Chapter 9 - Fission and Fusion

9.1 Nuclear Fission and Energy

• In 1905, Albert Einstein theorised that mass (m) and energy (E) are equivalent through the equation E = mc².

• This led to the realisation of vast amounts of energy in atomic nuclei.

• Nuclear fission was realised in 1945 with the first atomic bomb explosion in New Mexico, USA

• This section explores nuclear fission and the energy it unleashes.

Inside the Nucleus

• Current understanding of the nucleus comes from early 20th-century work by scientists like Becquerel, Rutherford, Chadwick, Geiger, Marsden, and Harkins

• Recall from Chapter 8: Strong nuclear force acts within the nucleus to overcome electrostatic repulsion between protons.

  • Nuclei are made of quarks held by gluons.

• Electrostatic vs strong nuclear forces

  

  • Protons repel each other via electrostatic force (longer range).

  • Strong nuclear force attracts at very short distances and holds nucleons together.

  • Example: Proton A repels proton B but is held by stronger attraction; proton A attracts and repels proton C but net stability due to adjacent nucleons.

Nuclear Fission

• Discovery of the neutron (James Chadwick, 1932) allowed exploration of larger nuclei.

• Neutrons are neutral → not repelled by positively charged nuclei → easily absorbed (Figure

• Nuclear fission: An atomic nucleus splits into two or more pieces, usually triggered by absorbing a neutron.

  

  • Fissile nuclides: Capable of undergoing fission after absorbing a neutron (mostly high atomic number elements, few in nature).

• Strong nuclear force: First proposed by Hideki Yukawa (1935); complex properties required mathematical modelling until 1975.

Fissile Materials and Release of Neutrons

• Common fissile nuclides: Uranium-235 and Plutonium-239.

  • Absorb slow-moving neutron (~2.2 km/s⁻¹) → become unstable → split.

• Uranium-238 and Thorium-232 are non-fissile (require very high-energy neutrons).

• Uranium: Heaviest naturally occurring element; isotopes formed ~6.6 billion years ago; radioactive decay contributes to Earth's core heat.

• Uranium-235 fission example:

  

  • Splits into two smaller nuclei + releases neutrons (average ~2.47 per fission).

  • Example: Krypton-91 + Barium-142 + 3 neutrons.

• Equation: ¹₀n + ²³⁵₉₂U → ⁹¹₃₆Kr + ¹⁴²₅₆Ba + ³₁₀n + energy

• Fission fragments (daughter nuclei): Krypton-91 and Barium-142.

• Plutonium-239: Average ~2.89 neutrons per fission (harder to induce fission than U-235).

Energy Released During Nuclear Reactions

• Mass of any nucleus < sum of individual nucleons (mass defect, Δm).

• Energy released from mass defect via Einstein’s equation: ΔE = Δmc² (where ΔE in joules, Δm in kg, c = 3.00 × 10⁸ m/s).

• Mass-energy equivalence:

  • Preferred units: dalton (Da) for mass (1 Da = 1.66 × 10⁻²⁷ kg); MeV for energy (mega electronvolts).

  • Conversion: ΔE (MeV) = Δm × 931 (where Δm in Da).

• Electronvolt (eV): Energy gained by electron accelerated by 1 volt = 1.60 × 10⁻¹⁹ J.

  • 1 MeV = 10⁶ eV.

• Typical fission energy release: ~200 MeV (mostly kinetic energy of fragments + neutrons + gamma radiation).

• Only ~0.1% of original mass converted to energy (e.g., 1 kg U-235 → ~0.999 kg remains).

Worked Examples and Calculations (Breakdown)

Products and Waste

• Fission products often radioactive → form high-level waste.

• Management depends on radiation type and decay.

Physics in Action: Enrico Fermi, Lise Meitner and Nuclear Fission

• Fermi: Bombarded U-238 with neutrons → produced transuranic elements (neptunium, plutonium).

• Hahn & Strassmann (1938): Found barium (lighter element) instead of heavier ones → fission insight.

• Meitner & Frisch: Explained energy release from mass defect.

• Fermi built first nuclear reactor (1942) producing ~200 W.

9.2 Chain Reactions and Nuclear Reactors

• Following discovery of nuclear fission, research focused on harnessing energy for both weapons and electricity.

• Section covers: chain reactions, fuels, reactors, waste storage.

Chain Reactions and Critical Mass

• Chain reaction: One fission releases 2–3 neutrons → each triggers more fissions → exponential increase.

  • Example: In U-235, rapid escalation in tiny fraction of a second (Figure 9.2.1: Uncontrolled chain reaction of uranium-235 nuclei — branching diagram showing neutron multiplication: 1 → 2 → 4 → 8 → 16...).

• In 1 kg U-235: ~8 × 10¹³ J energy released in ~1 millionth of a second (uncontrolled → explosion).

Nuclear Fuel

• Natural uranium: 99.3% U-238 (non-fissile), 0.7% U-235 (fissile).

• Enrichment: Increases U-235 proportion (difficult/expensive).

  • Methods: ultracentrifuge, electromagnetic, gaseous diffusion.

• Weapons: >90% U-235 (e.g., Hiroshima bomb: 40 kg at 95% purity).

