Nuclear Chemistry — Radioactivity and Medicine

Nuclear chemistry deals with changes in the nucleus of atoms — reactions that involve protons and neutrons rather than electrons. These reactions release vastly more energy than ordinary chemical reactions. Atomic notation: The nucleus contains protons and neutrons (collectively nucleons). An element is defined by its atomic number (Z = number of protons). The mass number (A) = protons + neutrons. Isotopes have the same Z but different A (same element, different number of neutrons). Nuclear stability: Not all nuclei are stable. The neutron:proton (n:p) ratio determines stability. Light elements prefer n:p ≈ 1:1 (e.g., carbon-12 with 6 protons, 6 neutrons). Heavy elements require more neutrons — lead-208 has n:p ≈ 1.5:1. Nuclei outside the band of stability are radioactive and decay toward stability. The strong nuclear force: Protons repel each other electrostatically. The strong nuclear force (strongest of the four fundamental forces) binds protons and neutrons together at very short range. It overcomes electrostatic repulsion but only within the nucleus. Very large nuclei (Z > 83, bismuth) are inherently unstable because the strong force can't hold the nucleus together. Binding energy: The mass of a nucleus is always less than the sum of its constituent protons and neutrons. This mass defect (Δm) is converted to binding energy by E = mc². The binding energy per nucleon peaks at iron-56 — elements lighter than iron release energy by fusion; elements heavier than iron release energy by fission.

Radioactive decay is the spontaneous transformation of an unstable nucleus to a more stable configuration, releasing energy and particles in the process. Alpha decay (α): Emission of an alpha particle — a helium nucleus (⁴₂He), containing 2 protons and 2 neutrons. The parent nucleus decreases by Z−2, A−4. Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He Alpha particles are relatively large and slow — stopped by a sheet of paper or a few centimetres of air. Dangerous if inhaled or ingested (internal exposure) as they deposit energy in a very small volume. Used in smoke detectors (americium-241). Beta decay (β⁻): Emission of a beta particle (electron, β⁻) and an antineutrino when a neutron converts to a proton: n → p + e⁻ + ν̄e. Z increases by 1, A unchanged. Example: ¹⁴₆C → ¹⁴₇N + β⁻ + ν̄e (carbon-14 dating) Beta particles penetrate further than alpha — stopped by a few mm of aluminium. Positron emission (β⁺): Emission of a positron (antielectron, β⁺) when a proton converts to a neutron: p → n + e⁺ + νe. Z decreases by 1, A unchanged. The positron rapidly annihilates with an electron producing two 511 keV gamma photons. Exploited in PET scanning. Gamma decay (γ): Emission of high-energy electromagnetic radiation (gamma ray) when an excited nucleus relaxes to ground state. No change in Z or A. Gamma rays are the most penetrating — require lead or thick concrete shielding. Electron capture: An inner-shell electron is captured by the nucleus: p + e⁻ → n + νe. Z decreases by 1, A unchanged. Produces characteristic X-rays.

Radioactive decay is a first-order process — the rate depends only on the number of radioactive nuclei present. Half-life (t₁/₂): The time required for half the radioactive nuclei in a sample to decay. Each radioisotope has a characteristic, constant half-life — independent of temperature, pressure, or chemical state. This is a fundamental difference from chemical reactions. Decay equation: N(t) = N₀ × (½)^(t/t₁/₂) or equivalently: N(t) = N₀ × e^(−λt) where λ = decay constant = ln2/t₁/₂ = 0.693/t₁/₂ Half-lives vary enormously: Polonium-214: t₁/₂ = 164 microseconds Carbon-11: t₁/₂ = 20.4 minutes (used in PET) Technetium-99m: t₁/₂ = 6.01 hours (most widely used medical radioisotope) Iodine-131: t₁/₂ = 8.02 days (thyroid treatment) Carbon-14: t₁/₂ = 5,730 years (archaeological dating) Uranium-238: t₁/₂ = 4.47 billion years Activity: Activity (A) = rate of decay = λN (measured in Becquerels, Bq = 1 decay/second, or Curies, Ci = 3.7×10¹⁰ Bq). Activity decreases with the same half-life as the number of nuclei. Radiocarbon dating: Living organisms maintain a constant ratio of ¹⁴C:¹²C by exchanging carbon with the atmosphere. At death, the ratio decreases as ¹⁴C decays with t₁/₂ = 5,730 years. Measuring the current ¹⁴C/¹²C ratio gives the age. Reliable for samples up to ~50,000 years old.

