Nuclei — Physics Class 12 Notes (CBSE & HBSE)
Free NCERT Physics notes for Nuclei (Class 12) on Siksha Sarovar, aligned to CBSE and Haryana Board (HBSE). This chapter is broken into 3 topics with clear explanations, formulas, solved examples and board-pattern practice — free to read, no sign-up required.
Board exam focus — Nuclei (CBSE & HBSE)
CBSE focuses on binding energy per nucleon graph, radioactive decay law derivation, half-life, nuclear fission and fusion processes. HBSE emphasizes nuclear composition, radioactivity types with properties, decay equations, and fission vs fusion comparison.
Nuclear Composition and Binding Energy
Nuclear Composition
The nucleus consists of protons (positive charge +e) and neutrons (no charge).
Notation: ᴬZ X (mass number A, atomic number Z, element X)
| Term | Symbol | Definition |
|---|---|---|
| Atomic number | Z | Number of protons |
| Neutron number | N | Number of neutrons |
| Mass number | A | A = Z + N (nucleons) |
| Nuclide | — | Specific nucleus with given Z, N |
Types of Nuclei:
- Isotopes: Same Z, different A (e.g., ¹H, ²H, ³H)
- Isobars: Same A, different Z (e.g., ⁴⁰Ca and ⁴⁰Ar)
- Isotones: Same N, different Z (e.g., ³H and ⁴He)
Nuclear Size
R = R₀A^(1/3)
where R₀ = 1.2×10⁻¹⁵ m = 1.2 fm (femtometre)
Nuclear density ρ ≈ 2.3×10¹⁷ kg/m³ = constant for all nuclei (independent of A!)
Mass Defect and Binding Energy
Mass defect: The actual nuclear mass is less than the sum of masses of constituent nucleons.
Δm = Z×m_p + N×m_n − M_nucleus
Binding Energy (BE): Energy equivalent of mass defect:
BE = Δm × c² (in Joules) BE = Δm × 931.5 MeV (Δm in atomic mass units, 1u = 931.5 MeV/c²)
Binding Energy per Nucleon
BE/A — average binding energy per nucleon; measures nuclear stability.
Key Features of BE/A vs A curve
| Region | A range | BE/A | Notes |
|---|---|---|---|
| Very light nuclei | A < 20 | Low (~1-7 MeV) | Peaks at ⁴He, ¹²C |
| Medium nuclei | A ≈ 56 | Maximum (~8.8 MeV) | Most stable (Fe, Ni) |
| Heavy nuclei | A > 100 | Decreasing (~7 MeV) | Less stable, fission possible |
Implications:
- Combining light nuclei (fusion) → more tightly bound → releases energy
- Splitting heavy nuclei (fission) → more tightly bound fragments → releases energy
1 atomic mass unit (u) = 1.66×10⁻²⁷ kg = 931.5 MeV/c²
Diagram Indicator: [Binding energy per nucleon vs mass number A curve; showing peak near A=56 (Fe), low values for light nuclei, and decrease for heavy nuclei; fusion and fission arrows labeled.]
Radioactivity: Alpha, Beta, Gamma Decay
Radioactivity
Radioactivity is the spontaneous emission of radiation from unstable nuclei. Discovered by Henri Becquerel (1896).
