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Nuclear Chemistry and Radioactivity

Ch. 13Std 11

Easy Overview

How do stars produce energy? How does a nuclear reactor work? How can we use radioactivity to diagnose disease or determine the age of ancient artifacts? Nuclear chemistry holds the answers — it deals with changes in the nucleus, not just the electron cloud. Unlike chemical reactions (energy changes ~1-10 eV per atom), nuclear reactions release millions of eV per atom. The nucleus contains protons and neutrons held together by the strong nuclear force. Unstable nuclei decay by emitting α, β, or γ radiation, transforming into different elements. The rate of decay follows first-order kinetics — half-life is characteristic of each radioisotope. Nuclear fission splits heavy nuclei (²³⁵U) releasing enormous energy — used in power plants and atomic bombs. Nuclear fusion combines light nuclei (²H + ³H → ⁴He + n) — the energy source of stars and hydrogen bombs. Radioactive isotopes find applications in medicine (diagnosis and therapy), industry (tracing, gauging), agriculture (sterilization), and archaeology (carbon-14 dating).

Composition of the Nucleus — Protons, Neutrons, Nuclides

Nucleus contains protons (p⁺, charge +1, mass 1.0073 amu) and neutrons (n⁰, no charge, mass 1.0087 amu). Strong nuclear force binds them — short-range (~10⁻¹⁵ m), much stronger than electrostatic repulsion between protons. Neutrons provide 'glue' — stable nuclei have n/p ratio ~1 for light elements, increasing to ~1.5 for heavy elements (too many protons → repulsion). Nuclide: species with specific Z and A. Isotopes: same Z, different A (¹H, ²H, ³H). Isobars: same A, different Z (⁴⁰Ar, ⁴⁰K, ⁴⁰Ca). Isotones: same N, different Z (¹⁴C, ¹⁵N — both 8 neutrons). Isomers: same Z and A, different energy states (⁹⁹mTc used in medical imaging). Nuclear stability: even Z + even N most stable (magic numbers: 2, 8, 20, 28, 50, 82, 126 — closed shells).

Radioactive Decay — Types and Characteristics

Alpha (α) decay: ⁴₂He nucleus emitted. Z decreases by 2, A decreases by 4. ²³⁸U → ²³⁴Th + α. Low penetrating power (stopped by paper), high ionizing power. Beta (β⁻) decay: neutron → proton + e⁻ + ν̄ₑ (antineutrino). Z increases by 1, A unchanged. ¹⁴C → ¹⁴N + β⁻ + ν̄ₑ. Moderate penetrating power (stopped by Al sheet). Positron (β⁺) decay: proton → neutron + e⁺ + νₑ (neutrino). Z decreases by 1. Electron capture: nucleus captures inner orbital e⁻, p + e⁻ → n + νₑ. Gamma (γ) decay: excited nucleus emits high-energy photon (no change in Z or A). High penetrating power (needs thick Pb or concrete). Internal conversion: nucleus transfers energy to orbital e⁻ which is ejected. Cherenkov radiation: blue glow from high-speed charged particles in water (nuclear reactors).

Radioactive Decay Series — Transforming One Element to Another

Heavy radioactive nuclei (Z > 82) decay through series of α and β emissions until reaching stable Pb. Uranium series (4n+2): ²³⁸U (4.5×10⁹ y) → ... → ²⁰⁶Pb (stable). Thorium series (4n): ²³²Th (1.4×10¹⁰ y) → ... → ²⁰⁸Pb. Actinium series (4n+3): ²³⁵U (7×10⁸ y) → ... → ²⁰⁷Pb. Neptunium series (4n+1): ²³⁷Np (2.1×10⁶ y) → ... → ²⁰⁹Bi (stable). All series stepwise transform elements: ²³⁸U → ²³⁴Th (α) → ²³⁴Pa (β⁻) → ²³⁴U (β⁻) → ²³⁰Th (α) → ... Radioactive equilibrium: in closed system, each intermediate achieves constant activity (secular equilibrium: half-life of parent >> daughter, e.g., ²²⁶Ra → ²²²Rn). Radioactive dating: measure ratio of parent to daughter isotopes.

