Radtech Integrals Physics of Diagnostic Radiation Flashcards

Fundamental Models and Concepts of the Atom

• The Atom as a Building Block: Atoms are the essential building blocks for understanding interactions between ionizing radiation and matter in radiography.
• Etymology: The term originates from the Greek word 'atomos', translating to indivisible.
• Definition: It is the smallest part of an element that retains all chemical properties of that element; it is the basic component and the smallest unit of matter.
• Normal State: Atoms are neutrally charged because the absolute number of protons equals the number of electrons.

Historical Atomic Models

• John Dalton: Proposed a model where elements were classified by integral values of atomic mass. He suggested elements consist of identical atoms reacting identically in chemical reactions. His "hook and eye model" explained chemical combinations.
• Dmitri Mendeleev: Demonstrated that arranging elements by increasing atomic mass causes a repetition of similar chemical properties. He developed the first periodic table using increasing atomic numbers.
• John Joseph Thomson: Discovered the electron and described the atom as a "plum pudding." In this model, electrons (plums) were negative charges embedded in a shapeless mass of uniform positive electrification (pudding).
• Robert Millikan: Calculated the charge of an electron to be precisely $1.60 \times 10^{-19}$ coulombs.
• Ernest Rutherford: Introduced the nuclear model. He described a small, dense, positively charged center called the nucleus, surrounded by a negative cloud of electrons.
• Niels Bohr: In 1913, he improved the Rutherford model by describing a miniature solar system where electrons revolve around the nucleus in prescribed orbits or specific energy levels.

Fundamental Particles and Atomic Structure

Characteristics of Fundamental Particles

• Primary Constituents: The three fundamental particles are the electron, proton, and neutron.
• The Electron:
  • Carries one unit of negative electric charge.
  • Mass is approximately $9.1 \times 10^{-31}\,kg$.
  • Mass in atomic mass units (amu): $0.000549\,amu$.
  • Relative mass number: $0$.
  • Location: Electron shells/orbits.
• The Proton:
  • Located in the nucleus.
  • Carries one unit of positive electric charge.
  • Mass is approximately $1.673 \times 10^{-27}\,kg$.
  • Mass in amu: $1.00728\,amu$.
  • Relative mass number: $1$.
  • Relative mass is approximately $1836$ times that of an electron.
  • Discovered by James Chadwick.
• The Neutron:
  • Located in the nucleus.
  • Electrically neutral (no charge).
  • Mass is approximately $1.675 \times 10^{-27}\,kg$ (slightly heavier than a proton).
  • Mass in amu: $1.00867\,amu$.
  • Relative mass number: $1$.
  • Relative mass is approximately $1838$ times that of an electron.
  • Discovered by Eugene Goldstein.

Atomic Mass Units (amu)

• Definition: One atomic mass unit is equal to one-half the mass of a carbon-$12$ atom.

Main Parts of the Atom

• Nucleus: The central core containing nearly all the atom's mass. It consists of nucleons (protons and neutrons).
• Orbits or Shells: Regions composed of electrons representing different energy levels.
  • Coding: Shells are identified by letters $K, L, M, N$, etc., starting from the shell closest to the nucleus moving outward.
  • Proximity and Energy: The closer an electron is to the nucleus (e.g., $K$-shell), the higher its binding energy ($E_b$).

Forces and Electron Dynamics

Electron Binding Energy ($E_b$)

• Strength of Attachment: This is the energy possessed by an electron in its orbit and the energy required to remove it.
• Relationship: Binding energy is inversely proportional to distance from the nucleus. $K$-shell electrons have higher binding energy than $L$-shell electrons.

Forces Acting on Electrons

• Centrifugal Force: An outward force pulling electrons away from the center.
• Centripetal/Electrostatic Force: The attractive force between negative electrons and the positive nucleus that keeps electrons in orbit.

