Medical Imaging in Practice

Role of Medical Imaging in Radiation Oncology

• Clinical Utility: Medical imaging is essential for diagnosing and treating cancer, used during the initial workup, treatment planning, patient positioning, treatment verification, and adaptive radiation therapy.

• Modalities Used:     * Computed Tomography (CT).     * Magnetic Resonance Imaging (MRI).     * Positron Emission Tomography (PET).     * Ultrasound.

• Real-Time Application: Real-time imaging ensures accurate radiation delivery during treatment sessions.

• Assessment: Repeat imaging is vital to assess tumor response and the effectiveness of therapy.

• Goals: The primary objective is to maximize the radiation dose to cancer cells while minimizing the dose to surrounding normal tissues.

• Technological Advances: Improvements in microprocessor speeds and computer memory allow for the handling of large datasets, leading to higher-quality images and robust image fusion across different modalities.

• Image Fusion: A complex process incorporating information from multiple imaging technologies into the simulation planning process.

Historical Overview and Units of Measurement

• Discovery: X-rays were discovered in $1895$ by Wilhelm Conrad Rntgen, a German mechanical engineer and physicist.

• Conventional Units:     * The Roentgen (R): The conventional unit for X-ray and gamma-ray exposure in air.     * The Rad: Conventional unit for absorbed dose in tissue.     * The Rem: Conventional unit for occupational dose.

• Standard International (SI) Equivalents:     * Air Kerma ($Gy_a$): Replaces the Roentgen ($R$).     * Gray ($Gy$): Replaces the Rad.     * Sievert ($Sv$): Replaces the Rem.

Components of the X-ray Tube

• Basic Requirements: X-ray production requires a vacuum in a closed system, a source of accelerated electrons, a target material, and high voltage.

• The Cathode (Negative Electrode):     * Filament: A small coil of tungsten wire. Tungsten is chosen for its high melting point of $3380^\circ\text{C}$. Heating this filament via electrical current (mA) causes electrons to "boil off" through thermionic emission.     * Dual Filaments: Modern tubes usually have two filaments (small and large) to control focal spot sizes, typically $0.6\,mm$ (small) and $1.0\,mm$ (large), though sizes range from $0.1\,mm$ to $2.0\,mm$.     * Focusing Cup: An oval depression in the cathode assembly with a negative charge that directs the electron stream toward the anode in a non-divergent path.

• The Anode (Positive Electrode):     * Function: Acts as a target for electrons, dissipates heat, and provides a path for high voltage.     * Construction: A circular disk composed of various metals. The target focal track is made of rhenium-alloyed tungsten for thermal conduction.     * Rotation: The rotor allows the anode to reach speeds of $3400\,rpm$ to help dispel the intense heat generated.     * Focal Spot: The area on the target where electrons strike to produce X-ray photons.     * Line Focus Principle: The target is angled between $7$ and $20$ degrees. This allows a larger geometric area to be heated while maintaining a small effective focal spot for image detail.

• Glass Envelope: Maintains a vacuum to permit uninterrupted electron flow from cathode to anode. Usually $20$ to $30\,cm$ long and up to $15\,cm$ in diameter. Some modern tubes use metal to prevent tungsten deposit buildup (which causes arcing and reduces tube life).

• Protective Housing: Lead-lined to prevent radiation leakage and electrical shock. It is filled with special oil to provide electrical insulation and cooling.

Physics of X-ray Production

• Electromagnetic Spectrum Characteristics: Radiations travel at the speed of light ($3 \times 10^{10}\,cm/s$). They are expressed as wavelength (distance between crests) and frequency (cycles per second).

• Quantum Theory: Max Planck (1900) established that frequency and energy are directly proportional, while wavelength and frequency are inversely proportional.

• Ionizing Radiation: X-rays and gamma rays possess high frequency and short wavelengths, carrying enough energy to remove tightly bound electrons and create ions, which can damage living cells.

• Thermionic Emission: As the electrical current ($mAs$) applied to the filament increases, the number of liberated electrons ("thermions") increases proportionately. This controls beam quantity.

