Residency · Residency · Nuclear Medicine

Atomic Structure and Radioactive Decay

Nuclear Structure Fundamentals

Atomic Composition

Every atom is built from a dense central nucleus of protons and neutrons, surrounded by a cloud of orbital electrons. Protons carry a positive charge and define the element's identity through the atomic number, Z. Neutrons carry no charge but are essential contributors to nuclear stability. Together, the number of protons and neutrons gives the mass number, A, and the standard notation for any nuclide is written as ^A_Z X -- for example, ^99_43 Tc for technetium-99.

Isotope Terminology

Several terms describe the relationships between different nuclides. Isotopes share the same atomic number but differ in neutron count, as seen with I-123, I-125, and I-131, all forms of iodine. Isobars have the same mass number but different atomic numbers, such as Mo-99 and Tc-99. Isotones share the same neutron number but differ in Z. Isomers have identical Z and A but exist in different nuclear energy states -- the most clinically important example being Tc-99m (a metastable excited state) versus Tc-99 (the ground state).

Nuclear Stability

The band of stability is a plot of neutron number versus proton number for all stable nuclides. For lighter elements, stable nuclei have roughly equal numbers of neutrons and protons. Heavier elements, however, require a neutron excess (N greater than Z) to remain stable, because additional neutrons help offset the growing electrostatic repulsion among protons. Any nucleus that falls outside this band of stability is inherently unstable and will undergo radioactive decay to reach a more energetically favorable configuration.

Modes of Radioactive Decay

Alpha Decay

In alpha decay, the nucleus ejects a helium-4 particle consisting of two protons and two neutrons. This reduces the atomic number by 2 and the mass number by 4. Alpha particles are high linear energy transfer (LET) radiation with an extremely short range in tissue of roughly 50 micrometers, spanning only a few cell diameters. Despite this limited range, alpha emitters are extremely cytotoxic because they induce double-strand DNA breaks with great efficiency. Clinically, Ra-223 (Xofigo) exploits alpha decay to treat bone metastases, and Ac-225 is under active investigation as a theranostic agent.

Beta-Minus Decay

Neutron-rich nuclei achieve stability through beta-minus decay, in which a neutron converts into a proton, an electron (the beta particle), and an antineutrino. The atomic number increases by 1 while the mass number stays unchanged. Importantly, the emitted beta particles have a continuous spectrum of energies rather than a single discrete value. The range of beta particles in tissue is on the order of millimeters, depending on the maximum energy. Major therapeutic radionuclides that undergo beta-minus decay include I-131 (used in thyroid therapy), Y-90 (used in radioembolization), and Lu-177 (used in PRRT and PSMA-targeted therapy).

Beta-Plus (Positron) Decay

Proton-rich nuclei can decay by emitting a positron, the antimatter counterpart of the electron. In this process a proton converts to a neutron, a positron, and a neutrino, decreasing Z by 1 while A remains unchanged. Positron emission requires the parent atom's mass to exceed the daughter's by at least 1.022 MeV (twice the electron rest mass of 511 keV). Once emitted, the positron travels a short distance through tissue before encountering an electron. The resulting annihilation produces two 511 keV photons traveling in opposite directions at approximately 180 degrees, and this back-to-back photon emission is the physical foundation of PET imaging. Key clinical positron emitters include F-18 (used in FDG), Ga-68 (used in DOTATATE and PSMA tracers), and Rb-82 (used in cardiac PET).

Electron Capture (EC)

Electron capture is an alternative pathway for proton-rich nuclei. Instead of emitting a positron, the nucleus captures an inner-shell orbital electron, converting a proton into a neutron and emitting a neutrino. Electron capture always competes with positron emission and is the sole decay mode when the energy difference between parent and daughter is less than 1.022 MeV. The resulting vacancy in the inner electron shell is filled by outer electrons, producing characteristic X-rays and Auger electrons. Clinical radionuclides that decay primarily by electron capture include I-123, In-111, Tl-201, and Ga-67.

Isomeric Transition (IT)

In isomeric transition, a nucleus in a metastable excited state releases its excess energy by emitting a gamma ray, dropping to the ground state. Neither Z nor A changes. This is the defining decay mode of Tc-99m, the workhorse of nuclear medicine, which emits a 140 keV gamma ray with a half-life of 6.01 hours. The energy of this gamma ray is nearly ideal for detection by sodium iodide gamma cameras, making Tc-99m exceptionally well-suited for diagnostic imaging.

Internal Conversion (IC)

Internal conversion is an alternative to gamma ray emission. Instead of releasing a photon, the nucleus transfers its transition energy directly to an inner orbital electron, which is then ejected with kinetic energy equal to the transition energy minus the electron's binding energy. The resulting shell vacancy produces characteristic X-rays as it is filled. Internal conversion competes with isomeric transition, and the ratio of conversion electrons to gamma ray emissions is quantified by the conversion coefficient.

Radioactive Decay Mathematics

Decay Law

Radioactive decay follows a simple exponential law. The number of radioactive atoms remaining at time t is given by N(t) = N_0 x e^(-lambda x t), and activity follows the same relationship: A(t) = A_0 x e^(-lambda x t). The decay constant lambda is related to the half-life by the expression lambda = 0.693 / T1/2.

Half-Life Concepts

Three types of half-life are relevant in nuclear medicine. The physical half-life (Tp) is the time required for a radionuclide's activity to decrease by 50% through decay alone. The biological half-life (Tb) is the time for the body to eliminate 50% of a radiopharmaceutical through biological processes such as excretion and metabolism. The effective half-life (Te) combines both processes using the reciprocal relationship 1/Te = 1/Tp + 1/Tb. Because both physical decay and biological clearance work simultaneously to remove activity, the effective half-life is always shorter than either the physical or biological half-life alone.