Forces Acting on the Nucleus

• Repulsive Force: Occurs between like-charged protons.
• Nuclear Binding Force: Holds the nucleus together due to the presence of neutrons.

Atomic Definitions

• Nuclide: Refers to any atomic species.
• Valence Electrons: Electrons located on the outermost shell (valence shell).
• Atomic Mass ($A$): Represents the total number of nucleons (protons + neutrons).
• Atomic Number ($Z$): Represents the number of protons (or electrons in a neutral atom).
• Element Notation: Represented as ${^A_Z}X$ (e.g., ${^4_2}He$).
• Neutron Calculation: Number of neutrons is calculated as $n = A - Z$.

Electron Shell Distribution and Nuclear Arrangements

Pauli Exclusion Formula

• Formula: $2(n^2)$
• Usage: Determines the maximum number of electrons that can occupy a specific shell, where $n$ is the principal quantum number (shell order).
• Shell Capacities:
  • $K$ ($n=1$): $2(1^2) = 2$
  • $L$ ($n=2$): $2(2^2) = 8$
  • $M$ ($n=3$): $2(3^2) = 18$
  • $N$ ($n=4$): $2(4^2) = 32$
  • $O$ ($n=5$): $2(5^2) = 50$

Nuclear Arrangements

• Isotopes: Atoms with the same atomic number ($Z$) but different mass numbers ($A$). Example: ${^{130}_{56}Ba}, {^{132}_{56}Ba}, {^{135}_{56}Ba}$.
• Isobars: Atoms with the same atomic mass ($A$) but different atomic numbers. Example: ${^{131}_{53}I}, {^{131}_{54}Xe}, {^{131}_{55}Cs}$.
• Isotones: Atoms with the same number of neutrons ($A - Z$). Example: ${^{129}_{53}I}, {^{130}_{54}Xe}, {^{131}_{55}Cs}$.
• Isomers: Atoms with the same atomic number and mass but existing at different energy states. Example: ${^{99}_{43}Tc}, {^{99m}_{43}Tc}$.

Radioactivity and Radioactive Decay

Radioactive Disintegration

• Definition: The process where unstable nuclei spontaneously emit particles and energy to achieve stability. These atoms are called radionuclides.
• Discovery: Discovered in 1896 by Antoine Henri Becquerel.
• Units:
  • Becquerel (Bq): The SI unit. $1\,Bq = 1\,\text{disintegration/second (dps)}$.
  • Curie (Ci): The old unit, named for Marie Curie. $1\,Ci = 3.7 \times 10^{10}\,Bq$.

Physical Characteristics

• Decay Constant (\lambda): The fraction or percentage of original atoms decaying per unit time.
• Half-Life ($T_{1/2}$): The time required for the radioactive material to decay to half of its original value. Radioactivity never technically reaches zero.

Types of Half-Life

• Biological Half-life: Time required for a biological system to eliminate half a substance through biological processes.
• Physical Half-life: Average time required for the decay of half the atoms in a radioactive substance.
• Effective Half-life: The combined effect of radioactive decay and biological excretion. Formula: $\text{Effective Half-life} = \frac{\text{Physical Half-life} \times \text{Biological Half-life}}{\text{Physical Half-life} + \text{Biological Half-life}}$.

Modes of Decay

• Alpha Decay (\alpha): Occurs in heavy nuclides. Emits an alpha particle resembling a helium nucleus (${^4_2}He$). Daughter element calculation: subtract $4$ from atomic mass and $2$ from atomic number.
• Beta Decay (\beta):
  • Negatron Emission: Occurs when neutron-to-proton ratio is too high. A neutron converts to a proton, and a negatively charged electron is emitted. Add $1$ to atomic number.
  • Positron Emission: Occurs with proton excess. A proton converts to a neutron, and a positively charged electron is emitted. Subtract $1$ from atomic number.
• Isomeric Transition: Emission of gamma rays from excited nuclei with no change in mass or atomic number.
• Internal Conversion (K-conversion): A gamma ray from the nucleus transfers energy to an orbital electron, causing its ejection (conversion electron).
• Electron Capture (K-capture): The nucleus captures an orbital electron. Characteristic X-rays are emitted as outer electrons fill the vacancy.