• Potential Difference: Applied voltage ($kVp$) creates a potential difference that repels electrons from the cathode and draws them to the anode at speeds approaching the speed of light. This determines beam quality (energy and penetration).

• Efficiency: Electrons colliding with the anode target produce two main types of interactions:     * Bremsstrahlung Radiation: Meaning "braking" radiation. Accounts for $75\%-80\%$ of the tube output. Occurs when high-speed electrons are deflected and decelerated by the nucleus of the tungsten atom.     * Characteristic Radiation: Created by direct interaction with inner-shell electrons. For Tungsten, K-shell electrons have a binding energy of $69.5\,keV$. When a K-shell electron is ejected and replaced by an L-shell electron, a characteristic photon of approximately $57.4\,keV$ is released.

X-ray Interactions with Matter (Body Tissues)

• Attenuation: The gradual reduction in the number of photons or exposure rate as the beam passes through matter, caused by absorption and scatter.

• Differential Absorption: The basis of radiographic imaging. Tissues with higher atomic numbers ($Z$) and densities (like bone) attenuate more photons and appear lighter. Low-density tissues (like air or fat) appear darker.

• Types of Interactions:     1. Classical (Rayleigh/Coherent) Scatter: Occurs at low energies (<10\,keV). The photon interacts with the whole atom; electrons vibrate but are not ejected. No ionization occurs, just a change in direction.     2. Compton Scatter (Incoherent): Predominant in the diagnostic range ($40$ to $150\,kVp$). The incident photon ejects an outer-shell ("loosely bound") electron, causing ionization. The photon is deflected with less energy. This is the primary source of occupational exposure hazard (e.g., in fluoroscopy) and causes image "fog."     3. Photoelectric Effect: Results in total absorption. The incident photon ejects an inner-shell (K-shell) electron and disappears. Probability increases with higher atomic number ($Z^3$).     4. Pair Production: Occurs at high energies (>1.022\,MeV). The photon interacts with the electromagnetic field of the nucleus, disappearing and re-emitting as an electron-positron pair ($\beta^- \beta^+$). Each has a rest mass energy of $0.511\,MeV$. The positron eventually undergoes an annihilation reaction with a free electron, producing two $0.511\,MeV$ photons traveling $180$ degrees apart.     5. Photodisintegration: Occurs at very high energies (>7\,MeV, commonly >10\,MeV in medical accelerators). The photon strikes the nucleus directly, causing it to emit neutrons and gamma rays. This creates a neutron hazard in radiation therapy, necessitating shielding like borated plastic.

Technical Factors and Beam Characteristics

• Image Density: The degree of darkening on an image. Directly proportional to the number of photons reaching the receptor.     * $mAs$ Rule: Doubling the $mAs$ doubles the density.     * $15\%$ Rule: Increasing $kVp$ by $15\%$ doubles the image density.

• Beam Hardening: The process of increasing the average energy of a polyenergetic beam by filtering out low-energy ("soft") X-rays. Filters (often aluminum) are used to reduce patient skin dose.

• Half-Value Layer (HVL): The thickness of a material required to reduce the beam intensity to half its original value. A "hard" beam has a higher HVL and greater penetrating ability.

• Radioactive Equilibrium:     * Secular Equilibrium: Occurs when the half-life of the parent isotope is much greater than the daughter ($T_{1/2 \text{ parent}} \gg T_{1/2 \text{ daughter}}$). Daughter activity eventually equals parent activity.     * Transient Equilibrium: Occurs when the parent half-life is longer but not vastly different from the daughter. Daughter activity eventually exceeds parent activity slightly before appearing to decay at the same rate.

Mathematical Relationships in Compton Scattering

• Energy of Scattered Photon ($h\nu'$):     * $h\nu' = \frac{h\nu}{1 + \epsilon(1 - \cos(\theta))}$

• Kinetic Energy of Compton Electron ($E_k$):     * $E_k = h\nu \times \frac{\epsilon(1 - \cos(\theta))}{1 + \epsilon(1 - \cos(\theta))}$

• Variable Definitions:     * $\epsilon = \frac{h\nu}{m_e c^2}$, where $m_e c^2 = 0.511\,MeV$.     * $\theta$ is the scattering angle of the photon.

