Learn7408Paper 3B · Option: Medical physicsX-ray imagingX-rays and CT scanning

X-ray imaging · Subtopic 1 of 1

X-rays and CT Scanning

X-rays are produced when high-speed electrons hit a metal target. An electron accelerated through p.d. $V$ can give at most all its energy $eV$ to one photon, so the minimum wavelength is $\lambda_{\min}=\dfrac{hc}{eV}$ . X-rays are attenuated exponentially in matter: $I=I_0e^{-\mu x}$ . Bone attenuates much more than soft tissue, giving contrast. CT scanning combines images from many angles to build 2D slices, then stacks them into a 3D image.

Cambridge 9702 Paper 4AQA 7408 Paper 3B≈ 40 minRevision 6 · updated 2026-10-27

Section 1 of 14

Learning objectives

Describe X-ray production in a tube and find $\lambda_{\min}$ .
Explain image sharpness and contrast.
Use $I=I_0e^{-\mu x}$ and half-value thickness.
Describe how CT builds a 3D image.

Pause and think

A chest X-ray shows bones clearly but soft organs only faintly. Why the difference?

Section 2 of 14

Core idea

Start hereShadows of bones

An X-ray image is a shadow: bones absorb X-rays strongly and appear white; soft tissue lets most through. The contrast comes from how quickly each material weakens the beam.

The big idea

X-rays from fast electrons hitting a target; $\lambda_{\min}=\frac{hc}{eV}$ . Attenuation $I=I_0e^{-\mu x}$ ; half-value thickness $\frac{\ln2}\mu$ .

1. Production

Attenuation through bone and soft tissue

After 2 cm, 67% gets through soft tissue but only 9% through bone. This difference is the contrast in the image.

Minimum wavelength

$E_{\max}=eV$
All of one electron's energy into one photon.
$\frac{hc}{\lambda_{\min}}=eV\Rightarrow\lambda_{\min}=\frac{hc}{eV}$
Rearrange.

Worked exampleTube at 100 kV

Find $E_{\max}$ and $\lambda_{\min}$ .

Goal: Two values.
Strategy: Formula.

$E_{\max}=100\text{ keV}$
$eV$ .
$\lambda_{\min}=\frac{1.99\times10^{-25}}{1.6\times10^{-14}}=1.24\times10^{-11}\text{ m}$
Formula.

Answer

100

keV;

1.24\times10^{-11}

✓ Check~99% of the energy heats the anode (rotating, cooled) ✓.

2. Attenuation

X-ray tube spectrum: continuous braking radiation plus characteristic lines

The maximum photon energy equals the electron energy

eV

(all its energy in one photon). The sharp lines come from inner-shell electrons in the target.

Worked exampleReading the graph

2 cm transmits 0.67 (tissue) and 0.09 (bone).

Goal: $\mu$ values; half-value thickness of bone.
Strategy: $\ln$ of the fraction.

$\mu=-\frac{\ln0.67}2=0.20\text{ cm}^{-1}$
Tissue.
$\mu=-\frac{\ln0.09}2=1.2\text{ cm}^{-1}$
Bone.
$x_{1/2}=\frac{\ln2}{1.2}=0.58\text{ cm}$
Half-value thickness.

Answer

0.20

1.2

^{-1}

;

0.58

cm.

✓ CheckBone ~6× more absorbing: good contrast ✓.

Edge caseCT scanning Many images from different angles combine into 3D slices.

Summary

$\lambda_{\min}=hc/eV$ .
$I=I_0e^{-\mu x}$ .

Attenuation coefficient: Fraction absorbed per unit thickness.

HistoryRöntgen's mysterious rays. In

1895

Wilhelm Röntgen noticed a screen glowing across his lab while a cathode-ray tube was covered in black card. He called the unknown radiation "X-rays". His first X-ray photograph, of his wife Anna Bertha's hand with her ring, made her exclaim "I have seen my death!"

Fun factShoe-fitting X-rays. In the

1930

s–

50

s, shoe shops had "fluoroscopes" so customers could see their toes inside new shoes. Children loved them, and nobody tracked the doses. They were banned once the dangers of ionising radiation were understood.

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