# X-ray imaging

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u28-x-ray-imaging/

This sub-topic covers X-ray production for medical diagnostics, exponential attenuation through body tissue, factors affecting image quality, and safety requirements for X-ray procedures.

**Prerequisites:** [Photon energy and electromagnetic spectrum](https://www.owlsprep.com/study/cie-9702-u20-electromagnetic-waves/); [Exponential decay of radiation](https://www.owlsprep.com/study/cie-9702-u27-radioactivity-decay-processes/)

## Learning objectives

- Explain how X-rays are produced for medical imaging
- Apply the exponential attenuation law to X-rays
- Describe factors affecting X-ray image contrast and resolution
- Outline safety precautions for X-ray imaging

## Production of Medical X-rays

Medical X-rays for imaging are high-energy photons (30 keV to 150 keV) produced in a vacuum X-ray tube. Electrons are emitted from a heated cathode, accelerated through a high potential difference towards a tungsten anode target.

When electrons collide with the target, ~99% of their kinetic energy is lost as heat, and only ~1% is converted to X-ray photons. The maximum energy of an X-ray photon equals the maximum kinetic energy of the accelerated electron.

**X-ray tube** — Vacuum device that produces X-rays by accelerating electrons to a high-density metal anode

*Example:* Tungsten is used as an anode because it has a high melting point and high atomic number, improving X-ray production efficiency.

**Worked example:** An X-ray tube operates at 80 kV. Calculate the maximum energy of an emitted X-ray photon, in joules.

1. Maximum photon energy equals the kinetic energy gained by an electron across the accelerating potential difference:
2. $$E_{\text{max}} = eV$$
3. Substitute $e = 1.6 \times 10^{-19}$ C and $V = 80 \times 10^3$ V:
4. $$E_{\text{max}} = (1.6 \times 10^{-19}) \times (80 \times 10^3) = 1.28 \times 10^{-14} \text{ J}$$

> **Exam tip:** A 1-mark question often asks what percentage of energy becomes X-rays: remember only 1% is X-rays, 99% is heat.

## X-ray Attenuation

When X-rays pass through body tissue, photons are absorbed or scattered, reducing intensity: this process is called attenuation. Attenuation follows an exponential relationship that depends on the type of tissue and X-ray energy.

**Linear attenuation coefficient** — Measure of how quickly X-ray intensity decreases per unit thickness of material. Higher values mean more attenuation.

*Notation:* \mu

$$I = I_0 e^{-\mu x}$$

Where $I_0$ = incident intensity, $I$ = transmitted intensity, $x$ = material thickness. Half-value thickness ($x_{1/2}$), the thickness that reduces intensity by half, is related to $\mu$ by $x_{1/2} = \frac{\ln 2}{\mu}$.

**Worked example:** Bone has $\mu = 0.35$ cm⁻¹, soft tissue has $\mu = 0.10$ cm⁻¹. Calculate the ratio $I_{\text{bone}}/I_{\text{soft}}$ for 2 cm thickness of each.

1. Cancel $I_0$ from the intensity ratio for both materials:
2. $$\frac{I_{\text{bone}}}{I_{\text{soft}}} = \frac{I_0 e^{-\mu_{\text{bone}} x}}{I_0 e^{-\mu_{\text{soft}} x}} = e^{-(\mu_{\text{bone}} - \mu_{\text{soft}})x}$$
3. Substitute values: $\mu_{\text{bone}} - \mu_{\text{soft}} = 0.25$ cm⁻¹, $x = 2$ cm:
4. $$\frac{I_{\text{bone}}}{I_{\text{soft}}} = e^{-(0.25)(2)} = e^{-0.5} \approx 0.61$$

> **info**
>
> Bone has a higher attenuation coefficient than soft tissue because it is denser and has a higher average atomic number, which creates the contrast we see in X-ray images of bones.

## X-ray Image Quality

Two key metrics describe X-ray image quality: contrast and sharpness (resolution). Both are controlled by practical choices when taking an X-ray.