• Scattering Angle Relationship:     * $\cot(\phi) = (1 + \epsilon) \times \tan(\frac{\theta}{2})$, where $\phi$ is the scattering angle of the electron.

• Specific Angle Scenarios:     * Direct Hit: The Compton electron travels straight forward ($\phi = 0$), and the photon backscatters ($180$ degrees) with minimum energy.     * Grazing Hit: Little energy is lost; the scattered photon retains nearly all original energy.     * $90$-Degree Scatter: The scattered photon reaches a maximum energy of $0.511\,MeV$ regardless of incident energy.

Radiation is the propagation of energy in matter, and radiation physics is the study of its interactions with it.

• All matter in its smallest form is composed of atoms.
• There are several models for the composition of the atom.

• Rutherford’s atomic model introduced the concept of a nucleus that consisted of protons and neutrons and the vast majority of the atom’s mass.

• Bohr’s atomic model is used often and demonstrates electrons orbiting the nucleus at discrete energy levels or “shells” similar to how planets orbit the sun (Figure 2.1).

• Atoms have a maximum number of required electrons in each shell.

• 2n2 is the formula used to find the maximum number of electrons in a shell. N represents the shell number or quantum number. Each shell, beginning with the inner shell, is assigned a letter, K, L, M, N or quantum number 1, 2, 3, 4, and so on.

• The mass of atoms is expressed in terms of atomic mass units (amu) or atomic weight; 1 amu = 1.66 × 10−27 kg.

• The mass in grams numerically equal to the atomic weight is the gram atomic weight.

• According to Avogadro’s law, every gram atomic weight of an element contains the same number of atoms.

• The number of atoms per gram is given by Avogadro’s number/atomic weight; Avogadro’s number is accepted as 6.0228 × 1023.

• Atoms are represented by the formula z X A.

• The X is the chemical symbol, Z is the atomic number (the number of protons or electrons), A is the atomic mass (the sum of protons and neutrons).

• Neutrons have no charge and protons have a positive charge; they have the ability to transition between positive and neutral charge; the nucleus is positively charged.

• Both neutrons and protons have a substantial mass as compared with orbiting electrons; protons are about 1800 times more massive than electrons and neutrons are slightly heavier than protons.

• The orbiting electrons may be stripped from the atom to go on to interact with other atoms or particles. The mass, charge, and linear energy transfer (LET) of some key particles is provided in Table 2.1.

• With electrons orbiting carrying a negative charge, they are bound to the atom by the attraction of their negative charges to positive charges in the nucleus; this attraction is known as electrostatic force.

• The closer the electrons are to the nucleus, the more tightly bound they are to the nucleus.

• The stability of the atoms in an element is determined by a balance of positive and negative charges and evenly paired electrons.

• An atom is electrically neutral or said to be in its ground state when it has as many positive charges as negative charges and has evenly paired electrons.

• An encounter with radiation can manipulate any of the atom’s components.

• Electrons can be stripped from the atom and interact with other atoms or positively charged particles.

• Neutrons may also be stripped from the atom but will not interact with electrons due to their neutral charge. They may, however, interact with other particles.

• Protons can be stripped and will likely interact with electrons or neutrons.

• Any encounter that would cause an electron to be raised to a higher electron shell or made to vibrate in place, would lead to an energy emission known as excitation (Figure 2.2).

• Any interaction with the atom that would cause an electron to be totally removed from the atom is known as ionization (Figure 2.3).

• Once an atom is ionized, it is no longer stable. Rather, it has charge. If an atom captures an electron then it is called a negative ion. If it loses an electron, then it is called a positive ion.

• Great energy has to be expended to raise electrons to a higher shell. The closer the electrons are to the nucleus, the stronger the binding energy, or electrostatic force.

• As electrons are held tight to the nucleus by energy and have energy at rest in the shell, any change in the status of an otherwise resting electron causes an energy loss or redistribution of energy.

• If the incoming or interacting energy of an atomic particle, or energy bundle, has at least 124 electron volts of energy and a wavelength shorter than 10–6 cm, it has the greatest potential to be ionizing.

