Chapter 2 Notes: Basic Physics for Radiation Protection – An Overview

Introduction

• Chapter focus: Basic physics underpinning radiation protection, atom structure, x-ray characteristics, and how ionizing radiation interacts with matter. Emphasizes understanding interaction processes to minimize patient risk, optimize image receptors, and relate atomic events to observable biological effects.
• Two major effects of radiation on tissue:
  • Stochastic (non-deterministic) effects
  • Deterministic (non-stochastic) effects
• Radiation interactions begin at the atomic level and propagate to cellular and tissue scales, explaining risks at exposure levels and how to keep them minimal.
• Historical context: x-ray imaging has been a vital medical facility for over a century; understanding atomic interactions justifies image quality optimization and dose control.
• Key aim: Build from atomic physics to explain how x-rays interact with matter and how these interactions influence dose, image quality, and safety.

Atomic Structure

The Element

• An element is the simplest form of matter consisting of a specific type of atom; cannot be broken down by chemical means but can participate in chemical reactions.
• There are 118 known elements; 98 occur naturally.
• Elements are listed on the periodic table in order of atomic number (Z).
• Understanding the element is foundational for understanding x-ray interactions with matter.

The Atom

• An atom consists of a nucleus surrounded by orbiting electrons at discrete distances from the nucleus (shells).
• The term atom originates from the Greek atomos (indivisible), but modern physics shows atoms contain subatomic particles (electrons, protons, neutrons) and, at deeper levels, quarks.
• The outer edge of electron orbitals is not sharply defined; atomic size generally ranges around 0.3–3 Å (angstroms).

The Nucleus of an Atom

• The nucleus is at the center and contains protons and neutrons (nucleons).
• Nucleons are held together by a strong nuclear force that overcomes electrostatic repulsion between protons.
• Proton: positively charged, charge = +e (e ≈ 1.6 × 10^-19 C).
• Neutron: electrically neutral.
• Hydrogen is the exception, lacking a neutron.
• Subatomic constituents include quarks: up (+2/3 e) and down (-1/3 e).
• The nucleus determines the element’s identity via its proton number Z; neutron number determines the isotope.

Atomic Number

• Atomic number Z equals the number of protons in the nucleus; fixes the element type (e.g., Z=1 for hydrogen, Z=8 for oxygen).
• All atoms of a given element have the same Z.

Effective Atomic Number

• In macroscopic materials, many elements contribute to attenuation; a structure’s effective atomic number Z_eff summarizes the overall interaction tendency of that structure for x-rays at a given photon energy.
• Z_eff depends on both material composition and photon energy.
• Examples (Z_eff for common materials, energy-dependent):
  • Air ≈ 7.78
  • Bone ≈ 12.3–14.0
  • Fat ≈ 6.46
  • Muscle ≈ 7.64
  • Water ≈ 7.5
  • PMMA ≈ 6.56
  • LiF ≈ 8.31
  • Polystyrene ≈ 5.74
• Note: These values depend on photon energy; higher energy photons “see” a different effective Z.

Isotopes

• Isotopes differ in neutron number while having the same proton number (same element).
• Stability depends on the neutron-to-proton ratio; unstable isotopes undergo radioactive decay to reach stability.
• Decay modes include alpha, beta (β- and β+), and gamma emissions; radioactive decay underpins nuclear medicine but is beyond the scope of this text.

Atomic Mass

• Atomic mass = total number of protons and neutrons in the nucleus (electrons contribute negligibly to mass).
• The nucleus accounts for nearly all of an atom’s mass despite occupying a tiny fraction of the atom’s volume.

Electrons

• Electrons carry negative charge; mass is tiny compared with protons/neutrons (approximately 0.05% of a proton’s mass per electron).
• In a neutral atom, the number of electrons equals the number of protons; deviations create positively or negatively charged ions.