Kinetics of Radioactive Decay — Half-Life and Activity

Radioactive decay follows first-order kinetics: rate = -dN/dt = λN, where λ is decay constant. Integrated: N = N₀e⁻λᵗ. Half-life: t₁/₂ = ln2/λ = 0.693/λ. Average lifetime: τ = 1/λ = 1.44×t₁/₂. Activity: A = λN (becquerel = 1 decay/s, curie = 3.7×10¹⁰ Bq). Units: 1 Bq = 1 s⁻¹, 1 Ci = 3.7×10¹⁰ Bq. For multiple isotopes: total activity = ΣA_i. Carbon-14 dating: t₁/₂ = 5730 y. Living organisms have constant ¹⁴C/¹²C ratio (from cosmic rays). After death, ¹⁴C decays — measure remaining activity → time since death. A wood sample with 25% of original ¹⁴C → age = 2 × t₁/₂ = 11,460 years.

Nuclear Reactions — Bombardment and Transmutation

Artificial transmutation: stable nucleus bombarded with particles → new nucleus. ¹⁴N + α → ¹⁷O + p (Rutherford, 1919 — first artificial transmutation). ⁹Be + α → ¹²C + n (Chadwick, 1932 — discovered neutron). Projectiles: α particles, protons, deuterons (²H), neutrons. Neutrons are ideal (no charge, not repelled by nucleus) — thermal neutrons (slow, ~0.025 eV at 25°C) easily captured. Nuclear equations: balance Z and A. ²⁷Al + n → ²⁴Na + α. ²³⁸U + n → ²³⁹U → ²³⁹Np + β⁻ → ²³⁹Pu + β⁻ (transuranium elements). Superheavy elements: Z=93 (Np) to Z=118 (Og) made by bombardment. Particle accelerators (cyclotron, synchrotron): accelerate charged particles to high energy to overcome nuclear repulsion.

Nuclear Fission — Splitting the Atom

Hahn and Strassmann (1938): ²³⁵U + n → ¹⁴¹Ba + ⁹²Kr + 3n + energy (~200 MeV per fission). Chain reaction: each fission produces neutrons that cause more fissions. Critical mass: minimum mass for self-sustaining chain reaction. Neutron moderation: slow neutrons more effective for ²³⁵U fission — use water, graphite, heavy water (²H₂O) to slow neutrons. Control rods (Cd, B): absorb excess neutrons to control reaction rate. Nuclear reactor: fuel (³.⁵% ²³⁵U in ²³⁸U), moderator, control rods, coolant, shielding. Pressurized water reactor (PWR): water as moderator and coolant, high pressure prevents boiling. Boiling water reactor (BWR): steam drives turbine directly. Breeder reactor: ²³⁸U + fast n → ²³⁹U → ²³⁹Pu (fissionable) — produces more fuel than it consumes.

Nuclear Fusion — Power of the Stars

Light nuclei combine to form heavier: ²H + ³H → ⁴He + n + 17.6 MeV. Requires extremely high T (~10⁸ K) to overcome Coulomb barrier — only in stars or hydrogen bombs. Sun: proton-proton cycle — 4¹H → ⁴He + 2e⁺ + 2νₑ + 26.7 MeV. Tokamak: magnetic confinement fusion — D-T plasma at 150 million °C. ITER: international fusion reactor under construction in France — aims for 500 MW fusion power. Challenges: plasma instability, materials for 10⁸ K, tritium breeding (from Li + n). Fusion vs fission: no chain reaction (inherently safe), more energy per gram, less radioactive waste (only short-lived activation products), abundant fuel (H from water). Fusion is the holy grail of clean energy.