• Energy ranges commonly used in radiation therapy are 100 keV to 250 MeV.

• The kilo electron volt (keV) is 103 electron volts or 1000 electron volts. • The mega electron volt (MeV) is 106 or 1,000,000 electron volts.

FIG. 2.1 Bohr’s model of the atom. TABLE 2.1

Particles With Mass, Charge, and LET

Mass (kilograms)
Cobalt gamma
250 kV x-rays 0
Beta 0.000548
Protons 1.67 × 10–27 0.5–4.7 +1 Neutrons 1.68 × 10–27 75 0 Alphaparticles 6.65 × 10–27 166 +2

Charge

LET(KeV/micrometer) 0 0.2 0
2.0 0
0.2–2.0 –1, +1

FIG. 2.2 Excitation occurs when an electron is raised to a higher shell or made to vibrate.

FIG. 2.3 Ionization occurs when an electron is ejected from the atom. Electromagnetic Spectrum
• Ionizing radiation is in the family of electromagnetic radiation.

• All radiation in the electromagnetic spectrum are photons, or bundles of energy, that travel in straight lines, have velocity as the speed of light, and have wavelength and frequency.

• Radiation in the electromagnetic spectrum includes visible light, heat, radio, microwaves, ultraviolet rays, gamma rays, and x-rays (Figure 2.4).

• These photons are called electromagnetic because they exhibit similar characteristics as electric and magnetic fields (oscillating wave patterns, frequency, wavelength, energy, and velocity).

• Frequency is measured in cycles per second using the unit Hertz. • Wavelength is measured in meters using the unit Angstrom.
• Energy is measured in joules or expressed in electron volts (eV).

• Radiation in the electromagnetic spectrum used in radiation therapy includes gamma and x-radiation; x-rays and gamma rays are found at the upper end of the spectrum with short wavelengths, high frequency, and high energies.

• X-rays and gamma rays are ionizing.
• X-rays and gamma rays only diker by where they originate.

• Gamma rays are a result of natural nuclear decay; x-rays have to be created and are a result of interaction or deceleration of electrons with the atoms of a target material.

• Positrons (positively charged electrons), electrons, protons, neutrons, alpha particles, and pi mesons are examples of other radiation known as particulates.

• Particulates may also be ionizing; electrons, protons, neutrons, and alpha particles may be used in radiation therapy.

• Positrons only exist in motion and are used in imaging, such as positron emission tomography (PET).

• Particulates like protons and electrons are directly ionizing. Gamma rays, x-rays, and neutrons are indirectly ionizing.

• Wavelength, frequency, and the speed of light are related according to the formula:

• The speed of light is constant at 3 × 108 m/sec in vacuum.

• The kinetic energy of an electromagnetic radiation is related to wavelength according to the formula:

• Kinetic energy is related to frequency according to the formula:

FIG. 2.4 The electromagnetic spectrum.

Particle Interactions and X-Ray Production

• The physical characteristics of heavy particles such as protons, neutrons, alpha particles (2 neutrons + 2 protons), or deuterons (1 neutron + 1 proton) allow them to penetrate and deposit energy at short range.

• The heavy particles have a high LET.

• The energy deposit increases to a maximum and produces a denser ionization near the end of its path. This ionization region is called a Bragg peak (Figure 2.5).

• The rate of energy loss by a charged particle is proportional to the square of the particle charge.

• Electrons are commonly used charged particles in radiation therapy. Electrons have a low mass and distribute energy in a finite range in an absorber. The electron’s low mass allows it to have a low LET and therefore does not show the same distribution pattern as Bragg’s peak.

• There are two types of electron interactions with matter. They are collision and radiative.

• Collision interactions involve electrons interacting with orbiting electrons in matter and transferring momentum and energy. Examples of such interactions are excitation and ionization.

• Radiative collisions occur when energy from the electrons is lost in the form of bremsstrahlung radiation.

• When an inner shell electron is ionized from the atom, a vacancy in the energy shell results. This vacancy may be filled with an orbiting electron in an outer energy shell. Any energy loss may exit the atom in the form of a photon.

• Orbiting electrons have a resting energy and a binding energy.