Electron Orbits (Shells) and Binding Energy

• Electrons are bound to the nucleus by binding energy; electrons reside in shells (K, L, M, …) with decreasing binding energy as distance from the nucleus increases.
• The binding energy is shell-specific and element-specific; outer (valence) electrons have the smallest binding energy and are easiest to remove.
• K-shell is the innermost shell; L, M, … follow in order.
• K-shell binding energies vary by element (e.g., tungsten has a relatively high K-shell binding energy).
• K-shell energies are tabulated for elements; these values determine the likelihood and energy of certain x-ray emissions following inner-shell ionization.

Electron Binding Energies (K-shell examples)

• K-shell binding energy values differ by element; heavier elements have higher binding energies.
• For tungsten, a representative example: K-shell binding energy is high, and K→L transitions produce characteristic x-rays with energies determined by the energy differences of shells (e.g., L→K ~58 keV, M→K ~67 keV).
• Binding energies for light elements are much lower (e.g., hydrogen ~0.01 eV for K-shell); however, the general principle is that binding energy increases with atomic number.

Types of Radiation

Particulate Radiations

• Particulate radiations are massive subatomic particles; many carry charge.
• The main types: alpha particles, beta particles, neutrons.
• Other particulate radiations include protons, neutrinos, mesons, muons.
• Key shared features: mass and subatomic nature; interaction with matter scales with mass and charge; penetration varies with particle type.
• Relevance to radiography: particulate radiation often has limited penetrating ability; x-rays (electromagnetic) are particularly well-suited for transmission imaging; particulate radiations have roles in some nuclear medicine techniques (e.g., positrons) but are generally more limited for transmission radiography.

Alpha Particles

• Composed of two protons and two neutrons (helium-4 nucleus).
• Very high positive charge (+2) and relatively large mass.
• Velocity can be up to about 1/20th the speed of light.
• Very high LET and poor penetrating ability; sheet of paper can absorb them; effectively irrelevant for external medical imaging.

Beta Particles

• Electrons (β−) or positrons (β+).
• Arise from beta decay: neutron-to-proton transitions producing electron and antineutrino (β−) or proton-to-neutron producing positron and neutrino (β+).
• Examples: Mo-99 decay emits a beta particle and a 740 keV gamma; Fluorine-18 is a common positron emitter used in PET.
• Mass is small; charge ±1; LET is lower than alpha but higher than many gamma/x-ray photons, so penetration is greater than alpha but still moderate.
• PET radiotracers rely on positron emission (β+ decay) and subsequent annihilation photons for imaging.

Neutrons

• Electrically neutral, similar mass to a proton.
• No charge; high LET and potentially high penetration depending on energy; can cause significant tissue interactions depending on energy.
• Produced as a byproduct of fission or fusion; relevant in some nuclear medicine contexts and radiation shielding considerations.

Other Particulate Radiations

• Protons, neutrinos, mesons, and muons exist and have various properties and uses in research and medicine.

Electromagnetic Radiation

• X-rays and gamma rays are forms of electromagnetic radiation: massless, uncharged packets of energy (photons).
• They do not have rest mass or charge; energy is carried by photons.
• Shared properties of the electromagnetic spectrum:
  • They travel through vacuum in straight lines at the speed of light, c ≈ 3.0 × 10^8 m/s.
  • They are oscillations of electric and magnetic fields perpendicular to the direction of travel.
  • They can be described by wavelength λ or frequency f, related by E = hf and c = fλ.
  • They are unaffected by external magnetic or electric fields.
  • They exhibit exponential attenuation in homogeneous materials and exhibit wave-particle duality (wave-like and photon-like behavior).
• Wave-particle duality and the photon energy relationship:
  • Photon energy: $E = hf$ where h = 6.626 × 10^-34 J·s.
  • Frequency and wavelength: $c = fλ$, so higher frequency implies higher energy.
• The electromagnetic spectrum spans from radio waves to gamma rays; x-rays occupy the high-frequency, short-wavelength region just before gamma rays.

