Radiologic Technology Board Exam Review: Radiation Physics and Characteristics

Matter and Energy Fundamentals

Matter is defined as anything that occupies space and has mass. It is the material substance that makes up physical objects. The fundamental characteristics of matter include its shape and form, its occupation of space, mass, electrical charge, and magnetism. A key principle in physics is that matter and energy are interchangeable, a concept represented by Albert Einstein's mass-energy equivalence formula: $E = mc^{2}$, where $E$ is energy, $m$ is mass, and $c$ is the speed of light in a vacuum ($3 \times 10^{8}\,m/s$). This concept is foundational to technologies like nuclear medicine imaging and atomic weaponry.

Mass is the quantity of matter contained in an object, measured in kilograms ($kg$). Unlike weight, mass remains constant regardless of the object's location or the gravitational forces acting upon it. Weight, conversely, is the force exerted on an object due to gravity and varies depending on the strength of the gravitational field; an object can be weightless in space, but its mass remains unchanged.

Energy is defined as the ability to do work. The SI unit for energy is the joule ($J$), where $1\,joule = 1\,newton \times 1\,meter\,(N\cdot m)$. In the field of radiology, the electron volt ($eV$) is the preferred unit. One electron volt is the energy gained by an electron when it moves through a potential difference of $1\,volt$. The conversion factor is $1\,eV = 1.602 \times 10^{-19}\,J$.

Major Forms of Energy and Transformations

Energy exists in several major forms. Potential energy is stored energy resulting from an object's position. Kinetic energy is the energy of motion. Chemical energy is released during chemical reactions. Electrical energy is produced when electrons move through an electric potential difference or voltage (e.g., household electricity at $110\,V$; unit: $joules/coulombs$ or $volts$). Thermal energy (heat) is energy of motion at the molecular level; higher molecular vibration correlates with higher temperature. Nuclear energy is the energy contained within the nucleus of an atom, utilized in power plants and nuclear medicine. Electromagnetic energy is a form of energy that includes radio waves, microwaves, ultraviolet, infrared, visible light, and vitally for radiology, x-rays.

Energy transformation is a central process in diagnostic imaging. In an x-ray system, electrical energy is converted into electromagnetic energy (x-rays). These x-rays are then converted into chemical energy on radiographic film or into electrical signals in digital receptors.

Evolution of Atomic Theory

The understanding of the atom has evolved through several historical models. The Early Greek Theory proposed that all matter consisted of four substances: Earth (solid/stable), Water (liquid/adaptable), Air (gaseous/light), and Fire (energy/transformative). The Greeks coined the term "atomos," meaning indivisible.

In $1808$, John Dalton introduced his atomic theory, suggesting that each element is made of identical atoms that behave the same chemically, while different elements have different atoms. He proposed the "hook and eye" model to explain how atoms combine in chemical reactions. In the late $1890s$, J.J. Thomson discovered the electron while studying cathode rays. He proposed the "Plum Pudding Model," where the atom is a sphere of positive charge (the pudding) with negative electrons (the plums) embedded within it.

In $1911$, Ernest Rutherford disproved Thomson's model by discovering the nucleus through his nuclear model. He described the atom as having a small, dense, positively charged center containing protons, with electrons surrounding it and most of the atom being empty space. In $1913$, Niels Bohr refined this by proposing the "Solar System Model," where electrons move around the nucleus in fixed paths called orbits or energy levels. This Bohr atom remains the standard for explaining basic atomic structure in radiology.

Fundamental Atomic Structure and Particles

An atom is the smallest particle of an element that retains its chemical properties. A neutral atom has an equal number of protons and electrons. The atom consists of two main parts: the nucleus (the dense central core containing nucleons) and the orbits or shells (regions surrounding the nucleus containing electrons).

There are three primary subatomic particles:

1. Electron ($e^{-}$): A negatively charged particle orbiting the nucleus. It is extremely small with a mass of $9.1 \times 10^{-31}\,kg$. Its relative mass is approximately $\frac{1}{1,826}$ to $\frac{1}{1,838}$ the mass of a proton (Atomic Mass Number = $0$; AMU = $0.000548$).

2. Proton ($p^{+}$): A positively charged particle ($+1$) located in the nucleus. Its mass is $1.673 \times 10^{-27}\,kg$ (AMU = $1.00728$). Eugen Goldstein is associated with the discovery of positive/canal rays related to protons. The number of protons determines the identity of an element.

