X-ray tube components and functioning

An X-ray tube operates as a sophisticated electrical device comprising:

• Cathode: This component emits a focused beam of electrons when heated by an electric current passing through a filament. It's typically shaped like a cup to direct the electrons efficiently.
• Anode: A target metal, often tungsten, where the electron beam is aimed. It is propelled by a high voltage across the tube, which accelerates the electrons towards it.

Upon striking the tungsten anode, the interaction between the electrons and the tungsten not only generates X-rays but also significant heat. To manage this heat, the anode is designed to rotate swiftly, allowing a copper mount to disperse the heat effectively.

Worked example - Calculating maximum X-ray energy

X-rays are produced in an X-ray tube with an accelerating potential of 100 kV. Calculate the maximum X-ray energy.

Step 1: Convert kV to V

to convert from kV to V, multiply by 1,000

100 kV = 100,000 V

Step 2: Formula

E = e V

Step 3: Substitution and correct evaluation

E = 1.6 x 10^-19 x 100,000 = 1.6 x 10^-14 J

Calculating X-ray wavelength from energy

For photons, including X-rays:

$\text{E = }\frac{\text{h c}}{\lambda }$

Where:

• E = photon energy (J)
• h = Planck’s constant ( 6.63 x 10^-34 J s)
• c = speed of light (3 x 10⁸ m s^-1)
• $\lambda$ = wavelength (m)

This equation implies that halving the maximum energy by reducing the potential difference will result in doubling the wavelength of the emitted X-rays.

Increasing X-Ray beam intensity

To enhance the X-ray beam's intensity, one can:

1. Increase the accelerating potential difference, which heightens the energy of the electrons.
2. Boost the heating current of the filament to produce more electrons per second.

These actions elevate the number of X-ray photons emitted, thereby increasing the beam's intensity.

Attenuation of X-Rays

X-rays diminish in intensity, or attenuate, as they traverse matter, primarily due to:

• Absorption
• Scattering

This attenuation follows an exponential decrease with depth, as described by:

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

Where:

• I = intensity after traversing a distance x (W m^-2)
• I₀ = initial intensity (W m^-2)
• $\mu$ = attenuation coefficient (cm^-1)
• x = depth within the material (m)

Worked example - Calculating attenuation of X-rays

Calculate the X-ray intensity after passing through 5 cm of material with an initial intensity of 1,000 W m^-2. The attenuation coefficient of the material is 0.2 cm^-1.

Step 1: Formula

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

Step 2: Substitution and correct evaluation

$\text{I = 1,000 }{e}^{-0.2\times 5}{\text{ = 367.9 W m}}^{-2}$

Contrast between bone and soft tissue

Due to their higher atomic numbers, bones absorb X-rays more efficiently than soft tissues, making them more prominent on X-ray images. Contrast can be further improved by administering contrast media, such as barium or iodine, which are visible on X-rays and help in visualising internal structures.

X-Rays in CAT Scans

Computerised Axial Tomography (CAT), or CT scans, use:

• A rotating X-ray beam and detectors to capture images of body slices.
• These images are processed to produce detailed cross-sectional views of soft tissues.
• Combining multiple slices generates three-dimensional models of internal body structures.