Nuclei
🟢 Lite — Quick Review (1h–1d)
Rapid summary for last-minute revision before your exam.
Nuclei — Key Facts for JEE Main • Mass-energy equivalence: E = mc² — mass defect converts to binding energy; used to calculate energy released in nuclear reactions • Radioactive decay law: N = N₀e^(−λt) — first-order kinetics; half-life T½ = ln2/λ; average life τ = 1/λ • Alpha decay: emits ₂He⁴ nucleus; helium core reduces atomic number by 2, mass number by 4; Q-value = [M(parent) − M(dα) − M(daughter)]c² • Beta decay: neutron → proton + electron + antineutrino; atomic number increases by 1, mass number unchanged; involves weak nuclear force • Gamma decay: high-energy photon emission; no change in A or Z; often follows alpha/beta decay to dispose of excess energy ⚡ Exam tip: JEE Main almost always has 1–2 questions on binding energy per nucleon curve — peak at Iron-56 (~8.8 MeV/nucleon); nuclei near Fe are most stable.
🟡 Standard — Regular Study (2d–2mo)
Standard content for students with a few days to months.
Nuclei — JEE Main / Advanced Study Guide Nuclear structure: atomic nucleus consists of protons (Z) and neutrons (N); mass number A = Z + N; nuclear radius R ≈ R₀A^(1/3) where R₀ = 1.2 fm. Isotopes have same Z, different N; isobars have same A, different Z; isotones have same N, different Z.
Mass defect and binding energy: Δm = [Z·mₚ + N·mₙ − M_nucleus]c²; packing fraction f = Δm/A in u. Binding energy per nucleon peaks at A ≈ 56 (Fe), explaining why nuclear fusion releases energy for light nuclei and fission for heavy nuclei.
Radioactive decay: activity A = λN = A₀e^(−λt); decay constant λ is probability per unit time. Half-life T½ = 0.693/λ; average life τ = 1/λ. Serial decay: N₁ → N₂ → N₃ with separate decay constants — transient equilibrium occurs when λ₁ > λ₂.
Q-value of nuclear reaction: Q = (M_i − M_f)c². For endothermic reactions Q < 0; threshold energy E_th = −Q·(M_target/M_projectile) for non-relativistic case.
Solved Example 1: A radioactive nucleus decays with T½ = 10 days. After 30 days, fraction remaining = (1/2)^(30/10) = (1/2)³ = 1/8. Answer: 1/8.
Solved Example 2: In α-decay of ²³⁸U (Z=92) → ²³⁴Th (Z=90), Q = [238.05079 − 234.04360 − 4.00260] × 931.5 MeV = 4.2 MeV.
⚡ Exam tip: Questions on radioactivedecay using N = N₀e^(−λt) and half-life calculations appear every year — practice problems with mixed decay series.
🔴 Extended — Deep Study (3mo+)
Comprehensive coverage for students on a longer study timeline.
Nuclei — Comprehensive JEE Notes Nuclear force: strongly repulsive at r < 0.5 fm (due to Pauliexclusion between nucleons), attractive at 0.5 fm < r < 2 fm, and vanishes beyond ~2 fm. This short-range, charge-independent nature explains nuclear saturation and the semi-empirical mass formula.
Semi-empirical mass formula (Weizsäcker): B = a_vA − a_sA^(2/3) − a_cZ(Z−1)/A^(1/3) − a_a(A−2Z)²/A ± δ. Volume term (a_vA) dominates; surface term corrects for fewer neighbours at surface; Coulomb term accounts for proton-proton repulsion (explains N > Z for heavy nuclei); asymmetry term penalises unequal N and Z; pairing term ±δ for even-even/odd-odd nuclei.
Nuclear models: liquid drop model explains average binding energy and fission; shell model (Maria Goeppert-Mayer) explains magic numbers (2, 8, 20, 28, 50, 82, 126) via discrete energy levels and spin-orbit coupling.
Nuclear fission: ²³⁵U + n → fission fragments + ~2.5 fast neutrons + ~200 MeV. Controlled chain reaction in reactors using moderator (heavy water/graphite) to slow neutrons; uncontrolled in nuclear weapons. Neutron reproduction factor k = ηεpfn needs k > 1 for sustained reaction.
Nuclear fusion: light nuclei fuse at extreme temperatures (10⁷–10⁸ K); D-T reaction: ²H + ³H → ⁴He + n + 17.6 MeV. Requires quantum tunnelling to overcome Coulomb barrier — explained by Gamow factor P ∝ e^(−2G) where G ∝ Z₁Z₂√(m/E).
⚡ JEE Advanced tip: Binding energy per nucleon curve (B vs A) with peak near Fe — understand why iron is the most stable element and how this dictates both fission of heavy nuclei and fusion of light nuclei as energy-releasing processes.
📊 JEE Main Exam Essentials
| Detail | Value |
|---|---|
| Questions | 90 (30 per subject) |
| Sections | Physics, Chemistry, Mathematics |
| Type | MCQ + Numerical Value (NAT) |
| Time | 3 hours |
| Marking | +4 correct, −1 wrong (MCQ); +4 correct, 0 wrong (NAT) |
| Sessions | January + April per year; best score considered |
🎯 High-Yield Topics for JEE Main
- Nuclei & Radioactivity — 3–4 marks
- Modern Physics (Semiconductors + Atoms) — 8 marks
- Electrostatics + Capacitance — 12 marks
- Electromagnetic Induction (EMI) — 8 marks
- Organic Chemistry (Name Reactions) — 12 marks
- Coordinate Geometry (Circle + Parabola) — 15 marks
📝 Previous Year Question Patterns
- Q: “Half-life of a radioactive substance is 10 days. After 30 days, activity becomes…” [2025 Physics — 3 marks]
- Q: “Binding energy per nucleon vs mass number curve is nearly flat near…” [2024 Physics — 3 marks]
- Q: “In α-decay of Uranium, the kinetic energy of the α-particle depends on…” [2024 Physics — 4 marks]
💡 Pro Tips
- Nuclear Physics is high-scoring because it follows predictable patterns — master the half-life and decay equations
- Numericals on half-life and activity are nearly guaranteed — practice 10+ problems
- Binding energy curve: peak at Fe-56; understand surface-area, volume, Coulomb, and asymmetry terms
- Q-value calculations for alpha and beta decay appear frequently in JEE Main
🔗 Official Resources
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📐 Diagram Reference
Clean educational diagram showing atomic nucleus structure with protons and neutrons, nuclear forces, binding energy per nucleon curve, radioactive decay types with alpha beta gamma emission, white background, exam-style illustration
Diagrams are generated per-topic using AI. Support for AI-generated educational diagrams coming soon.