X-ray Attenuation Mechanisms (OCR A Level Physics)

• 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:

• 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