• The binding energy of an inner shell electron is large; the binding energy of an outer shell electron is small.

• The potential energy dikerence between where the ionized orbiting electron used to be and the electron filling the vacancy will be the resulting energy of the exiting photon.

• The exiting photon is in the form of characteristic x-rays (Figure 2.6).

• If the electron encountering the atom does not interact with an orbiting electron but is drawn to the positive charge in the nucleus, its velocity is slowed and its direction changes.

• The change in velocity causes a loss in the kinetic energy of the incoming electron; the energy loss exits the atom in the form of bremsstrahlung radiation (Figure 2.7).

• When x-rays are produced, both characteristic and bremsstrahlung radiation are emitted from the target atoms.

• X-ray production requires a high voltage source, cathode, anode, glass envelope, and vacuum (Figure 2.8).

• The deceleration of electrons as they encounter the atoms of the target causes both x-ray and heat emission.

• In diagnostic tubes about 99% of the electron energy is converted to heat, whereas only 1% is converted to x-ray.

• During megavoltage x-ray production, a higher proportion of electron energy is converted to photons.

• The proportion is influenced by the atomic number of the target and maximum energy of the electrons in MeV.

• The following equation may be used to figure the converted energy to photons: F = 3.5 × 10−4 (Z) (E)
F = fraction of the incident electron energy converted to photons
Z = atomic number of the target

E = maximum energy of electrons in MeV

FIG. 2.5 Examples of Bragg peaks.
FIG. 2.6 Characteristic x-ray production. FIG. 2.7 Bremsstrahlung x-ray production.

FIG. 2.8 The basic x-ray tube. (From: Drake RL, Vogl W, Mitchell AWM, Horn A. Gray’s Basic Anatomy. Third edition. Elsevier; 2023. Ch 1: The Body, Fig. 1.2: Cathode ray tube for the production of X-rays. ISBN: 978032383442-1.)

Photon Interactions
• There are three major types of photon interactions with matter. They are: a. Photoelectric ekect
b. Compton ekect
c. Pair production

• Photoelectric ekect occurs when a photon ejects one of the orbiting electrons. The entire energy of the photon is first absorbed by the atom and then transferred to the atomic electron. This happens in the innermost shells. The ejected electron is called a photoelectron. When a vacancy occurs, another electron from another energy shell drops in to fill the space, and energy emitted is in the form of characteristic x-rays or Auger electrons. The probability of this interaction increases when the incident photon is in the low kilovoltage range and the interacting material has a high atomic number.

• Compton ekect occurs when a high energy photon (>150 KeV) interacts with an electron as though it were a free electron. This happens in the outer shells. The encountered electron receives some energy from the photon and is emitted at an angle from the atom. The photon, with reduced energy, is also scattered at an angle. There could be a direct hit where the electron will move out and forward and the photon will travel backward. The higher the energy, the greater the probability of this type of interaction. The Compton ekect is independent of atomic number of the interacting material.

• Pair production occurs when the photon energy is greater than 1.02 MeV. The photon interacts with the electromagnetic field of the nucleus and gives up all its energy in the

process of creating a pair of particles consisting of an electron and a positron. The particles are emitted in the forward direction; probability of this type of interaction increases with atomic number. Figure 2.9 illustrates each of the three major photon interactions.

FIG. 2.9 Illustration of the three major photon interactions. (From: Radiation Oncology: Rationale, Technique, Results, NINTH EDITION, 2010, FIGURE 1-1: The first step in the absorption of a photon of x-rays or gamma rays is the conversion of the energy of the photon into the kinetic energy of an electron, or electron-positron pair. At higher energies, when the energy of the incident photon greatly exceeds the binding energy of the planetary electrons in the atoms of the absorber, the Compton process dominates. The photon interacts with the electron in a classic “billiard-ball collision.” Part of the photon energy is given to the electron as kinetic energy, while the photon is deflected and has reduced energy. At lower energies, when the binding energy of the planetary electrons of the atoms of the absorber is not small compared with the photon energy, the photoelectric ekect is most important. The photon disappears completely as it interacts with a bound electron. The electron is ejected with kinetic energy equal to the photon energy, less the energy required to overcome the electron bond. The vacancy caused by the removal of the electron must be filled by an electron dropping from an outer orbit, giving rise to a photon of characteristic radiation. At sukiciently high photon energies, the photon may interact with the powerful nuclear forces to produce an electron-positron pair. The first 1.02 MeV of photon energy is used to create the rest mass of the pair, and the remainder is distributed equally between them as kinetic energy. ISBN: 978-0-323-04971-9. Image Identifier: pii:B9780323049719000019/gr1.)