X-Rays and Gamma Rays: Properties and Distinctions

• X-rays and gamma rays share massless, uncharged nature but differ in production and typical energies.
• X-rays: produced in x-ray tubes (bremsstrahlung and characteristic radiation); energies in diagnostic imaging typically range from 0 to ~150 keV.
• Gamma rays: produced by radioactive decay and nuclear transitions; energies are characteristic to the parent nuclide (line spectra) and can range from tens of keV up to several MeV (typical clinical energies include 140 keV for Tc-99m and 511 keV annihilation photons in PET).
• Production modes:
  • Characteristic x-rays: result from electronic transitions following inner-shell ionization (e.g., K-shell vacancies filled by outer-shell electrons).
  • Bremsstrahlung (braking) radiation: produced when high-speed electrons are deflected by nuclei, yielding a continuous spectrum of x-ray energies.
  • Gamma production: isomeric transitions in unstable nuclei produce gamma photons with energies specific to the nuclide; example: Mo-99 → Tc-99m → Tc-99 decay chain.
• Internal conversion (competing with gamma emission): an excited nucleus transfers energy to an orbital electron, ejecting an internal conversion electron; described by the internal conversion coefficient (ratio of internal conversion rate to gamma emission).
• Interaction implications for medical imaging: energy distribution, filtration, and dose considerations rely on the mix of characteristic lines and bremsstrahlung continuum; x-ray production efficiency is low (roughly ~1% of electron energy becomes x-rays) and depends on kVp and anode material; most energy becomes heat.

Electromagnetic Spectrum: Key Features

• Wavelengths and frequencies span many orders of magnitude; gamma rays have extremely short wavelengths and very high frequencies compared to x-rays.
• Photons can be treated as particles (photons) or waves (classical field) depending on the interaction context; the duality is described by E = hf and wave equations.

X-Ray Production and Interactions

Production of X-Rays in an Anode Target

• Two primary types of x-ray production in an x-ray tube target (e.g., tungsten):
  • Characteristic radiation: occurs when an incident electron ionizes an inner-shell electron (e.g., K-shell). Outer-shell electrons fill vacancies, releasing characteristic x-rays with energies characteristic of the shell transitions (element-dependent).
  • Bremsstrahlung radiation: occurs when incident electrons are decelerated by the nuclear electric field, producing a continuous spectrum of x-rays with energies up to the maximum electron energy set by the tube potential (kVp).
• For tungsten, representative energy differences:
  • L→K transition energy ≈ 58 keV (example: K-shell binding ~69.5 keV; L-shell binding ~11.5 keV; difference ≈ 58 keV).
  • M→K transition energy ≈ ~67 keV (M-shell binding ~2.5 keV; difference with K-shell ~69.5 keV).
• Practical notes:
  • Not all shell transitions produce x-rays that escape the target; if the incident energy (kVp) is insufficient to ionize a given shell, the corresponding characteristic line will not appear.
  • The resultant spectrum contains both characteristic lines and a broad bremsstrahlung continuum.
  • Filtration: many low-energy x-rays are absorbed before reaching the patient; inherent filtration (glass, oil) removes ~50% of generated x-rays; added filtration (e.g., aluminum) removes a further ~80% of the remainder.
  • Efficiency: only about 1% of the electron energy is converted to x-rays; 0.5% may reach the patient after inherent filtration; ~0.1% passes added filtration; efficiency rises with higher Z anode material and higher kVp.

