Nuclear chemistry examines the properties and reactions of atomic nuclei, encompassing radioactivity, nuclear transformations, and the practical applications of radionuclides. A nuclide is characterized by its atomic number Z (number of protons) and mass number A (total nucleons). Nuclides with the same Z but different A are isotopes. The stability of a nucleus depends on the neutron-to-proton ratio (N/Z). For light elements (Z ≤ 20), stable nuclei have N/Z ≈ 1. As Z increases, the stable N/Z ratio rises to approximately 1.5 for heavy elements because additional neutrons provide strong force attraction without increasing Coulomb repulsion. The belt of stability on a plot of N versus Z defines the region of stable nuclides.
Types of Radioactive Decay
Unstable nuclei achieve greater stability through several decay modes. Alpha decay (α) involves emission of a ⁴He²⁺ nucleus, reducing A by 4 and Z by 2. Alpha decay is most common for heavy elements (Z > 83) and the emitted α particles have discrete energies characteristic of the parent nuclide. Beta-minus decay (β⁻) converts a neutron into a proton with emission of an electron and an antineutrino: n → p + e⁻ + ν̅_e. This increases Z by 1 while A remains constant. Beta-plus decay (β⁺, positron emission) converts a proton to a neutron: p → n + e⁺ + ν_e. Electron capture (EC) is an alternative to β⁺ decay where the nucleus captures an inner-shell electron, converting a proton to a neutron. Gamma emission (γ) follows other decay processes when the daughter nucleus is formed in an excited state; it releases excess energy as high-energy photons without changing Z or A.
Radioactive Decay Kinetics
Radioactive decay follows first-order kinetics. The decay rate (activity A) is proportional to the number of radioactive atoms N: A = λN, where λ is the decay constant. The integrated rate law is N = N₀e^{-λt}, and the half-life t_{½} = ln2/λ = 0.693/λ. Half-lives range from fractions of a second to billions of years. The average lifetime τ = 1/λ. For a series of radioactive decays (decay chain), secular equilibrium is reached when the activity of a long-lived parent equals that of its shorter-lived daughter. Radiometric dating uses known half-lives to determine the age of materials: radiocarbon dating (¹⁴C, t½ = 5730 years) for organic materials up to ~50,000 years, and uranium-lead dating (²³⁸U → ²⁰⁶Pb, t½ = 4.47 × 10⁹ years) for geological samples.
Nuclear Fission and Fusion
Nuclear fission involves the splitting of a heavy nucleus (e.g., ²³⁵U or ²³⁹Pu) into two smaller nuclei, accompanied by the release of neutrons and energy. The fission of ²³⁵U can be induced by absorption of a thermal neutron: ²³⁵U + n → ²³⁶U* → fission products + 2-3 n + ~200 MeV. The emitted neutrons can induce further fissions, creating a self-sustaining chain reaction. Nuclear reactors control this chain reaction using control rods (B, Cd, Hf) that absorb neutrons and a moderator (H₂O, D₂O, graphite) that slows neutrons to thermal energies. Nuclear fusion combines light nuclei into heavier ones, releasing even more energy per nucleon. The fusion of deuterium and tritium: ²H + ³H → ⁴He + n + 17.6 MeV is the most promising for energy production, but achieving the required temperature (~100 million K) and confinement remains a formidable engineering challenge.
Binding Energy and Nuclear Models
The mass of a nucleus is always less than the sum of the masses of its constituent protons and neutrons. This mass defect (Δm) corresponds to the nuclear binding energy via Einstein’s equation: E = Δmc². Binding energy per nucleon peaks at around 8.8 MeV for iron-56 (the most stable nucleus), decreasing for both lighter and heavier elements. This curve explains why energy is released in both fission (splitting heavy nuclei) and fusion (combining light nuclei). The liquid drop model treats the nucleus as an incompressible charged fluid and reproduces the general trend of binding energies through the semi-empirical mass formula, accounting for volume, surface, Coulomb, asymmetry, and pairing terms. The shell model explains magic numbers (2, 8, 20, 28, 50, 82, 126) where nuclei have enhanced stability due to filled nucleon shells.
Radiochemical Techniques
Radiochemistry employs sensitive methods based on radioactivity detection. Isotopic dilution analysis adds a known amount of radioactive isotope to a sample; after chemical isolation, the decrease in specific activity reveals the amount of non-radioactive analyte originally present. Neutron activation analysis (NAA) is an exceptionally sensitive elemental analysis technique: a sample is irradiated with neutrons, inducing radioactivity in the elements present. The characteristic gamma rays emitted by each radionuclide are then measured, providing qualitative identification and quantitative determination of up to 70 elements at parts-per-billion levels. Autoradiography uses photographic film or imaging plates to visualize the distribution of radioactivity in biological or geological samples. Radiochemical separations exploit differences in chemical behavior between elements; ion exchange and solvent extraction are common methods for isolating specific radionuclides from complex mixtures.
Applications in Medicine, Dating, and the Environment
Radioisotopes have transformative applications. In medicine, technetium-99m (t½ = 6 h, γ emission at 140 keV) is used in ~85% of diagnostic nuclear medicine procedures, including bone scans, cardiac imaging, and brain imaging. Fluorine-18 (t½ = 110 min, β⁺ emitter) is the workhorse of positron emission tomography (PET), incorporated into FDG (fluorodeoxyglucose) for cancer imaging. Iodine-131 (t½ = 8 days, β⁻ and γ) is used for thyroid cancer therapy. Cobalt-60 (γ emitter, t½ = 5.27 years) is employed in radiotherapy for cancer treatment. Radiocarbon dating of archaeological artifacts and geological samples relies on the constant production rate of ¹⁴C in the upper atmosphere by cosmic ray neutrons. Environmental radioactivity monitoring tracks fallout from nuclear accidents (Chernobyl, Fukushima), and radionuclides like ¹³⁷Cs and ⁹⁰Sr serve as tracers for studying ocean currents, soil erosion, and atmospheric transport processes.
