Nuclear Physics: The Heart of Matter

Nuclear Structure

The nucleus: tiny (10⁻¹⁵ m, ~100,000× smaller than the atom), dense (2.3×10¹⁷ kg/m³), contains 99.95% of the atom's mass. Nucleons: protons (p, charge +1) and neutrons (n, charge 0), bound by the strong nuclear force (residual strong force). Nuclear notation: ᴬ_Z X — A = mass number (protons + neutrons), Z = atomic number (protons). Isotopes: same Z, different N — hydrogen (¹H), deuterium (²H), tritium (³H). Nuclear binding energy: mass defect — the nucleus weighs less than the sum of its parts (E = Δmc²). Binding energy per nucleon: peaks at ⁵⁶Fe (8.79 MeV/nucleon) — iron is the most tightly bound nucleus. Elements lighter than Fe release energy through fusion; heavier elements release energy through fission. Nuclear force: short-range (~1-2 fm), strongly attractive at ~1 fm, repulsive at <0.5 fm, spin-dependent. Liquid drop model (Bethe-Weizsäcker): semi-empirical mass formula — volume, surface, Coulomb, asymmetry, and pairing terms. Nuclear shell model (Goeppert Mayer, Nobel 1963): magic numbers (2, 8, 20, 28, 50, 82, 126) — especially stable nuclei.

Radioactive Decay

Radioactive decay: unstable nuclei spontaneously transform to reach a more stable configuration. Alpha decay (α): emission of ⁴He nucleus (2p + 2n) — reduces Z by 2, A by 4. Common in heavy nuclei (Z > 82). Example: ²³⁸U → ²³⁴Th + ⁴He (t½ = 4.5 billion years). Beta decay (β⁻): neutron → proton + electron + antineutrino (mediated by weak force). β⁺: proton → neutron + positron + neutrino. Gamma decay (γ): excited nucleus emits high-energy photon — no change in Z or A. Electron capture: orbital electron captured by nucleus, proton → neutron + neutrino. Half-life (t½): time for half the radioactive atoms to decay — ranges from femtoseconds (⁸Be: 8.2×10⁻¹⁷ s) to billions of years (²³⁸U: 4.5×10⁹ years). Decay chains: series of decays from parent to stable daughter — uranium series (²³⁸U → ²⁰⁶Pb, 14 steps). Applications: carbon-14 dating (t½ = 5,730 years, organic material up to ~50,000 years), potassium-argon dating (rocks, millions of years), medical diagnostics (technetium-99m).

Fission and Fusion

Nuclear fission: heavy nucleus splits into lighter fragments + neutrons + energy. Discovered by Hahn and Strassmann (1938), explained by Meitner and Frisch. ²³⁵U fission: absorbs neutron → ²³⁶U* → fragments + 2-3 neutrons + ~200 MeV. Chain reaction: neutrons from fission trigger more fissions — critical mass (~52 kg for ²³⁵U sphere). Nuclear reactors: controlled chain reaction — 440 reactors worldwide, providing ~10% of global electricity. Reactor types: PWR (pressurized water, most common), BWR (boiling water), CANDU (heavy water), RBMK. Generation IV reactors: molten salt (MSR), sodium-cooled fast (SFR), high-temperature gas (HTGR) — improved safety, efficiency, waste reduction. Nuclear fusion: light nuclei combine into heavier ones + energy. D-T reaction: ²H + ³H → ⁴He + n + 17.6 MeV — the easiest fusion reaction to achieve. Conditions: temperature >100 million °C (plasma), sufficient density and confinement time (Lawson criterion). Stellar fusion: pp-chain (Sun) and CNO cycle — converting hydrogen to helium, powering stars for billions of years. Nucleosynthesis: elements up to Fe made in stars, heavier elements in supernovae (r-process) and neutron star mergers.

Accelerators and Applications

Particle accelerators: machines that accelerate charged particles to high energies for research, medicine, and industry. Large Hadron Collider (LHC, CERN): 27 km circumference, 13.6 TeV center-of-mass energy, discovered Higgs boson (2012, Nobel 2013). Future: FCC (Future Circular Collider, 91 km, 100 TeV) or muon collider — under study. Medical applications: proton therapy for cancer — precise dose delivery, sparing surrounding tissue. 100+ proton therapy centers worldwide. PET scanning: positron-emitting isotopes (¹⁸F-FDG) → positron-electron annihilation → 511 keV gamma ray pairs → 3D image. SPECT: single-photon emission — Tc-99m most widely used medical isotope (30 million procedures/year). Radiotherapy: cobalt-60, linear accelerators — external beam radiation for cancer treatment. Industrial applications: ion implantation (semiconductor manufacturing), neutron activation analysis, nuclear gauging, food irradiation. Nuclear forensics: isotopic analysis for attribution of nuclear materials — homeland security. Transmutation: converting long-lived nuclear waste into shorter-lived isotopes using accelerators or fast reactors.

❓ Frequently Asked Questions

The nucleus: tiny (10⁻¹⁵ m, ~100,000× smaller than the atom), dense (2.3×10¹⁷ kg/m³), contains 99.95% of the atom's mass. Nucleons: protons (p, charge +1) and neutrons (n, charge 0), bound by the stro...

Radioactive decay: unstable nuclei spontaneously transform to reach a more stable configuration. Alpha decay (α): emission of ⁴He nucleus (2p + 2n) — reduces Z by 2, A by 4. Common in heavy nuclei (Z ...

Nuclear fission: heavy nucleus splits into lighter fragments + neutrons + energy. Discovered by Hahn and Strassmann (1938), explained by Meitner and Frisch. ²³⁵U fission: absorbs neutron → ²³⁶U* → fra...

Particle accelerators: machines that accelerate charged particles to high energies for research, medicine, and industry. Large Hadron Collider (LHC, CERN): 27 km circumference, 13.6 TeV center-of-mass...

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