CBSE Class 12 Physics: Atoms & Nuclei — Complete Notes 2026

Rutherford's Nuclear Model

• Alpha scattering experiment (1911): most particles passed through; few deflected at large angles; very few bounced back
• Conclusion: atom is mostly empty; tiny dense positive nucleus; electrons around nucleus
• Limitation: accelerating electrons should radiate energy and spiral into nucleus (classically unstable)

Bohr's Model of Hydrogen Atom

• Postulates: electrons in fixed circular orbits; only certain orbits allowed (quantised angular momentum); L = nh/2π
• Energy of orbit: Eₙ = −13.6/n² eV; radius rₙ = 0.529 n² Å (Bohr radius for n=1: 0.529 Å)
• Spectral lines: Lyman (UV), Balmer (visible), Paschen (IR); 1/λ = R(1/n₁² − 1/n₂²)

Nuclear Composition

• Nucleus: protons (Z) + neutrons (N); mass number A = Z + N; notation: ᴬ_Z X
• Nuclear forces: strong nuclear force; short range (2–3 fm); overcomes proton-proton repulsion
• Nuclear density: ~2×10¹⁷ kg/m³; same for all nuclei; nucleus very dense

Mass-Energy Equivalence and Binding Energy

• E = mc²; nuclear mass < sum of constituent proton and neutron masses (mass defect)
• Binding energy per nucleon: peaks at Fe-56 (~8.8 MeV/nucleon); explains stability
• Fission (U-235) and fusion (H-2 → He-4): both release energy; BE/nucleon increases

Radioactivity

• Alpha decay: ᴬ_Z X → ᴬ⁻⁴_(Z-2) Y + ⁴₂He; loses 4 mass units, 2 atomic numbers
• Beta decay: neutron → proton + electron + antineutrino; Z increases by 1, A unchanged
• Gamma decay: high energy photon emitted; no change in Z or A; accompanies alpha/beta

Radioactive Decay Law

• N(t) = N₀ e^(−λt); λ = decay constant; half-life T½ = 0.693/λ
• Activity A = λN = A₀ e^(−λt); unit Becquerel (1 decay/second); older unit: Curie (3.7×10¹⁰ Bq)
• Applications: C-14 dating (T½ = 5730 years), nuclear medicine (Tc-99m), power generation

CBSE Board Focus

• Atoms & Nuclei: 8–10 marks; Bohr model derivation, radioactive decay law, mass defect/BE most important
• Numerical: find radius/energy of nth orbit; half-life calculations; decay constant from activity
• Draw: energy level diagram for hydrogen; nuclear binding energy curve