• Reactors: ~4% U-235 (lower enrichment for safety/control).

Critical Mass

• Minimum fissile material for sustained chain reaction (depends on purity, shape, size).

• Subcritical: Too many neutrons escape (e.g., flat sheet).

• Supercritical: Sustains/explodes (e.g., spherical shape retains more neutrons)

• Larger pieces or better geometry → higher chance of sustained reaction.

Nuclear Reactors

• Since 1950s: Control fission for electricity (over 440 plants worldwide; ~10% global electricity).

• Australia: Exports uranium; operates OPAL research reactor (Lucas Heights) for medical isotopes (not power).

Thermal Nuclear Reactor (most common):

• Uses slow (thermal) neutrons for U-235 fission.

• Design elements:

  • Fuel rods: Pellets of enriched uranium in tubes (~3–5 m long; ~1000 per core).

  • Moderator: Slows neutrons (graphite, normal water, heavy water, CO₂).

  • Control rods: Absorb neutrons (cadmium/boron steel) — raise/lower to control rate.

  • Coolant: Removes heat (water, etc.) → steam for turbines.

  • Radiation shield: Concrete/steel/graphite to contain radiation.

Moderators (breakdown):

• Slow fast neutrons without absorbing too many.

• Heavy water: Best but expensive.

• Normal water: Cheap, common.

• Graphite: Good but less effective than water in some ways.

Putting It All Together:

• Core heat → primary coolant → steam → turbines → electricity.

Australia Context:

• No commercial power reactors; focuses on renewables + uranium exports.

• OPAL: Research/medical use.

PhysicsFile - Nuclear Disasters; Fukushima

• Fukushima (2011): Earthquake + tsunami → loss of cooling → meltdowns, hydrogen explosions, radiation release.

Management of Nuclear Waste

• Major challenge: Spent fuel rods (~25 tonnes/year per 1000 MW reactor).

• Waste types:

  • Low-level: Contaminated items (compacted/buried).

  • Intermediate-level: Reactor parts/sludges (solidified, trenches).

  • High-level: Fission products + transuranics (highly radioactive, long-lived).

• Storage: Cooling ponds → dry casks → geological repositories .

• Activity decreases over time.

(Physics in Action) - Generation IV Fission Reactors

• Improve safety, efficiency, sustainability, reduce waste/proliferation risk.

• Examples;

  • Gas-cooled fast reactor (GFR)

  • Lead-cooled fast (LFR)

  • Molten salt (MSR)

  • Sodium-cooled fast (SFR)

  • Supercritical water-cooled (SCWR)

  • Very high-temperature gas (VHTR)

9.3 Nuclear Fusion

• Nuclear fusion: Combining (fusing) small nuclei (e.g., hydrogen, helium) to form a larger nucleus.

• Releases more energy per nucleon than fission; powers the Sun and stars; no long-lived radioactive waste.

• Experimental reactors: ITER (France, delayed to ~2025+); NIF (USA) achieved "target gain" (more energy out than in for ignition) in 2022–2023

Energy and Mass Changes in Nuclear Fusion

• Fusion example: Two hydrogen-2 (deuterium) nuclei → helium-4 + energy

• Equation: ²₁H + ²₁H → ⁴₂He + energy.

• Mass defect (Δm): Total mass of reactants > products → converted to energy via ΔE = Δmc² (or ΔE = Δm × 931 in MeV/Da).

• Atomic & mass numbers conserved.

Challenges of Achieving Fusion

• Nuclei are positively charged → strong electrostatic repulsion (long-range).

• Need extremely high kinetic energy to overcome repulsion so strong nuclear force (short-range) can bind them.

• Requires temperatures of hundreds of millions °C (as in Sun's core) → plasma state.

• Energy barrier

Binding Energy

• Binding energy: Energy needed to separate nucleus into individual protons/neutrons (from mass defect).

• Binding energy per nucleon:

  

  • Peaks around iron (Fe-56) — most stable.

  • Light nuclei (e.g., H, He): Low binding energy → fusion releases energy (increases per nucleon).

  • Heavy nuclei (e.g., U): Fusion not favourable; fission releases energy.

• Small nuclei fuse → higher stability/energy release; large nuclei fission.

Worked Example 9.3.1

Fusion in the Sun and Stars

• Main reactions (Figure 9.3.7: Proton-proton chain):

  • ¹H + ¹H → ²H + e⁺ + ν (positron + neutrino).

  • Further steps produce ⁴He + energy.

• Sun: ~657 million tonnes H → 653 million tonnes He per second; tiny mass defect powers life on Earth for billions of years.

Nuclear Fusion Reactors

• Goal: Controlled fusion for clean power (deuterium from seawater — vast supply).

• Tokamak design (magnetic confinement of plasma) — e.g., ITER

• Challenges: Sustain 100+ million °C; contain plasma; net energy gain; materials durability.

• Progress: JET tokamak records; ITER aims for full operation ~2030s.

From the Big Bang to the First Stars

• Big Bang → rapid expansion → cooling → formation of protons, neutrons, light nuclei (H, He, Li) via fusion

• First stars: Gravitational collapse → high temperatures → fusion → heavier elements (up to iron) via supernovae.