Electromagnetic Radiation and Photons

Photon Characteristics

• Definition: Photons are energy disturbances traveling at the speed of light ($c = 3.0 \times 10^8\,m/s$). They have wavelength ($\lambda$), frequency ($f$), velocity, and amplitude.
• Amplitude: One-half the range from crest to valley.
• Wavelength: Distance between consecutive crests or valleys.
• Frequency: Number of cycles per unit time, measured in Hertz ($Hz$).

Governing Equations

• Wave Equation: $c = f\lambda$. Frequency is inversely proportional to wavelength.
• Planck’s Quantum Theory: $E = hf$. Where $h$ is Planck's constant ($6.62 \times 10^{-34}\,J\text{-}s$ or $4.15 \times 10^{-15}\,eV\text{-}s$).
• Einstein’s Theory of Relativity: $E = mc^2$.
• Inverse Square Law: Describes radiation intensity relative to distance. $I_1 (d_2)^2 = I_2 (d_1)^2$. Doubling distance reduces intensity to one-fourth.

Radiation Types

• Non-ionizing: Not capable of ionizing matter (e.g., radiofrequency, infrared, visible light).
• Ionizing: Capable of ionization (e.g., X-rays, Gamma rays, alpha, beta).
  • Particulate: Possesses mass/charge (alpha, beta, neutrons).
  • Electromagnetic: No mass/charge (X-rays, Gamma rays).

Diagnostic Radiation Units and Terms

• Exposure (X): Ionization of air. Measured in $C/kg$ or Roentgen (R). $1\,R = 2.58 \times 10^{-4}\,C/kg$.
• Absorbed Dose (D): Energy transferred to any medium. Units: rad or Gray ($Gy$). $1\,Gy = 1\,J/kg$.
• Equivalent Dose (H): Specifically for radiation workers. $H = D \times Q \times N$. Units: rem or Sievert ($Sv$).
• Linear Energy Transfer (LET): Rate energy is transferred to soft tissue. Measured in $keV/\mu m$.
• Specific Ionization (SI): Number of ion pairs formed per unit path length.
• Range: Maximum distance traveled by radiation in a medium.

X-ray Production and Interactions with Matter

X-ray Production Mechanisms

• Characteristic Interaction: Caused by projectile electrons ionizing inner-shell target electrons. Vacancies are filled by outer electrons, emitting X-rays.
• Bremsstrahlung Interaction: "Braking radiation." Caused by projectile electrons decelerating near the target nucleus.

Interactions with Matter

• Classical (Thomson) Scattering: Low energy ($<10\,keV$). Direction changes, but no energy loss or ionization occurs.
• Compton Effect: Moderate energy. Ionizes outer-shell electrons. Produces scatter radiation and is the major source of worker dose.
• Photoelectric Effect: Total absorption of incident X-ray and ejection of inner-shell electron (photoelectron). Responsible for image contrast and patient dose.
• Pair Production: Energy $> 1.022\,MeV$. Photon interacts with nuclear field to create an electron and a positron ($0.511\,MeV$ each).
• Photodisintegration: Energy $> 10\,MeV$. Photon is absorbed by nucleus, which then emits fragments.

Electricity and Electromagnetism

Laws of Electrostatics

1. Unlike charges attract; like charges repel.
2. Electrostatic force is directly proportional to the product of charges and inversely proportional to the square of the distance.
3. Charge distribution is uniform throughout nonconductors and on the surface of conductors.
4. Charge concentration is greatest on the sharpest curvature of a conductor.

