X-ray Attenuation Mechanisms (OCR A Level Physics): Revision Note

X-ray Attenuation Mechanisms

• X-ray attenuation is defined as:

  The reduction in energy, or intensity, of a beam of X-rays due to their interaction with matter

• There are four main methods in which X-rays can be attenuated:

  • Simple scattering

  • Photoelectric effect

  • Compton scattering

  • Pair production

• These mechanisms occur within the material the X-rays are travelling in

Simple Scattering

• Simple scattering occurs when:

  A low-energy X-ray photon encounters an electron in an atom causing it to be scattered without a change in energy

• Simple scattering occurs with lower-energy X-ray photons

  • In this scenario, 'low-energy' means the energy of the X-ray photon is not sufficient to cause ionisation

• During simple scattering, photons are deflected from their initial path by interaction with the atoms of the material. However, there are:

  • No change in energy of the X-ray photon

  • No absorption of the X-ray photon 

• This mechanism causes blurring or 'noise' in X-ray imaging

  • This is because scattered X-rays arrive at the detector from several angles as well as from the main beam

Photoelectric Effect

• The photoelectric effect occurs when:

  An X-ray photon is absorbed by an inner shell electron causing it to be ejected from the atom as a photoelectron

• As a result of the photoelectric effect, the X-ray photon is completely absorbed and all its energy is imparted to the photoelectron

• Since energy is always conserved, the energy of an incident X-ray photon is equal to:

  The work function + the maximum kinetic energy of the photoelectron

• The energy within a photon is equal to hf

  • This energy is transferred to the electron to release it from a material (the work function) and the remaining amount is given as kinetic energy to the emitted photoelectron

• This equation is known as the photoelectric equation:

$E=hf=\varphi +\frac{1}{2}m{v^2}_{max}$

• Where:

  • h = Planck's constant (J s)

  • f = the frequency of the incident radiation (Hz)

  • Φ = the work function of the material (J)

  • ½ mv²_max = E_k(max) = the maximum kinetic energy of the photoelectrons (J)

Compton Scattering

• The Compton Effect is when:

  An X-ray photon is deflected by an interaction with an orbital electron causing the wavelength of the photon to increase and the ejection of the electron from the atom at a high speed

• This process is similar to simple scattering, except the X-ray photon imparts some of its energy to the orbital electron

• Because of this exchange of energy:

  • The X-ray is deflected from its initial path

  • The X-ray’s wavelength increases, as its energy decreases

  • The electron involved is ejected from the atom involved in the interaction

• The electron and X-ray are deflected in different directions due to conservation of momentum

Pair Production

• Pair production occurs when:

  A high energy X-ray photon passes close to the nucleus of an atom causing the production of an electron-positron pair

• This arises as a consequence of Einstein's mass-energy equivalence principle:

E = mc²

• Where:

  • E = the energy of the X-ray photon (J)

  • m = the mass of the electron and position = 2m_e (kg)

  • c = the speed of light (m s⁻¹)

• Pair production can, therefore, only occur with high energy X-rays

  • This is because the energy of the X-ray photon must be above a certain value to provide the total rest mass energy of the electron-positron pair

• The minimum energy, E_min, for a photon to undergo pair production is the total rest mass energy of the particles produced:

E_min = hf_min = 2m_ec²

• As a result of pair production, the X-ray photon is completely absorbed and all its energy is imparted to the electron-positron pair

When a photon with enough energy interacts with a nucleus it can produce an electron-positron pair