Gamma Radiation Production and Energies

• Gamma rays are produced from unstable isotopes via isomeric transitions; energies are unique to the mother nuclide (line spectra).
• Useful energies for medical imaging typically range from about 100 keV to 511 keV; 511 keV photons arise from positron annihilation.
• Example:
  • Molybdenum-99 decays to technetium-99m, emitting a 740 keV gamma (via beta decay) and a 99mTc isomeric transition to 99Tc with a 140 keV gamma emission.
  • 99mTc has a half-life of ~6 hours; 99Tc ground state has a half-life of ~2.11 × 10^5 years.
• A common clinical pathway: Tc-99m is delivered as a radiopharmaceutical; after localization and imaging, the 140 keV gamma is detected; the short half-life minimizes dose to patient.
• Internal conversion can compete with gamma emission, reducing gamma yield by transferring energy to an orbital electron and emitting an Auger electron rather than a gamma photon; the internal conversion coefficient quantifies this effect.
• PET example: Ga-68 radiotracers (e.g., in combination with sestamibi for myocardial perfusion) emit positrons that yield 511 keV photons upon annihilation, enabling functional imaging.

Ionizing Radiation

• Ionization occurs when x-ray, gamma, or certain particulate radiations eject electrons from atoms, creating ion pairs (a free electron and a positively charged residual atom).
• Two ionization pathways:
  • Direct ionization: the photon interacts directly with an electron, ejecting it.
  • Indirect ionization: the ejected electron goes on to cause further ionizations.
• Excitation: energy transfer raises an electron to a higher energy level without ejection; subsequent return to ground state can emit visible/ultraviolet light (luminescence such as fluorescence/phosphorescence).
• Ionizing radiation includes x-rays, gamma rays, alpha and beta particles; non-ionizing radiation (e.g., visible light, radio waves) does not ionize.
• Biological implications: ionization can initiate biological changes and is the basis for risks in radiation exposure.

X-Ray and Gamma Radiation Interactions

• Four main interaction processes (in order of typical relevance for diagnostic energies):
  • Elastic (coherent, Rayleigh) scattering
  • Photoelectric absorption
  • Compton scattering
  • Pair production
• A fifth related concept: internal conversion (competition with gamma emission for de-excitation of nuclei).
• The dominant interaction depends on photon energy relative to electron binding energies (and on atomic number Z of the interacting medium).
• Key points for each interaction:
  • Elastic (coherent/Rayleigh) scattering
  • No energy loss; photon energy is conserved; direction changes.
  • Occurs when photon energy is much less than electron binding energies.
  • Probability ∝ Z^2 and inversely with energy; more likely at low energies and with high-Z materials.
  • Examples include Rayleigh and Thomson scattering (single-electron elastic scattering).
  • Photoelectric absorption
  • Photon energy must be near or slightly above the binding energy of the interacted electron (usually inner shells, notably K-shell).
  • All photon energy is absorbed by ejecting the electron (photoelectron) with energy Ephoton - Ebinding.
  • The vacancy created leads to outer-shell electron transitions that emit characteristic x-rays or Auger electrons.
  • Probability factors:
    • Increases with higher Z: ∝ Z^3
    • Decreases with higher photon energy: ∝ 1/E^3 (approximately; at very high energies it trends toward ∝ 1/E^2 and finally ∝ 1/E)
  • For biological tissues (low Z), characteristic x-rays tend not to travel far; density and composition influence dosimetry and contrast.
  • Importance for image contrast: higher-Z tissues (e.g., bone) show greater photoelectric absorption, enhancing contrast at lower energies.
  • Practical implication: to enhance image contrast, use lower kVp to increase photoelectric absorption, but this increases dose; balance is required.
  • Compton scattering
  • Occurs when photon energy is well above the binding energy of an outer/valence electron.
  • Photon loses energy and changes direction (inelastic scattering); a Compton electron is ejected.
  • Predominantly involves outer-shell electrons; probability ∝ electron density; largely independent of atomic number Z.
  • Scattered photons may reach the image receptor at locations not corresponding to the actual object, reducing contrast and increasing dose elsewhere.
  • The energy and angle of the scattered photon satisfy the Compton relation; energy loss increases with larger scattering angles.
  • Compton scattering cannot be eliminated in diagnostic imaging; radiographers optimize kVp and geometry to manage its impact.
  • Energy-angle relationship (classic formula):
    • Wavelength shift: $\Delta\lambda = \frac{h}{m_e c}\left(1 - \cos\theta\right)$
    • With energy relationships, the scattered photon energy is: $E' = \frac{E}{1 + \frac{E}{m_e c^2}(1 - \cos\theta)}$
  • Practical takeaway: Compton scattering depends on electron density and scattering angle; high-energy photons scatter more readily at larger angles, producing more dose to surrounding tissues.
  • Pair production
  • Requires photon energy ≥ 1.022 MeV (2 m_e c^2).
  • Photon interacts with the nucleus, producing an electron-positron pair; excess energy becomes kinetic energy of the pair: total energy = 2 m_e c^2 + (kinetic energies).
  • If positron slows and annihilates with an electron, two 511 keV photons are produced traveling in opposite directions, enabling PET imaging.
  • In diagnostic x-ray imaging, pair production is not a dominant process (requires energies typical of gamma rays from nuclear processes).
• Internal conversion (a competing de-excitation process):
  • An excited nucleus may transfer energy to an orbital electron, ejecting it (internal conversion electron) rather than emitting a gamma photon.
  • Internal conversion coefficient = (internal conversion rate) / (gamma emission rate); higher coefficients reduce gamma yield.
• Attenuation and energy distribution in diagnostic beams:
  • Diagnostic beams include both characteristic and bremsstrahlung components; the spectrum spans low energies (filtered out to limit dose) up to the tube maximum energy (kVp).
  • Practical considerations include beam hardening, filtration, and the need to minimize patient dose while preserving image quality.

