Chapter 13

• Introduction to Modern Physics
• Topics covered


  • Electromagnetic radiation & electromagnetic spectrum
  • Elementary quantum theory
  • Generation of x- and γ- rays
  • Interactions of x- and γ- rays with matter: classical Scattering, photo-absorption/photoelectric effect, Compton scattering, pair- production & Photodisintegration
  • Radioactive decay law & Activity
  • Attenuation of radiation – absorption coefficients; attenuation of homogeneous and heterogeneous beams
  • Radiographic image formation and characteristics
• Mechanical Wave


  A periodic disturbance in a medium that carries energy from one point to another
• Types of mechanical waves

  • Longitudinal
  • Transverse
• Wavelength (λ)


  The horizontal distance along a wave between similar particles of the wave
• Displacement


  The distance of a particle of the wave from the equilibrium position at any particular time
• Amplitude (a)


  The maximum displacement of a particle of the wave from its equilibrium position
• Period (T)


  The time for one complete oscillation of the wave
• Frequency (γ)


  The number of waves produced per second
• Velocity (v)


  The velocity of a particle of a wave in the direction the wave is travelling
• James Clerk Maxwell


  • Scottish mathematician and physicist
  • Defined the Non-mechanical waves in a vacuum of space
  • Unified existing laws of electricity and magnetism
  • Oscillating electric field produces a magnetic field (and vice versa) – propagates an EM wave
  • The Wave model can be described by 4 differential equations
• Electromagnetic (EM) wave


  • Electric field (E) perpendicular to magnetic field (M)
  • Travels at velocity, c (3x10^8 ms^-1, in a vacuum)
• At the atomic scale, electromagnetism governs the interactions between atoms and molecules
• At the macroscopic scale, electromagnetism manifests itself in the familiar phenomena that give the force its name
• Maxwell's Equations


  • Four equations relating electric (E) and magnetic fields (B) – vector fields
  • ε0 is electric permittivity of free space (or vacuum permittivity - a constant)
  • μ0 is magnetic permeability of free space (or magnetic constant – a constant)
• EM Spectrum


  The velocity (c) of propagation of EM radiation through space is constant but the wavelengths (λ) and frequencies (γ) varies
• EM spectrum results from these waves propagating at different wavelengths and frequencies
• Line spectra are the result of interaction between atoms (can also be atomic nuclei or molecule) and a single photon
• When a photon has sufficient energy to change the energy state of the atom (where an electron changing orbitals), the photon is absorbed
• The previously, absorbed energy will be re-emitted as light
• The sum of the energies of the photons emitted will be equal to the energy of the one absorbed
• Spectral lines are highly atom-specific, and can be used to identify the chemical composition of any medium capable of letting light pass through it (typically gas is used)
• The line spectrum of an element results from the emission of photons with specific energies from the atoms of that element
• Quanta


  A discrete quantity of energy proportional in magnitude to a particular frequency (γ) of EM radiation and corresponding to a single photon or to a transition of an atom between two internal energy states
• Photon energy


  E = hγ, where h is Planck's constant and γ is the frequency of the wave
• If only certain energies are allowed, the allowed energies correspond to the differences between energy levels
• 1. ray Production


  • X-rays are produced when rapidly moving electrons that have been accelerated through a potential different of the order 10^3 - 10^6 volts strike a metal target
  • Electron are "boiled off" from the heated cathode by the principle of thermionic emission and these electrons accelerated towards the anode (the target) by a large potential different Vac
  • The most energetic photon (with λ and γ) is produce when all the electron's kinetic energy goes to produce on photon (bremsstrahlung limits)
• Characteristic X-ray


  The second process gives peaks in the x-ray spectrum at characteristic frequencies and wavelengths that do depend on the target material
• 1. ray tube


  • Requires an electron source, electron acceleration potential, and target for X-ray production
• The intensity of the electron beam determines the intensity of the X-ray radiation
• The electron energy determines the shape of the bremsstrahlung's x-ray spectrum
• Low energy X-rays are absorbed in the tube material to produce the characteristic x-ray spectrum
• The X-ray energy determines also the emission of characteristic lines from the target material
• Gamma radiation (γ-rays)


  • EM waves of an extremely high frequency and are therefore high energy photons
  • Produced by the decay of atomic nuclei as transition from a high energy state to a lower state known as gamma decay
• Five forms of x-ray Interactions

  • Classical or Coherent Scattering
  • Compton Effect
  • Photoelectric Effect
  • Pair production
  • Photodisintegration
• Coherent Scattering


  • Also known as classical, elastic, unmodified or Rayleigh scattering
  • The incident photon interacts with and excites the total atom
  • Occurs at low energy photons of less than 30keV
  • The wavelength of the incident and scattered photon/wave remain unchanged after the interaction
  • No net energy has been absorbed by the atom
  • Electrons are not ejected and thus ionization does not occur
• In soft tissue, Rayleigh scattering accounts for less than 5% of x-ray interactions above 70 keV and at 12% of interactions at approximately 30 keV
• Compton Scattering


  • Compton scattering (inelastic or non-classical) is the predominant interaction of x-ray photons in the diagnostic energy range with soft tissue
  • This interaction is most likely to occur between photons and outer ("valence") shell electrons, which are loosely bounded in the outer shell electron cloud
  • The ejected electron is called a Compton or recoil electron and scattered photon is called a Compton photon
  • The energy of the incident photon (Ei) is equal to the sum of the energy of the scattered photon (Esc) and the kinetic energy of the ejected electron (Ee-)
  • The freed electron possesses excess kinetic energy (Ek) and is capable of ionizing atoms
• In radiography, photons scattered in the forward direction can reach the film and add to background fog and reduce image contrast
• In diagnostic radiology, the probability of occurrence of Compton scattering relative to that of the photoelectric absorption is not influence increase as the energy of the x-ray photon increases