3. Neutron ($n^{0}$): A neutral particle discovered by James Chadwick, located in the nucleus. It is slightly heavier than a proton at $1.675 \times 10^{-27}\,kg$ (AMU = $1.00867$).

Protons and neutrons are collectively called nucleons and are composed of smaller particles called quarks. They are held together within the nucleus by the strong nuclear force. Atomic particles are often measured in atomic mass units ($amu$), where $1\,amu$ is defined as $\frac{1}{12}$ the mass of a carbon-12 atom.

Electron Arrangement and Shell Dynamics

Electrons are arranged in shells or orbitals around the nucleus. The shell closest to the nucleus is the K-shell, followed sequentially by L, M, N, O, P, and Q. Each shell is identified by a principal quantum number ($n$), where K corresponds to $n=1$. The maximum number of electrons a shell can hold is determined by Pauli's exclusion formula: $2n^{2}$. Based on this:

• K-shell ($n=1$): $2(1)^{2} = 2\,e^{-}$

• L-shell ($n=2$): $2(2)^{2} = 8\,e^{-}$

• M-shell ($n=3$): $2(3)^{2} = 18\,e^{-}$

• N-shell ($n=4$): $2(4)^{2} = 32\,e^{-}$

• O-shell ($n=5$): $2(5)^{2} = 50\,e^{-}$

• P-shell ($n=6$): $2(6)^{2} = 72\,e^{-}$

• Q-shell ($n=7$): $2(7)^{2} = 98\,e^{-}$

The Octet Rule states that the outermost shell (valence shell) of an atom usually does not exceed $8$ electrons. Atoms with exactly $8$ electrons in their outer shell are chemically stable and inert (e.g., noble gases). Valence refers to the combining power of an atom, determined by the number of electrons it can give, receive, or share to reach stability.

Two forces keep electrons in orbit: centrifugal force (the "flying-out" effect caused by circular motion) and centripetal force (the electrostatic attractive force pulling the negative electron toward the positive nucleus). In a stable atom, these forces are balanced.

Physical Properties of Elements and Bonding

The Periodic Table, first arranged by Dmitri Mendeleev, lists elements by increasing atomic number ($Z$). Horizontal rows are called periods, representing the number of electron shells ($n$). Vertical columns are called groups, representing elements with the same number of electrons in the outermost shell and similar chemical behaviors. For example, Barium is in Period $6$, Group II.

Chemical bonding occurs as atoms seek stability:

• Ionic Bond: Formed when one atom gives up an electron and another accepts it (e.g., $Na^{+1}$ and $Cl^{-1}$ form $NaCl$).

• Covalent Bond: Formed when atoms share electrons (e.g., two $H^{+1}$ and one $O^{-2}$ form $H_{2}O$).

A molecule is formed when two or more atoms combine chemically; a compound is specifically when two or more different elements are chemically bonded. Important elements in radiology include hydrogen ($H$), carbon ($C$), and oxygen ($O$) (human body constituents); iodine ($I$) and barium ($Ba$) (contrast media); tungsten ($W$) and molybdenum ($Mo$) (x-ray tube targets); and lead ($Pb$) (radiation protection).

Electron Binding Energy and Nomenclature

Electron binding energy ($E_{b}$) is the strength of the attachment of an electron to the nucleus, measured in $eV$ or $keV$. Energy required to remove an electron must be equal to or greater than its binding energy. $E_{b}$ is highest for the K-shell and increases as the atomic number ($Z$) increases because a stronger nuclear charge exerts a greater pull. For example, the K-shell binding energy of Tungsten ($W$) is approximately $69\,keV$.

Atomic Nomenclature:

• Chemical Symbol: Alphabetic abbreviations (e.g., $Ba$ for Barium).

• Atomic Number ($Z$): The number of protons in the nucleus; it identifies the element.

• Atomic Mass Number ($A$): The total number of protons and neutrons. $A = \text{protons} + \text{neutrons}$.

• Neutron Number ($N$): The difference between $A$ and $Z$ ($N = A - Z$). For Tungsten ($A=184$, $Z=74$), $N = 110$.

Nuclide Families:

• Isotopes: Same atomic number ($Z$), different mass number ($A$) (e.g., ${}^{130}_{56}Ba$ to ${}^{138}_{56}Ba$).