Applications of Radioactivity — Medicine and Industry

Medical diagnosis: ⁹⁹mTc (γ-emitter, t₁/₂=6 h) — most used medical radioisotope (80% of all nuclear medicine scans). Imaging: gamma camera detects γ rays from injected Tc compound. ¹¹¹In, ¹²³I, ²⁰¹Tl for specific organ imaging. PET scans: ¹⁸F-FDG (fluorodeoxyglucose) — tracer accumulates in metabolically active tissues (cancers, brain). Medical therapy: ⁶⁰Co (γ, t₁/₂=5.3 y) — cancer radiotherapy (teletherapy). ¹³¹I (β⁻, t₁₂=8 d) — thyroid cancer treatment (concentrates in thyroid, destroys tissue). ¹²⁵I seeds: brachytherapy for prostate cancer. Industry: thickness gauging (β source measures paper/steel thickness), level detection, radiography (check welds for defects — ¹⁹²Ir, ⁶⁰Co). Tracer studies: leak detection, flow measurement, mixing studies, wear analysis. Food irradiation: ⁶⁰Co γ rays kill bacteria, insects — extends shelf life (potatoes, onions, spices, meat). Sterilization: medical equipment (syringes, surgical gloves) sterilized by γ radiation.

Carbon-14 Dating and Archaeological Applications

Cosmic rays produce ¹⁴C in upper atmosphere: ¹⁴N + n → ¹⁴C + p. ¹⁴C combines with O₂ → ¹⁴CO₂, incorporated into plants (photosynthesis), then animals (food chain). Living organisms maintain constant ¹⁴C/¹²C ratio (= 1.3×10⁻¹²). After death, ¹⁴C decays (t₁/₂ = 5730 y) without replenishment. Age = -(t₁/₂/0.693) × ln(A/A₀). A₀ = activity when alive (15.3 disintegrations/min/g C). Limitations: effective up to ~50,000 years (after that too little ¹⁴C remains). Calibration needed (production rate varies with solar activity — calibration curves from tree rings used). Accelerator mass spectrometry (AMS): counts individual ¹⁴C atoms directly — needs only mg samples instead of grams. Other cosmogenic isotopes: ¹⁰Be (t₁/₂ = 1.5×10⁶ y) — dating of geological formations; ³⁶Cl — dating of groundwater; ²⁶Al — exposure dating of rocks.

Biological Effects of Radiation

Ionizing radiation damages DNA — can cause cell death, mutation, or cancer. Acute effects: high dose (>1 Sv) in short time — radiation sickness (nausea, hair loss, bone marrow damage). LD₅₀/₃₀: ~4 Sv (50% die within 30 days). Chronic effects: low doses over long time — increased cancer risk (stochastic). Sources: natural (radon gas from soil ~50% of background, cosmic rays, terrestrial ⁴⁰K, internal from food), artificial (medical X-rays/CT scans ~15%, nuclear fallout ~0.3%). Radon: second leading cause of lung cancer (after smoking). Dose units: gray (Gy = J/kg absorbed), sievert (Sv = Gy × quality factor — accounts for biological effect). α: QF=20 (most damaging internally), β: QF=1, γ: QF=1. Protection: time (minimize exposure), distance (inverse square law), shielding (α: paper, β: plastic/Al, γ: Pb/concrete).

Safety of Nuclear Reactors and Waste Disposal

Nuclear reactor accidents: Chernobyl (1986, RBMK reactor, design flaw + operator error → steam explosion and graphite fire, widespread ¹³¹I/¹³⁷Cs contamination, 30 immediate deaths, increased thyroid cancers). Three Mile Island (1979, partial meltdown, no casualties). Fukushima (2011, earthquake/tsunami led to cooling failure, hydrogen explosions, radioactive water release). Modern safety: multiple barriers (fuel pellets → cladding → pressure vessel → containment building), passive safety systems (gravity-driven cooling), negative temperature coefficient (natural feedback shuts down). Waste disposal: low-level (contaminated clothing, tools — shallow burial), intermediate-level (resins, filters — engineered storage), high-level (spent fuel — vitrified in glass, stored in deep geological repositories). Finland's Onkalo: first permanent HLW repository, 450 m deep in granite, designed for 100,000 years. Reprocessing: extract ²³⁹Pu and unused ²³⁵U from spent fuel.