Practical Applications and Implications

• Image contrast vs dose: photoelectric absorption enhances contrast (bone vs soft tissue) due to Z^3 dependence and energy dependence; lower kVp improves contrast but increases dose; higher kVp reduces contrast but improves penetration and reduces dose in some contexts.
• Scatter management: grids and collimation reduce scatter reaching the detector, improving image quality and reducing patient dose by limiting scattered photons from reaching the receptor.
• Radiation protection context: understanding interaction mechanisms underpins ALARA (As Low As Reasonably Achievable) principles, filtration design, and shielding strategies.

Gamma Ray Production: An Example Pathway in Nuclear Medicine

• Molybdenum-99 decays to Technetium-99m (isomeric state): emission of a beta particle and a gamma photon of 740 keV.
• Tc-99m decays to Tc-99 by gamma emission at 140 keV; Tc-99 has a long half-life (~2.11 × 10^5 years).
• The 140 keV gamma from Tc-99m is widely used in nuclear medicine for imaging due to its relatively short half-life and favorable tissue penetration.
• Annihilation radiation (511 keV) arises from positron annihilation in PET imaging, enabling highly sensitive functional imaging.
• Internal conversion can reduce gamma yield by ~9% in some contexts, altering the gamma-to-conversion balance.
• Typical PET radiotracers utilize positron emitters (e.g., Ga-68) that ultimately yield 511 keV photons through annihilation.

Descriptive Terms or Concepts Associated With Radiation

Linear Energy Transfer (LET)

• LET measures the energy deposited per unit length along the track of a radiation particle or beam:
  • High-LET examples: alpha particles deposit energy densely over micrometers (e.g., within a sheet of paper).
  • Low-LET examples: x-rays and gamma rays deposit energy sparsely over larger volumes.
• Impact on biology: high-LET radiation tends to cause more complex, denser ionizations and is typically more damaging per unit dose than low-LET radiation.

Linear Attenuation Coefficient (μ)

• Defines the fractional reduction in x-ray intensity per unit thickness of an attenuator for a given energy.
• It accounts for both absorption and scattering in the material.
• Often written as μ, with units of inverse length (e.g., mm^-1, m^-1).
• The total linear attenuation coefficient is the sum of the linear absorption and linear scatter coefficients.
• Related concept: Half-Value Layer (HVL)
  • HVL is the thickness of material required to reduce the x-ray beam intensity by 50%:
  • HVL = the thickness t such that I(t) = I0/2.

