3.1 Atomic Structure, Nuclear Decay & Radiation Interactions

A profound understanding of radiation physics is the bedrock of nuclear medicine. To excel on the ARRT Nuclear Medicine exam, you must confidently navigate atomic structure, the various modes of radioactive decay, decay mathematics, and how radiation interacts with matter.

Atomic Structure & Nuclide Notation

Atoms consist of a central nucleus containing protons (positively charged) and neutrons (neutral), surrounded by electron shells. The standard nuclide notation provides essential information about an atom:

Standard Notation: ^A_Z X

• X = Chemical symbol of the element
• A = Mass number (total number of protons + neutrons in the nucleus)
• Z = Atomic number (total number of protons in the nucleus)

For example, in ^99m_43 Tc (Technetium-99m), the atomic number is 43, and the mass number is 99. The 'm' indicates a metastable state, which is crucial for diagnostic imaging. Isotopes have the same Z but different A (same element, different number of neutrons). Isobars have the same A but different Z. Isotones have the same number of neutrons. Isomers have the same A and Z but exist in different nuclear energy states (e.g., Tc-99m and Tc-99).

Radioactive Decay Modes

Unstable nuclei seek stability through radioactive decay. The mode of decay depends on the specific instability of the nucleus (proton-rich vs. neutron-rich vs. simply too large).

Alpha Decay

Primarily occurring in heavy, unstable elements (Z > 82), alpha decay involves the emission of an alpha particle (2 protons, 2 neutrons—essentially a helium nucleus).

• Change in nucleus: A decreases by 4, Z decreases by 2.
• Characteristics: Alpha particles are heavy, highly ionizing, but have very low penetrability (stopped by paper or a few centimeters of air). Alpha emitters are highly toxic if internalized (e.g., Ra-223 used in targeted alpha therapy for bone metastases).

Beta Minus (β⁻) Decay

Occurs in neutron-rich nuclei. A neutron is converted into a proton, emitting a beta minus particle (an electron) and an antineutrino.

• Change in nucleus: A remains unchanged, Z increases by 1.
• Characteristics: Beta particles are more penetrating than alpha but less than gamma rays. Examples include I-131, Y-90, and Lu-177, which are extensively used in therapeutic applications due to their localized tissue destruction capabilities.

Positron (β⁺) Decay

Occurs in proton-rich nuclei. A proton is converted into a neutron, emitting a positron and a neutrino. This requires a minimum transition energy of 1.022 MeV.

• Change in nucleus: A remains unchanged, Z decreases by 1.
• Characteristics: The emitted positron quickly encounters an electron, resulting in an annihilation reaction that produces two 511 keV gamma photons emitted at ~180 degrees to each other. This is the foundation of PET imaging (e.g., F-18, Ga-68, Rb-82).

Electron Capture

An alternative to positron decay for proton-rich nuclei, especially when the transition energy is less than 1.022 MeV. The nucleus captures an inner-shell electron (usually from the K-shell), converting a proton into a neutron and emitting a neutrino.

• Change in nucleus: A remains unchanged, Z decreases by 1.
• Characteristics: The vacancy in the inner shell is filled by an outer-shell electron, resulting in the emission of characteristic X-rays or Auger electrons. Examples include I-123, Tl-201, and In-111.

Isomeric Transition and Gamma Emission

After undergoing alpha, beta, or electron capture, a nucleus may still be in an excited state. It sheds this excess energy by emitting a gamma ray photon without changing its atomic or mass number. When a nucleus remains in this excited state for a measurable period, it is termed 'metastable' (e.g., Tc-99m). The transition from the metastable state to the ground state via gamma emission is an isomeric transition.

Radioactive Decay Mathematics

Radioactive decay is a random, statistical process. The rate of decay is proportional to the number of radioactive atoms present. The fundamental decay equation is:

A = A0 * e^(-λt)

• A = Activity remaining at time t
• A0 = Initial activity
• e = Base of the natural logarithm (~2.718)
• λ (lambda) = Decay constant for the specific radionuclide
• t = Elapsed time

The decay constant (λ) is related to the physical half-life (T1/2) by the equation: λ = 0.693 / T1/2. Therefore, the decay equation can also be written as: A = A0 * (0.5)^(t / T1/2).

Exam Tip: For quick calculations, remember the rule of thumb for half-lives: after 1 half-life, 50% remains; after 2, 25%; after 3, 12.5%; after 4, 6.25%, and after 10 half-lives, less than 0.1% remains (effectively background).

Radiation Interactions with Matter

When ionizing radiation passes through matter, it interacts by transferring energy. For the ARRT exam, focus on the three primary photon interactions:

1. Photoelectric Effect

The incident photon transfers all its energy to an inner-shell electron, ejecting it from the atom (the photoelectron). The photon ceases to exist.

• Probability: High at low photon energies and in materials with high atomic numbers (Z). Proportional to Z^3 / E^3.
• Significance: This is the ideal interaction in radiation detectors (complete energy absorption) and shielding (lead). It contributes to patient dose in diagnostic radiology but is less dominant at standard nuclear medicine energies in soft tissue.

2. Compton Scattering

The incident photon interacts with a loosely bound outer-shell electron. It ejects the electron (Compton electron) and scatters in a new direction with reduced energy.

• Probability: Dominant interaction in soft tissue at intermediate energies (e.g., the 140 keV of Tc-99m or 511 keV of PET isotopes).
• Significance: Scattered photons degrade image quality (creating fog/background noise) and pose a radiation hazard to personnel. This is why collimation and energy windowing are critical in gamma cameras.

3. Pair Production

Requires a high-energy photon (minimum 1.022 MeV). The photon interacts with the strong nuclear field of an atom, disappearing and creating an electron-positron pair. The positron subsequently annihilates, creating two 511 keV photons.

• Significance: Important primarily in high-energy radiation therapy or industrial settings, not typically a factor in diagnostic nuclear medicine outside of the annihilation photons themselves in PET.