• Isobars: Same mass number ($A$), different atomic number ($Z$) (e.g., Iodine-131, Xenon-131, Cesium-131).

• Isotones: Same number of neutrons ($N$), different protons ($Z$).

• Isomers: Same $A$ and $Z$, but different energy states (metastable). An example is Technetium-$99m$ ($Tc\text{-}99m$).

Characteristics of Radiation and Energy Spectrum

Radiation is the emission and transfer of energy through matter or space. It is classified into particulate and electromagnetic radiation. Particulate radiation consists of moving tiny particles with mass and often an electric charge. Types include Alpha particles (${}^{4}_{2}He^{2+}$, heavy, $+2$ charge, short range of $5\,cm$ in air, highly ionizing), Beta particles (light particles from the nucleus; $\beta^{-}$ or negatron and $\beta^{+}$ or positron), and Neutrons (uncharged particles that interact primarily with the nucleus).

Electromagnetic (EM) radiation consists of photons, which are discrete packets of energy with no mass and no charge. EM radiation travels at the speed of light ($c \approx 3 \times 10^{8}\,m/s$) in straight lines. It exhibits wave-particle duality. Wave theory describes EM radiation using the wave equation: $c = f \lambda$, where $c$ is velocity, $f$ is frequency (measured in hertz, $Hz$), and $\lambda$ is wavelength (measured in meters or Angstroms, $\mathring{\text{A}}$). One Angstrom ($1\,\mathring{\text{A}}$) equals $10^{-10}\,m$. Diagnostic x-rays typically range from $0.1$–$0.5\,\mathring{\text{A}}$.

Particle theory uses Planck's equation: $E = h \nu$, where $E$ is energy, $h$ is Planck's constant ($4.15 \times 10^{-15}\,eV\cdot s$), and $\nu$ is frequency. Energy and frequency are directly proportional, while frequency and wavelength are inversely proportional.

Selected Electromagnetic Spectrum Regions

• Radiofrequency ($RF$): Low energy, long wavelength, used in MRI.

• Microwaves: Short-wavelength $RF$, used in communication and deep heating (diathermy).

• Infrared Light: Radiant heat with wavelengths longer than visible light.

• Visible Light: Small portion seen by the human eye ($400$–$700\,nm$).

• Ultraviolet ($UV$): Between visible light and ionizing radiation; cause of sunburn.

• X-rays and Gamma Rays: High energy, high frequency, short wavelength. Gamma rays originate from the nucleus; X-rays originate from the electron cloud.

Ionization, Radioactivity, and Decay Processes

Ionization occurs when an electron is completely removed from an atom, producing an ion pair (a free negative electron and a remaining positive atom). Excitation occurs when an electron is raised to a higher energy level but not removed, often producing heat. Radiation is ionizing if it possesses enough energy to remove orbital electrons. Ionization potential for tissue atoms is approximately $34\,eV$ ($12.6\,eV$ for water).

Sources of ionizing radiation are categorized as Natural Environmental (avg. $3\,mSv/year$: radon, cosmic, terrestrial, internal radionuclides) and Man-made (avg. $3.3\,mSv/year$: medical imaging like CT and x-ray, consumer products). Radon is the largest natural source, contributing dose primarily to the lungs via alpha emission.

Radioactivity is the process where unstable nuclei release energy and particles (disintegrations) to reach stability. Units include the becquerel ($1\,Bq = 1\,\text{disintegration/second}$) and the curie ($1\,Ci = 3.7 \times 10^{10}\,Bq$). Nucles are stable based on their neutron-to-proton ($N/Z$) ratio: $1:1$ for low-$Z$ elements and $1.5:1$ for high-$Z$ elements.

Decay Types:

• Alpha Decay: Occurs in heavy nuclides (A > 150); $A$ decreases by $4$, $Z$ decreases by $2$.

• Beta-Minus Decay: A neutron converts to a proton; an electron ($\beta^{-}$) and an antineutrino are emitted; $Z$ increases by $1$.

• Beta-Plus (Positron) Decay: A proton converts to a neutron; a positron ($\beta^{+}$) and a neutrino are emitted; $Z$ decreases by $1$.

• Annihilation Radiation: A positron and electron destroy each other, producing two $0.511\,MeV$ photons traveling $180^{\circ}$ apart (total energy $1.02\,MeV$).

