Nuclei Revision Notes for NEET Physics PDF Download
⚛️ ATOMS & NUCLEI · Modern Physics
Rutherford model • Bohr's postulates • Energy levels • Nuclear composition • Radioactivity • NEET problems
🔬 ATOMIC MODELS
Rutherford's model (α‑scattering): Nucleus (small, positive) at center, electrons revolve around.
Drawback: Couldn't explain stability (classical physics predicts collapse).
📐 Rutherford's gold foil experiment
🌀 BOHR'S ATOMIC MODEL (Hydrogen)
Postulates: stationary orbits, angular momentum quantization, frequency condition.
Radius of nth orbit: rn = n²a₀, a₀ = 0.529 Å (Bohr radius).
Energy of nth orbit: En = –13.6/n² eV.
Velocity of electron: vn = c/137 × (1/n).
📊 Bohr's energy levels & transitions
🌈 HYDROGEN SPECTRAL SERIES
Lyman (UV)
n₂ = 2,3,… → n₁ = 1
1/λ = R(1/1² – 1/n²)
Balmer (Visible)
n₂ = 3,4,… → n₁ = 2
1/λ = R(1/2² – 1/n²)
Paschen (IR)
n₂ = 4,5,… → n₁ = 3
1/λ = R(1/3² – 1/n²)
Brackett & Pfund (IR)
n₁ = 4, 5 respectively
Rydberg constant R = 1.097×10⁷ m⁻¹
🔋 NUCLEUS – COMPOSITION & PROPERTIES
Nucleus contains protons (Z) and neutrons (A–Z). Atomic mass number A = Z + N.
Nuclear radius: R = R₀ A^{1/3}, R₀ = 1.2×10⁻¹⁵ m.
Nuclear density: ~2×10¹⁷ kg/m³ (constant for all nuclei).
💪 MASS DEFECT & BINDING ENERGY
Δm = [Zmp + (A–Z)mn] – mnucleus.
Binding energy: B.E. = Δm × c² (in MeV). 1 u = 931.5 MeV/c².
Binding energy per nucleon is maximum for Fe (≈8.8 MeV) → most stable.
📈 B.E. per nucleon curve
☢️ RADIOACTIVITY
Spontaneous decay of unstable nuclei. Types: α (He nucleus), β⁻ (electron), β⁺ (positron), γ (photon).
Decay law: N = N₀ e–λt (λ = decay constant).
Half‑life: T1/2 = ln2/λ = 0.693/λ.
Mean life: τ = 1/λ = T1/2/0.693.
📉 Radioactive decay curve
⚡ NUCLEAR REACTIONS
Fission: Heavy nucleus splits into lighter fragments + energy (e.g., U‑235).
Fusion: Light nuclei combine to form heavier nucleus + energy (e.g., H → He in stars).
Q‑value = (Σminitial – Σmfinal)c² (positive → exothermic).
💡 NEET TIPS & SHORTCUTS
- Energy of electron in hydrogen: En = –13.6/n² eV. For He⁺, En = –13.6 × Z²/n².
- Rydberg formula: 1/λ = RZ²(1/n₁² – 1/n₂²).
- Number of atoms in 1 g of element = NA/A.
- Activity after n half‑lives = A₀/2ⁿ.
⚠️ COMMON MISTAKES
- Using Rydberg constant incorrectly (in m⁻¹ vs Å⁻¹).
- Forgetting that nuclear density is constant.
- Confusing half‑life and mean life.
- In β⁻ decay, n → p + e⁻ + ν̅e; in β⁺ decay, p → n + e⁺ + νe.
📌 QUICK REVISION CARD
Bohr radius: a₀ = 0.529 Å
Energy: En = –13.6/n² eV
Rydberg: 1/λ = R(1/n₁² – 1/n₂²)
Nuclear radius: R = R₀ A^{1/3}
Binding energy: B = Δm·c²
Decay law: N = N₀ e–λt, T1/2 = 0.693/λ