Radiation Intensity and Beam Quality

• Intensity is defined as the amount of energy present per unit of time per unit of area perpendicular to the beam direction.

• Beam quality refers to the energy of the beam expressed in electron volts or the absorbing potential or penetrating power of the beam expressed in half-value layers (HVL) of material.

• Intensity of the beam is reduced by two ekects: beam divergence and attenuation.

• Beam divergence is an expression of the scattering of photons away from the original point source.

• An area at a certain distance from the source (distance 1) would have an amount of photons passing through it (intensity 1). At a greater distance (distance 2), the same

amount of photons would be scattered apart further and result in a less intense beam (intensity 2) (Figure 2.10).

• The inverse square law governs the principle of divergence and demonstrates that the intensity of the beam is inversely proportional to the square of the distance from the original point source:

• Beam attenuation is the removal of energy from the beam.

• When a photon or particulate beam passes through matter, some energy is removed from the beam as a result of absorption and scattering; the energy that is removed or absorbed by the material is said to be attenuated.

• The number of photons passing perpendicular through an area of 1 square meter may be referred to as photon fluence.

• The energy passing perpendicularly through an area of 1 square meter would be called energy fluence.

• Some photons or particles are unakected by the attenuator and pass through; the photons or particles passing through are referred to as transmission.

I0 = original intensity I = final intensity

• Some photons are totally absorbed; some may be partially absorbed and exit the material with reduced energy and changed direction.

• Photons that are totally or partially absorbed in tissue contribute to the absorbed dose. Figure 2.11 illustrates attenuation, fluence, and transmission.

• Refer to Figure 2.11 and consider the following: FIG. 2.10 Illustration of beam divergence.

FIG. 2.11 Photon fluence, attenuation, and transmission illustration.

If N0 is the number of photons incident on a slab of material (photon fluence) and it encounters a thickness of material (t) to absorb some energy, the following mathematical equation could help us solve for the number of photons transmitted.

μ = linear attenuation coekicient
The energy attenuated or transmitted is influenced by the incident beam energy and the

type of material it passes through.

• The amount of material that would reduce the incident photon fluence to half its original value would be called its half-value thickness (HVT) or HVL.

• The HVT and linear attenuation coekicient are related by the formula:

μ = linear attenuation coekicient
• As the material thickness increases, the intensity of the attenuated beam decreases.

• If we use a photon source with only one energy, the attenuation of the beam follows the relationship:

• The meaning of the equation is that each millimeter of thickness added to an absorber reduces the beam intensity by a constant percent.

• In low energy x-ray tubes, filters may be used as absorbers to harden the beam.

• Beam hardening refers to the phenomenon where the ekective energy of the beam increases as it passes through the filter: the filter absorbs the low energy rays and allows the higher energy rays to be transmitted. Because the hardened beam has more high-

energy rays, the amount of material needed to decrease the original intensity by subsequent increments of 50% actually decreases due to beam hardening.

• 2 HVLs is not exactly HVL(2), due to beam hardening.
• HVT or HVL can be used to express the beam quality in lower energy beams.

• HVL is also used in the design of beam shielding blocks; the acceptable transmission of shielding blocks is approximately 3% or 5 HVLs of material.

• HVL is not used to specify beam energy for high energy photon or electron beams. Rather, an equivalent energy is used to characterize high energy beams used in radiation therapy.

• In radiation therapy, the beam energy is expressed in eV (KeV for imaging and MeV for therapy).

• The energy specified refers to the maximum energy in the spectrum of energies exiting. Radioactivity and Nuclear Transformation

• Atoms represented by the formula zXA are called nuclides. When elementary particles of the stable atom are manipulated, they become unstable elements grouped by radionuclide families of isotopes, isotones, isobars, or isomers (Table 2.2).