Applications of Radioactive Isotopes as Tracers

Tracers: chemically identical radioactive isotope added to system, detected by radiation. Chemical: reaction mechanisms — ¹⁴C labeling follows carbon atoms through metabolic pathways (Calvin cycle in photosynthesis). Medical: ⁵⁹Fe follows iron absorption and utilization (anemia diagnosis), ⁵¹Cr labels RBCs for blood volume studies. Agricultural: ³²P in fertilizers traces phosphate uptake by plants — optimize fertilizer application (less runoff, more efficient). ¹⁴C-labeled pesticides: track degradation in environment. Industrial: ¹⁹²Ir traces flow in pipelines — detect leaks, blockages, flow rates (inject at one point, detect downstream). ⁸²Br: leachate monitoring in landfills. ²⁴Na: detect leaks in underground water pipes (inject ²⁴NaHCO₃ solution, monitor with Geiger counter). Autoradiography: photographic film exposed by radiation from labeled sample — locates labeled compounds in TLC, gels (Western blot), tissue sections.

Key Points

  • •Nucleus: p⁺ + n⁰; strong nuclear force; n/p ratio determines stability
  • •Radioactive decay: α (⁴He), β⁻ (e⁻ + ν̄ₑ), β⁺ (e⁺ + νₑ), γ (high-energy photon)
  • •Decay series: U (4n+2), Th (4n), Ac (4n+3), Np (4n+1) → stable Pb or Bi
  • •First-order kinetics: N = N₀e⁻λᵗ; t₁/₂ = 0.693/λ; A = λN
  • •Activity: Bq = 1 decay/s; Ci = 3.7×10¹⁰ Bq
  • •Transmutation: nucleus + projectile (α, p, d, n) → new nucleus
  • •Fission: ²³⁵U + n → fragments + n + energy; chain reaction needs critical mass
  • •Fusion: ²H + ³H → ⁴He + n + 17.6 MeV; requires 10⁸ K
  • •Nuclear reactor: fuel + moderator + control rods + coolant + shielding
  • •Breeder reactor: ²³⁸U → ²³⁹Pu — produces more fuel than consumed
  • •¹⁴C dating: t₁/₂=5730 y, effective up to ~50,000 years
  • •Medical: ⁹⁹mTc (imaging), ¹³¹I (thyroid therapy), ⁶⁰Co (radiotherapy)
  • •Radiation dose: Gy (absorbed), Sv (biological effect); α most damaging internally
  • •Protection: time, distance, shielding (α: paper, β: plastic, γ: Pb)
  • •Tracers: ¹⁴C, ³²P, ⁵⁹Fe, ¹⁹²Ir — follow through chemical/biological/industrial systems

Practice Questions

  • Complete nuclear equations: ²³⁸U (α decay), ¹⁴C (β⁻ decay), ²²Na (β⁺ decay).
  • Calculate half-life if 75% of sample decays in 40 days. Also find decay constant.
  • A ¹⁴C sample has 12 disintegrations/min/g C. Living organisms give 15.3. Find age (t₁/₂=5730 y).
  • Explain nuclear fission with ²³⁵U. What is chain reaction and critical mass?
  • Differentiate between nuclear fission and fusion with examples.
  • Describe construction and working of a nuclear reactor.
  • How is radioactivity used in medicine? Explain with ⁹⁹mTc and ¹³¹I.
  • What are biological effects of radiation? Explain units and protection methods.
  • Explain carbon-14 dating — principle, procedure, and limitations.