Three types of radiation: α (alpha), β (beta), γ (gamma)
Alpha (α) Decay
Emission of α-particle (⁴₂He nucleus):
ᴬZ X → ᴬ⁻⁴Z₋₂ Y + ⁴₂He
Example: ²³⁸₉₂U → ²³⁴₉₀Th + ⁴₂He
Properties of α-particles:
- Charge: +2e
- Mass: 4u (~4× proton mass)
- Speed: ~10⁷ m/s
- Range in air: ~2-8 cm
- Can be stopped by: Paper sheet
- Ionizing power: Highest
Beta (β) Decay
Two types:
β⁻ decay: Neutron → Proton + electron + antineutrino ᴬZ X → ᴬZ₊₁ Y + e⁻ + ν̄_e
β⁺ decay: Proton → Neutron + positron + neutrino ᴬZ X → ᴬZ₋₁ Y + e⁺ + ν_e
Properties of β-particles:
- Charge: ±e
- Mass: electron mass (9.11×10⁻³¹ kg)
- Speed: ~10⁸ m/s (near c)
- Range in air: ~1-2 m
- Can be stopped by: Aluminium (few mm)
- Ionizing power: Medium
Gamma (γ) Radiation
Emission of high-energy photons from excited nucleus:
**ᴬZ X → ᴬZ X + γ*
Properties of γ-radiation:
- No charge, no mass
- Speed: c (3×10⁸ m/s)
- Range: Very long (several meters in lead)
- Can be stopped by: Dense materials (lead, concrete)
- Ionizing power: Lowest
- Penetrating power: Highest
Comparison: α, β, γ
| Property | α | β | γ |
|---|---|---|---|
| Nature | He nucleus | Electron/Positron | Photon |
| Charge | +2e | ±e | 0 |
| Mass | 4u | ~0 | 0 |
| Speed | ~10⁷ m/s | ~10⁸ m/s | c |
| Ionization | High | Medium | Low |
| Penetration | Low | Medium | High |
| Stopped by | Paper | Al (3mm) | Thick lead |
Radioactive Decay Law
The rate of decay is proportional to the number of undecayed nuclei:
dN/dt = −λN
N = N₀e^(−λt) where λ = decay constant
Half-life: T₁/₂ = ln2/λ = 0.693/λ
Mean life: τ = 1/λ = T₁/₂/0.693 = 1.44 T₁/₂
Activity: A = λN = A₀e^(−λt); Unit: Becquerel (Bq) = 1 decay/s 1 Curie = 3.7×10¹⁰ Bq
Diagram Indicator: [Exponential decay curve N vs t showing N₀, N₀/2, N₀/4 at t=0, T₁/₂, 2T₁/₂; also nuclear equations showing α, β, γ emission with conservation of mass number and atomic number.]
Nuclear Fission and Fusion
Nuclear Fission
Fission is the splitting of a heavy nucleus into two medium-mass fragments with release of energy.
Example: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + Energy (~200 MeV)
Energy released per fission: ~200 MeV ≈ 3.2×10⁻¹¹ J
Comparison: Chemical reaction: ~few eV; Fission: ~200 MeV → 50 million times more energy per reaction!
Chain Reaction
Each fission releases 2-3 neutrons → each can cause more fissions → chain reaction.
Critical mass: Minimum mass of fissile material for sustained chain reaction.
Types:
- Controlled chain reaction (Nuclear reactor): One neutron on average causes next fission
- Uncontrolled chain reaction (Atom bomb): Supercritical, exponential growth
Nuclear Reactor Components
| Component | Material | Function |
|---|---|---|
| Fuel | ²³⁵U or ²³⁹Pu | Fissile material |
| Moderator | Heavy water, graphite | Slow down neutrons |
| Control rods | Boron, Cadmium | Absorb excess neutrons |
| Coolant | Heavy water, CO₂ | Remove heat, generate steam |
| Reflector | Beryllium, graphite | Reflect neutrons back |
Nuclear Fusion
Fusion is the combining of light nuclei to form a heavier nucleus with release of energy.
Solar fusion (pp chain): ⁴ × ¹H → ⁴₂He + 2e⁺ + 2ν + 26.7 MeV
Deuterium-Tritium reaction: ²H + ³H → ⁴He + ¹n + 17.6 MeV
Requirements: Temperature ~10⁷ − 10⁸ K (overcoming Coulomb repulsion)
Fission vs Fusion Comparison
| Property | Fission | Fusion |
|---|---|---|
| Process | Splitting heavy nucleus | Combining light nuclei |
| Fuel | ²³⁵U, ²³⁹Pu | ²H, ³H, ⁴He |
| Energy per nucleon | ~1 MeV/nucleon | ~3.5 MeV/nucleon (higher!) |
| Temperature needed | Low (room temp + neutron) | Very high (10⁸ K) |
| Products | Radioactive waste | Mostly helium (clean) |
| Controlled use | Yes (nuclear reactor) | Not yet achieved (research) |
| Uncontrolled | Atom bomb | Hydrogen bomb |
Stars as Fusion Reactors
The Sun converts ~4×10⁹ kg of mass to energy per second via fusion. P = 3.8×10²⁶ W (Sun's luminosity)
Diagram Indicator: [Nuclear fission chain reaction diagram showing ²³⁵U splitting into Ba and Kr, releasing 3 neutrons that cause 3 more fissions; also fusion diagram showing D+T → He+n with energy release labeled.]
Frequently asked questions
Are these Nuclei notes free?
Yes — the Nuclei notes for Physics (Class 12) on Siksha Sarovar are completely free to read, with no account required.
Do these notes follow CBSE and HBSE?
Yes. The Nuclei notes are NCERT-aligned and include guidance for both CBSE and Haryana Board (HBSE), with important questions and MCQs for revision.
What does the Nuclei chapter cover?
Concept explanations, key formulas and definitions, fully solved examples and board-pattern practice questions for Nuclei.