Nuclear fission: Heavy nuclei (uranium, plutonium) split into smaller nuclei when struck by a neutron, releasing enormous energy and additional neutrons. A chain reaction can occur if sufficient fissile material (critical mass) is present. ²³⁵₉₂U + ¹₀n → ²³⁶₉₂U → ⁹⁴₃₆Kr + ¹³⁹₅₆Ba + 3¹₀n + ~200 MeV energy Nuclear reactors: controlled fission chain reaction. Control rods (boron, cadmium) absorb neutrons to regulate the reaction rate. Coolant (water, heavy water) removes heat and moderates neutrons. Nuclear power: uranium-235 fission produces ~50 million times more energy per gram than burning coal. No CO₂ emissions but produces radioactive waste requiring secure long-term storage. Nuclear fusion: Light nuclei (hydrogen isotopes) fuse to form heavier nuclei, releasing even more energy than fission. This is the energy source of the sun. ²₁H + ³₁H → ⁴₂He + ¹₀n + 17.6 MeV Fusion requires temperatures of ~100 million °C to overcome electrostatic repulsion (the Coulomb barrier). Sustained controlled fusion for energy production remains a major technological challenge. Thermonuclear weapons (hydrogen bombs) use a fission bomb to trigger fusion. Radiation doses and units: Gray (Gy): absorbed dose = 1 J of energy deposited per kg of tissue. Sievert (Sv): effective dose = Gray × radiation weighting factor. Accounts for biological damage (alpha particles cause ~20× more damage per gray than gamma rays). Annual background radiation: ~2–3 mSv. Chest X-ray: ~0.02 mSv. CT scan: ~2–10 mSv.

Nuclear medicine exploits radioactive isotopes for diagnosis and treatment: Diagnostic imaging — gamma cameras and SPECT: Radiopharmaceuticals (radioactive drugs) are injected, inhaled, or swallowed. They concentrate in target organs based on their biochemical properties. Gamma cameras detect emitted gamma rays to produce images of organ function (not just anatomy). Technetium-99m (⁹⁹ᵐTc): The most widely used medical radioisotope. t₁/₂ = 6.01 hours — long enough for imaging, short enough to minimise patient dose. Pure gamma emitter (140 keV). Produced in hospital generators from molybdenum-99 (t₁/₂ = 66 hours). Used for bone scans, cardiac perfusion, lung scans, renal scans. PET scanning (Positron Emission Tomography): Positron-emitting isotopes (¹⁸F-fluorodeoxyglucose, FDG) are injected. Positrons annihilate with electrons, emitting two 511 keV gamma photons in opposite directions. Coincidence detection produces 3D images of metabolic activity. FDG-PET detects cancer (high glucose uptake), Alzheimer's disease (reduced glucose metabolism), and cardiac viability. Iodine-131 therapy: The thyroid gland selectively absorbs iodine. ¹³¹I (β⁻ emitter, t₁/₂ = 8 days) accumulates in thyroid tissue and destroys it — used to treat hyperthyroidism and thyroid cancer. The beta particles travel only 1–2 mm in tissue, limiting damage to adjacent structures. Radiotherapy: High-energy gamma rays (from cobalt-60 or linear accelerators) or charged particles (protons, carbon ions) are directed at tumours. Ionising radiation damages DNA, causing cell death. Multiple beams are angled to converge on the tumour, minimising dose to surrounding tissue. Radiation protection: Three principles: distance (inverse square law — doubling distance reduces intensity 4-fold), shielding (lead aprons, lead glass), and time (minimise exposure duration). Health workers wear dosimeters to track cumulative exposure.