- **Contrast**: The difference in brightness between different regions of the image. Improved by lower X-ray energy, contrast media (like barium), and anti-scatter grids.
- **Resolution (Sharpness)**: The ability to distinguish small adjacent objects. Improved by using a small focal spot on the anode, and minimizing patient movement.

**Worked example:** Explain why barium is used to image the intestine.

1. Intestinal wall tissue has a similar attenuation coefficient to surrounding soft tissue, so it produces very little contrast on a standard X-ray.
2. Barium has a high atomic number, so it has a much higher attenuation coefficient than body tissue.
3. When the intestine is filled with barium, it strongly attenuates X-rays, creating a high-contrast outline that allows radiologists to see abnormalities like tumors.

## Patient Dose and Safety

X-rays are ionizing radiation, so they can damage living cells and increase long-term cancer risk. All exposure must be kept as low as reasonably achievable (the ALARA principle).

Intensifying screens are used to reduce patient dose. These screens contain fluorescent material that converts each absorbed X-ray photon into many visible light photons, which expose the film. This means far fewer X-ray photons are needed for the same image exposure, cutting patient dose significantly.

- Key safety rules: Shield sensitive tissue (reproductive organs) with lead aprons
- Staff must stand behind lead shielding during exposure
- Keep exposure time as short as possible
- Avoid X-rays for pregnant patients where possible

> **warning**
>
> Never confuse the purpose of intensifying screens: they reduce patient dose, not increase it.

## Common pitfalls

- **Wrong:** Using mismatched units for $\mu$ and $x$ in the attenuation formula.
  - Why it fails: If $\mu$ is in m⁻¹ and $x$ is in cm, the exponent will be wrong and give an incorrect intensity.
  - Correct: Always convert thickness to match the length unit of $\mu$ (e.g. convert x to metres if $\mu$ is in m⁻¹).
- **Wrong:** Stating most energy in an X-ray tube becomes X-rays.
  - Why it fails: This is a common factual recall question that students often get backwards.
  - Correct: Remember: 1% of energy becomes X-rays, 99% becomes heat.
- **Wrong:** Confusing contrast and resolution.
  - Why it fails: Exam questions often ask to define or compare these two, and marks are lost for mixing them up.
  - Correct: Contrast = difference in brightness between tissues; Resolution = ability to see small separate objects.
- **Wrong:** Claiming intensifying screens increase patient dose.
  - Why it fails: Students incorrectly think more photons mean higher patient dose, but the extra photons are visible light, not X-rays.
  - Correct: Intensifying screens reduce the number of X-rays needed, so they decrease patient dose.

## Cheatsheet

| Concept | Formula / Key Fact |
| --- | --- |
| Max X-ray energy | $E_{max} = eV$ |
| Exponential attenuation | $I = I_0 e^{-\mu x}$ |
| Half-value thickness | $x_{1/2} = \frac{\ln 2}{\mu}$ |
| X-ray tube energy split | 1% → X-rays, 99% → heat |
| Image contrast | Difference in intensity from different attenuation |
| Image resolution | Ability to distinguish adjacent small objects |
| Intensifying screen purpose | Reduce patient X-ray dose |
| Contrast media purpose | Increase contrast for soft tissue imaging |

## What's next

X-ray imaging is the foundation of modern diagnostic radiology, and the principles of attenuation and image quality you learned here apply to all other medical imaging techniques covered in this unit. Understanding how X-ray production and attenuation work is critical for tackling more advanced topics like computed tomography (CT) scanning, which is a frequent extended response question in CIE A-Level Paper 4. These concepts also connect to radiation safety principles you learned earlier in the radioactivity unit, which often are combined with medical imaging questions in exams.

- [Radiation Safety and Dose](https://www.owlsprep.com/study/cie-9702-u27-radiation-safety/)
- [CT scanning](https://www.owlsprep.com/study/cie-9702-u28-ct-scanning/)
- [Ultrasound imaging](https://www.owlsprep.com/study/cie-9702-u28-ultrasound-imaging/)

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