Rutherford's model (α‑scattering): Nucleus (small, positive) at center, electrons revolve around.

Drawback: Couldn't explain stability (classical physics predicts collapse).

Radius of nth orbit: r_n = n²a₀, a₀ = 0.529 Å (Bohr radius).

Energy of nth orbit: E_n = –13.6/n² eV.

Velocity of electron: v_n = c/137 × (1/n).

Nuclear radius: R = R₀ A^{1/3}, R₀ = 1.2×10⁻¹⁵ m.

Nuclear density: ~2×10¹⁷ kg/m³ (constant for all nuclei).

Decay law: N = N₀ e^–λt (λ = decay constant).

Half‑life: T_1/2 = ln2/λ = 0.693/λ.

Mean life: τ = 1/λ = T_1/2/0.693.

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 = (Σm_initial – Σm_final)c² (positive → exothermic).

💡 NEET TIPS & SHORTCUTS

• Energy of electron in hydrogen: E_n = –13.6/n² eV. For He⁺, E_n = –13.6 × Z²/n².
• Rydberg formula: 1/λ = RZ²(1/n₁² – 1/n₂²).
• Number of atoms in 1 g of element = N_A/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⁻ + ν̅_e; in β⁺ decay, p → n + e⁺ + ν_e.

Bohr radius: a₀ = 0.529 Å

Energy: E_n = –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, T_1/2 = 0.693/λ