Mass Attenuation Coefficient (μ/ρ)

• Normalizes attenuation to the material's density: (μ/ρ) is the fractional attenuation per unit mass.
• Definition:
  • Mass attenuation coefficient: $\left(\frac{\mu}{\rho}\right)$
  • Relationship to linear coefficient: $\mu = \left(\frac{\mu}{\rho}\right) \cdot \rho$
• Advantage: independent of the specific attenuating material; useful for comparing attenuation across different materials.

Inverse Square Law

• Applies to electromagnetic radiation (x-rays, gamma rays) emitted from a point source: the intensity I is inversely proportional to the square of the distance d from the source:
  • $I \propto \frac{1}{d^2}$
• Practical interpretation: doubling distance from the source reduces intensity by a factor of 4 (assuming negligible attenuation and a point-like source).
• Practical difficulties in x-ray practice:
  • Real x-ray sources are not true point sources; focal spots have finite size.
  • Attenuation by materials (the anode heel effect) causes directional differences in intensity.
  • In clinical setups, geometry and filtration modify the simple 1/d^2 relationship, but the inverse square law remains a foundational principle for dose planning and shielding.

Summary of Key Concepts

• The atom consists of a nucleus with protons and neutrons and orbiting electrons; the nucleus accounts for most of the mass, while electrons determine chemical and magnetic properties.
• Elements are defined by their proton number Z; isotopes vary in neutron number; many nuclei are stable, while some are radioactive.
• The effective atomic number Zeff summarizes a material’s x-ray interaction behavior for a given photon energy; Zeff depends on energy.
• There are five main types of radiation; the first three (alpha, beta, neutrons) are particulate and mass-bearing; gamma rays and x-rays are electromagnetic and massless.
• X-ray production involves two processes: characteristic radiation (line spectra specific to the target element) and bremsstrahlung radiation (continuous spectrum due to deceleration near the nucleus).
• Gamma rays originate from nuclear transitions; isomeric transitions yield gamma energies specific to the nuclide; Tc-99m is a widely used gamma emitter in nuclear medicine.
• Ionizing radiation creates ion pairs, with direct or indirect ionization paths, and can also cause excitation without ionization.
• Four main interactions govern x-ray and gamma-ray attenuation in matter: elastic scattering, photoelectric absorption, Compton scattering, and pair production (the latter relevant at energies above ~1.022 MeV).
• The probability of photoelectric absorption increases with Z^3 and decreases with energy roughly as 1/E^3; Compton scattering probability scales with electron density and is relatively independent of Z; elastic scattering depends on Z^2 and decreases with energy.
• Pair production is a nuclear-interaction process that requires photons with energy above 1.022 MeV and produces an electron-positron pair, followed by annihilation photons of 511 keV.
• Internal conversion offers an alternative de-excitation pathway that reduces gamma emission by transferring energy to an atomic electron.
• LET, μ, μ/ρ, HVL, and the inverse square law are essential tools for understanding dosimetry, shielding, and image quality.
• Practical imaging considerations require balancing contrast (favoring lower energies for photoelectric absorption) with dose and penetration (which may favor higher energies or filtration). Scatter management via grids and collimation improves image quality and reduces dose to non-target tissues.

Discussion Questions

• What are the constituents of the atom, and how do protons, neutrons, and electrons contribute to atomic structure and properties relevant to x-ray interactions?
• Why are some electromagnetic radiations more suitable for medical imaging than particulate radiations? Consider penetrating power, image contrast, and dose.
• What are the two key interaction processes that dominate x-ray interactions with human tissues, and how do they influence image quality and dose?
• Define and distinguish between LET, μ, μ/ρ, and the inverse square law; provide practical examples of how each concept informs radiographic practice.

References

• Dowsett DJ, Kenny PA, Johnston RE. The Physics of Diagnostic Imaging, 2nd edition. London: Hodder Arnold; 2006.