Secular and Transient Equilibrium

When a parent radionuclide decays to produce a radioactive daughter, two types of equilibrium can be established. Secular equilibrium occurs when the parent's half-life is vastly longer than the daughter's, as with Ra-226 decaying to Rn-222. In this case, the daughter's activity eventually equals the parent's activity and remains constant as long as the parent is present. Transient equilibrium occurs when the parent's half-life is longer than the daughter's but not overwhelmingly so, as with the Mo-99/Tc-99m system. Here, the daughter's activity initially rises, transiently exceeds the parent's activity, and then both decay together at the parent's half-life. The Mo-99/Tc-99m generator, the mainstay of clinical nuclear medicine, operates under transient equilibrium.

Units of Radioactivity

The SI unit of radioactivity is the Becquerel (Bq), defined as one disintegration per second. The older conventional unit is the Curie (Ci), equal to 3.7 x 10^10 disintegrations per second. In clinical practice, activities are typically expressed in megabecquerels (MBq) or millicuries (mCi), with the conversion 1 mCi = 37 MBq.

Decay Schemes

Reading Decay Schemes

Decay schemes are energy level diagrams that depict the relationship between parent and daughter nuclides. Horizontal lines represent nuclear energy states, and arrows indicate transitions between them. The direction of the arrow conveys the type of decay: left-pointing arrows signify an increase in atomic number (beta-minus decay), while right-pointing arrows indicate a decrease in atomic number (electron capture or beta-plus decay). Branching ratios annotated on the diagram show the probability of each decay pathway when multiple routes exist.

Clinically Important Decay Schemes

Several decay schemes are essential knowledge for nuclear medicine practice. Tc-99m undergoes isomeric transition with a 140 keV gamma ray at 89% abundance, making it ideal for gamma camera imaging. I-131 undergoes beta-minus decay with a maximum beta energy of 606 keV and also emits a 364 keV gamma ray at 81% abundance, enabling both therapy and post-therapy imaging. F-18 decays by positron emission 97% of the time and by electron capture 3% of the time, with a half-life of 110 minutes. Ga-68 emits positrons 89% of the time with electron capture at 11%, and has a 68-minute half-life. Lu-177 undergoes beta-minus decay with a maximum energy of 497 keV and emits a 208 keV gamma ray at 10% abundance, permitting post-therapy imaging while delivering its therapeutic beta radiation.

<image>A detailed decay scheme diagram showing the Mo-99 to Tc-99m to Tc-99 decay chain, with energy levels marked in keV, branching ratios, and half-lives labeled. The diagram should show the beta-minus decay of Mo-99 (T1/2 = 66h) to the metastable state of Tc-99m (140.5 keV above ground state, T1/2 = 6.01h), and the subsequent isomeric transition to Tc-99 with emission of a 140 keV gamma ray. Include the transient equilibrium curve showing activity vs. time.</image>

<image>A comparison chart showing the five major modes of radioactive decay (alpha, beta-minus, beta-plus, electron capture, isomeric transition) side by side, with illustrations of each process at the nuclear level, showing the parent and daughter nuclei, emitted particles, changes in Z and A, and one clinical example radionuclide for each mode. Use a clean medical textbook style with color coding for each decay type.</image>

<image>An annotated diagram of the band of nuclear stability plotting number of neutrons (N) vs. number of protons (Z), showing the valley of stability in green, regions of beta-minus decay (neutron-rich, above the band) in blue, regions of beta-plus/EC decay (proton-rich, below the band) in red, and the region of alpha decay (heavy nuclei) in orange. Key medical radionuclides (Tc-99m, F-18, I-131, Ga-68, Lu-177, Ra-223) should be marked with their positions relative to the band.</image>

Clinical Pearls

Tc-99m is the workhorse of nuclear medicine for several converging reasons: its 140 keV gamma ray is ideal for detection by NaI(Tl) crystal detectors, its 6-hour half-life strikes an excellent balance between allowing adequate imaging time and limiting patient radiation dose, and it is readily available on demand from Mo-99/Tc-99m generators.

The two 511 keV annihilation photons produced by positron decay are the foundation of PET imaging. Because they travel at 180 degrees from one another, opposing detectors can register them simultaneously through coincidence detection, eliminating the need for physical collimation and enabling far greater sensitivity than SPECT.

Alpha emitters such as Ra-223 and Ac-225 deposit extremely high radiation doses over very short distances of roughly 50 to 80 micrometers. This makes them ideal for targeted destruction of micrometastases while largely sparing surrounding healthy tissue.

I-131 holds a unique position as a natural theranostic agent, combining beta particles for therapeutic cell killing with gamma rays that allow post-therapy imaging to verify targeting and distribution.

Understanding effective half-life is critical for dosimetry. A short biological half-life (rapid clearance from the body) significantly reduces the radiation dose delivered, even when a radionuclide has a long physical half-life.

For board examinations, remember that transient equilibrium (as in the Mo-99/Tc-99m generator) means the daughter activity transiently exceeds the parent activity before both decline together at the parent's half-life.

References

• Cherry SR, Sorenson JA, Phelps ME. Physics in Nuclear Medicine. 4th ed. Elsevier; 2012. Chapters 1-4.
• Bushberg JT, et al. The Essential Physics of Medical Imaging. 4th ed. Lippincott Williams & Wilkins; 2020.
• Saha GB. Fundamentals of Nuclear Pharmacy. 7th ed. Springer; 2018.
• Mettler FA, Guiberteau MJ. Essentials of Nuclear Medicine and Molecular Imaging. 7th ed. Elsevier; 2019.

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