Quick Revision - Nuclei
One-page summary, flashcards, formulas, memory tricks
Complete Nuclei Chapter in 5 Minutes
🧬 Nuclear Structure
- Composition: Protons (Z) + Neutrons (N) = Nucleons (A)
- Radius: R = R₀A^(1/3), R₀ = 1.2 fm
- Density: ρ = 2.3 × 10¹⁷ kg/m³ (constant)
- Force: Strong nuclear force, short-range (~10⁻¹⁵ m)
⚡ Mass-Energy
- Einstein: E = mc²
- Key Unit: 1 u = 931.5 MeV/c²
- Mass Defect: Δm = [Zmₚ + Nmₙ] - M
- Binding Energy: BE = Δm × 931.5 MeV
- Stability: Max BE/A at Fe-56 (8.8 MeV)
☢️ Radioactivity
- α-decay: A→A-4, Z→Z-2 (He nucleus)
- β⁻-decay: A same, Z→Z+1 (electron)
- β⁺-decay: A same, Z→Z-1 (positron)
- γ-decay: No A, Z change (photon)
📉 Decay Laws
- Exponential: N = N₀ e^(-λt)
- Half-Life: T½ = 0.693/λ
- Mean Life: τ = 1/λ = 1.44T½
- Activity: A = λN (unit: Bq)
- Quick Form: N = N₀/(2^n), n = t/T½
⚛️ Nuclear Reactions
- Q-Value: Q = Δm × 931.5 MeV
- Q > 0: Exothermic (energy out)
- Q < 0: Endothermic (energy in)
- Fission: Heavy→Light (~200 MeV)
- Fusion: Light→Heavy (requires 10⁷ K)
🔬 Applications
- C-14 Dating: t = (T½/0.693)ln(N₀/N)
- Reactors: Controlled fission chain
- Medical: PET, radiotherapy
- Safety: Ionizing radiation hazards
🃏 Interactive Flashcards
Click card to flip. Use arrows to navigate. Shuffle for random practice.
Card 1 of 20
📋 Formula Dump (Print & Paste)
🧠 Memory Tricks & Mnemonics
Alpha (α): A-4, Z-2 (Loses 4 mass, 2 charge)
Beta⁻ (β⁻): A same, Z+1 (Electron out, charge up)
Beta⁺ (β⁺): A same, Z-1 (Positron out, charge down)
Gamma (γ): No change (Just energy)
α < β < γ
Mnemonic: "Alphabetical order = Penetration order"
α stopped by paper, β by aluminum, γ needs lead
If N₀/N = 2 → 1 half-life
If N₀/N = 4 → 2 half-lives
If N₀/N = 8 → 3 half-lives
Pattern: 2^n where n = number of half-lives
1 u = 931.5 MeV/c²
Write this on your answer sheet first thing!
90% of numerical errors come from forgetting this.
Fe-56 = Peak (most stable, 8.8 MeV)
Left of peak (light): Fusion releases energy
Right of peak (heavy): Fission releases energy
At peak: Neither works!
τ = 1.44 × T½
Memory: "Mean life is about one-and-a-half times half-life"
τ always longer than T½
Q = (Reactants - Products) × 931.5
Positive Q: Mass lost → Energy OUT (Exothermic)
Negative Q: Mass gained → Energy IN (Endothermic)
Isotope: "ISO-Z" → Same Z
Isobar: "ISO-A" → Same A
Isotone: "ISO-N" → Same N
✅ Pre-Exam Checklist
Theory Checklist
- ☐ Nuclear structure & composition
- ☐ Mass-energy equivalence derivation
- ☐ All 4 types of decay (α, β⁻, β⁺, γ)
- ☐ Decay law derivation
- ☐ BE/A curve and stability
- ☐ Fission vs Fusion differences
- ☐ C-14 dating principle
- ☐ Nuclear reactor components
Formula Checklist
- ☐ R = R₀A^(1/3)
- ☐ 1 u = 931.5 MeV/c²
- ☐ BE = Δm × 931.5 MeV
- ☐ N = N₀e^(-λt) and N = N₀/(2^n)
- ☐ T½ = 0.693/λ, τ = 1.44T½
- ☐ A = λN
- ☐ Q = Δm × 931.5 MeV
- ☐ All decay equations
Numerical Skills
- ☐ Mass defect calculations
- ☐ Binding energy problems
- ☐ Half-life problems (both forms)
- ☐ Activity calculations
- ☐ Q-value in reactions
- ☐ C-14 dating age calculations
- ☐ Graph interpretation (ln N vs t)
- ☐ Unit conversions (u ↔ MeV)
Constants to Memorize
- ☐ mₚ = 1.007276 u
- ☐ mₙ = 1.008665 u
- ☐ R₀ = 1.2 fm
- ☐ 1 u = 931.5 MeV/c²
- ☐ C-14 T½ = 5730 years
- ☐ 1 Ci = 3.7 × 10¹⁰ Bq
- ☐ ln 2 = 0.693
- ☐ Fe-56 BE/A = 8.8 MeV
- 1 Week Before: Complete all flashcards daily, solve 1 PYQ daily
- 3 Days Before: Revise formulas, practice high-weightage topics (decay law, BE)
- 1 Day Before: Read this page completely, solve 5 easy numericals for confidence
- Exam Day Morning: Flashcards + Formula dump + Deep breathing