• Radioactivity was discovered by Henri Becquerel in 1896 while exploring the naturally irradiative element, uranium.

• At around the same time, similar irradiative characteristics were found in radium by Marie and Pierre Curie.

• Radioactive decay, or disintegration, is a phenomenon in which radiation is emitted by the nucleus in the form of particles or electromagnetic radiation as an unstable element attempts to become stable again.

• On the periodic table of elements, the elements with atomic numbers higher than 82 tend to be unstable and are at some point attempting to become stable; as they are emitting particles or electromagnetic radiation, we refer to them as radioactive.

• Disintegrations are a statistical phenomenon and occur exponentially; 1 disintegration per second = 1 dps.

• The mathematics of radioactive decay is based on the fact that the number of atoms disintegrating per unit of time is proportional to the number of radioactive atoms present. There is constant proportionality known as the decay constant.

• The symbol for the decay constant is λ and may be found by the equation:

• T1⁄2 is the half-life; this is the time required for the number of radioactive atoms to decay to half the initial value.

• Ta is the mean or average life; this is the average lifetime for the decay of radioactive atoms.

• In theory, the time it takes for all atoms to decay is infinite.

• Activity refers to the rate of decay or the strength of radioactive material. The traditional unit for activity is the Curie (Ci). The standard international unit is the Becquerel (Bq).

• Important equations to remember related to nuclear transformations are:

• Radioactive nuclides undergo successive transformations in which the original nuclide— known as the parent (X)—gives rise to a radioactive product nuclide known as the daughter (Y).

• Naturally occurring radioactive materials are grouped into three decay series: uranium series, actinium series, and thorium series.

• If the half-life of the parent (X) is much longer than that of the daughter (Y), then after a certain time, a condition of equilibrium occurs where the ratio of the daughter activity to the parent activity becomes constant. This is known as secular equilibrium.

• If the parent activity is not very long compared to the daughter activity, then the type of equilibrium established is called transient equilibrium.

• Nuclear transformations manifest as: a. Alpha decay
b. Beta decay (negative and positive)
c. Electron capture

d. Internal conversion

• Alpha decay occurs with very high atomic number nuclides in which two protons and two neutrons are emitted; an example would be in the decay of radium-226.

• Beta negative decay occurs when there is an excessive number of neutrons or high neutron to proton ratio; the element tends to emit negative electrons; the decay of phosphorus-32 is an example.

• Beta positive decay occurs when there is a deficit of neutrons and results in the emission of a positron. The decay may be accompanied by the emission of gamma rays. The excess energy in the nucleus must be at least 1.02 MeV; sodium-22 decay is an example.

• Electron capture occurs when the excess energy in the nucleus is less than 1.02 MeV. One of the orbital electrons is captured by the nucleus, transforming a proton into a neutron. The captured electron leaves an empty space in an electron shell, which in turn will be filled by another orbiting electron causing a release of energy known as characteristic x-rays.

• The characteristic x-ray may eject an outer shell electron from the atom as it is expelled; such an electron is referred to as an Auger electron.

• Internal conversion occurs with the emission of gamma rays from the nucleus. In most transformations, the daughter nucleus loses energy immediately in the form of gamma radiation. Orbiting electrons may bombard the nucleus and receive some energy from the nucleus. The energized electron may subsequently be ejected from the atom and travel away with an energy equal to the dikerence between the energy lost by the nucleus and the binding energy that held the electron.

• Other interactions include fission and fusion; these interactions are a result of producing radioactive materials.

• Fission is a result of bombarding certain high atomic number nuclides with heavy neutrons; the nucleus splits into nuclei of a lower atomic number.

• Fusion can be considered the reverse of fission; low mass nuclei are combined to produce one nucleus.

TABLE 2.2 Radionuclide Families

Isotopes Isotones Isobars Isomers

Same number of protons but dikerent number of neutrons
Same number of neutrons but dikerent number of protons
Same number of nucleons but dikerent number of protons
Same number of protons and neutrons except in a dikerent nuclear state