuation — the intensity of a beam falls exponentially as it passes through matter:

I = I₀ e^(−μx)

where μ is the attenuation coefficient, depending on the material and the photon energy. This is a third appearance of exponential decay, alongside capacitor discharge and radioactive decay.

Half-value thickness — the thickness that halves the intensity, equal to ln 2 / μ. The parallel with half-life is exact.

Why bone shows white — attenuation rises very steeply with atomic number, roughly as Z³. Bone contains calcium (Z = 20) while soft tissue is mostly carbon, hydrogen and oxygen, so bone absorbs far more and casts a shadow. The image is a shadow, not a picture.

Contrast media — soft tissue against soft tissue gives almost no contrast, so a high-Z substance is introduced: a barium meal for the digestive tract, or iodine in blood vessels. Both work purely because Z is large.

Example: the great limitation of a plain X-ray is that it compresses a three-dimensional body onto a two-dimensional plate. Everything along the beam is superimposed, and depth information is lost entirely.

CT scanning solves exactly that. The tube rotates around the patient, taking many images from different angles, and a computer reconstructs a three-dimensional picture from them.

Advantages — full 3D imaging, and far better soft-tissue discrimination.

Disadvantage — the radiation dose is much higher than a single X-ray, typically by a factor of tens to hundreds, so the clinical benefit has to justify the risk.