• Electron Capture: The nucleus captures an orbital electron (K or L shell) to convert a proton into a neutron.

• Isomeric Transition: An excited (metastable) nucleus releases gamma rays to reach ground state.

• Internal Conversion: The nucleus transfers excess energy directly to an orbital electron, ejecting it (Internal Conversion Electron).

Half-Life categories:

1. Physical Half-Life ($T_{1/2}$ or $T_{p}$): Time for activity to decrease by half via decay.

2. Biologic Half-Life ($T_{b}$): Time for half the material to be excreted by the body.

3. Effective Half-Life: Combined effect of physical decay and biological elimination. $\text{Effective half-life is always shorter than physical or biological alone}$.

X-ray Production and Target Interactions

X-ray production requires a source of electrons (filament), a means to accelerate them (high $kVp$), and a target for interaction (anode). Projectile electrons hitting the target convert kinetic energy: >99.8\% becomes heat (infrared) and <1\% becomes x-rays. Efficiency increases with higher $kVp$ and higher target $Z$.

Target Interactions:

1. Characteristic Radiation: Projectile electron ejects an inner-shell (K-shell) electron. An outer-shell electron drops to fill the vacancy (electron cascade), releasing a photon with energy equal to the difference in shell binding energies ($E = E_{b\,vacant} - E_{b\,transition}$). These are discrete/predictable energies. For Tungsten, only K-characteristic x-rays ($69\,kVp$ threshold) are useful.

2. Bremsstrahlung Radiation: "Braking radiation." A projectile electron is slowed and deflected by the nuclear force field. The kinetic energy lost is emitted as an x-ray photon. This produces a continuous spectrum of energies up to the maximum $kVp$.

Related phenomena include Auger Electron emission (energy from a shell transition is transferred to another orbital electron, ejecting it instead of a photon) and Fluorescent Yield (the probability of characteristic x-ray emission vs. Auger emission; it increases with $Z$).

Factors Affecting the X-ray Emission Spectrum

• mA/mAs: Affects quantity (amplitude) only. Increasing $mAs$ makes the spectrum taller without changing the energy profile.

• kVp: Affects both quantity and quality. Increasing $kVp$ makes the spectrum taller and shifts it to the right (higher average energy).

• Added Filtration: Decreases quantity but increases quality. It "hardens" the beam by removing low-energy x-rays, shifting the average energy higher.

• Target Material: High-$Z$ targets increase production efficiency and shift characteristic peaks to higher energies.

X-ray Interaction with Matter

As the x-ray beam passes through matter, it undergoes attenuation (reduction in photon number via absorption or scatter). Interactions depend on photon energy:

1. Coherent (Classical/Unmodified) Scattering: Very low energy (< 10\,keV). The photon interacts with the whole atom; the atom vibrates and releases a photon of the same energy in a different direction. No ionization occurs.

2. Compton Scattering: Moderate energy ($30$–$150\,keV$). Interaction with outer-shell electrons. Produces a recoil electron and a scattered photon of lower energy. This is the primary source of scatter, radiation fog, and occupational dose.

3. Photoelectric Effect: Diagnostic range. Interaction with inner-shell electrons. Total absorption of the photon; a photoelectron is ejected. This interaction provides subject contrast (difference between bone and soft tissue) but increases patient dose. Probability is proportional to $\frac{Z^{3}}{E^{3}}$.

4. Pair Production: High energy ($\ge 1.022\,MeV$). Interaction with the nuclear field. The photon disappears and creates a negatron and a positron. Not significant in diagnostic imaging.

5. Photodisintegration: Very high energy (> 10\,MeV). The photon is absorbed by the nucleus, which then emits a nuclear fragment (proton, neutron, or alpha particle). Not relevant to diagnostic radiology.

Linear Energy Transfer and Specific Ionization

Specific Ionization is the number of ion pairs produced per unit length ($IP/mm$). It increases with higher particle charge and lower velocity. Linear Energy Transfer (LET) is the energy deposited per unit path length ($eV/cm$ or $keV/\mu m$). High LET radiation (alpha, protons) is more biologically damaging than low LET radiation (x-rays, gamma, beta).

Path length is the actual distance a particle travels, while range is the depth of penetration. For heavy particles, these are nearly equal; for electrons, path length is much greater than range due to their tortuous, irregular tracks.