Electrical Circuits and Units

• Units: Potential (Volt, $V$), Current (Ampere, $A$), Resistance (Ohm, $\Omega$).
• Ohm’s Law: $V = IR$.
• Series Circuit: $R_{\text{total}} = R_1 + R_2 + R_3$; Current ($I$) remains constant.
• Parallel Circuit: Voltage ($V$) remains constant; $R_{\text{total}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}}$.
• Power (P): $P = IV = I^2 R$. Measured in Watts ($W$).

Magnetism

• Magnetic Susceptibility: Degree to which a material can be magnetized.
• Classifications:
  • Diamagnets: Weakly repelled (water, plastic).
  • Paramagnets: Weakly attracted (gadolinium).
  • Ferromagnets: Strongly attracted (iron, cobalt, nickel).
• Magnetic Force Units: Tesla ($T$) and Gauss ($G$). $1\,T = 10,000\,G$.

The X-ray System and Tube

Principal Parts

1. Operating Console: Low-voltage section controlling quantity (mAs) and quality (kVp).
2. High-Voltage Generator: Contains high-voltage transformer, filament transformer, and rectifiers immersed in oil for insulation.
3. The X-ray Tube: A vacuum-sealed diode ($30$ to $50\,cm$ long).

X-ray Tube Components

• Cathode: Negative electrode. Contains the filament (thoriated tungsten) and the focusing cup.
  • Thermionic Emission: Boiling off of electrons when current ($3\text{-}6\,A$) is applied.
  • Focusing Cup: Negatively charged metal shroud that directs the electron beam.
• Anode: Positive electrode. Stationary or rotating.
  • Target: Typically an alloy of tungsten ($Z=74$) and rhenium.
  • Heel Effect: Radiation intensity is greater on the cathode side because of absorption in the anode heel.
  • Line-Focus Principle: Angling the target allows a large area for heating while maintaining a small effective focal spot for spatial resolution.

Radiobiology and Radiation Protection

Cellular Radiobiology

• Direct Effect: Initial ionizing event occurs directly on the target molecule (DNA).
• Indirect Effect: Initial event occurs on a different molecule (usually water), producing free radicals that then damage DNA. This is the primary effect in humans.
• Radiolysis of Water: Dissociation of water into molecular products and free radicals ($H^*, OH^*$).
• Radiosensitivity: Defined by the Law of Bergonie and Tribondeau. Stem cells and young tissues are more sensitive; mature cells are resistant.

Radiation Protection Principles

• Cardinal Principles: Minimize Time, Maximize Distance, and use Shielding.
• ALARA: As Low As Reasonably Achievable.
• Dose Limits:
  • Occupational (Whole body): $50\,mSv/yr$.
  • Lens of Eye: $150\,mSv/yr$.
  • Skin/Extremities: $500\,mSv/yr$.
  • Fetus (Declared pregnancy): $0.5\,mSv/month$.
  • Public (Frequent): $1\,mSv/yr$.
• Half-Value Layer (HVL): Thickness needed to reduce radiation intensity by $50\%$.
• Tenth-Value Layer (TVL): Thickness needed to reduce radiation intensity to $10\%$. $1\,TVL = 3.3\,HVL$.

Mammography Physics

• Definition: Soft-tissue radiography designed for breast pathology.
• Differential Absorption: Since breast tissues have similar densities, low energy ($23\text{-}28\,kVp$) is used to maximize the photoelectric effect.
• Tube Components:
  • Target Material: Molybdenum ($Z=42$) or Rhodium ($Z=45$) are preferred over Tungsten for low-energy characteristic X-rays.
  • Window: Made of Beryllium ($Z=4$) to prevent absorption of the low-energy beam.
  • Focal Spot: Very small ($0.3/0.1\,mm$) for high spatial resolution.
• Compression: Essential to reduce breast thickness, reduce scatter, lower dose, and improve resolution.
• Grid: Low-ratio grids ($4:1$ or $5:1$) are used to improve contrast.