Nuclear Fission and Fusion
Nuclear Fission and Fusion
Nuclear fission is the splitting of a heavy nucleus into two lighter nuclei, and nuclear fusion is the combining of light nuclei to form a heavier nucleus. Both processes release energy because the products have a higher binding energy per nucleon than the reactants.
Mass-Energy Equivalence
Einstein's equation: E = mc²
where:
- E = energy (J)
- m = mass (kg)
- c = speed of light = 3.00 × 10⁸ m s⁻¹
1 unified atomic mass unit (u) = 1.661 × 10⁻²⁷ kg = 931.5 MeV/c²
This means that 1 u of mass, if completely converted to energy, releases 931.5 MeV.
Nuclear Fission
Induced fission: A heavy nucleus (typically uranium-235 or plutonium-239) absorbs a slow (thermal) neutron and becomes unstable, splitting into two medium-mass fission fragments plus 2–3 neutrons and energy.
Example: ²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + energy
The energy released per fission is approximately 200 MeV (~3.2 × 10⁻¹¹ J).
Why Fission Releases Energy
The fission fragments (A ≈ 90–145) have a higher binding energy per nucleon than uranium-235. The increase in total binding energy is released as kinetic energy of the fragments and neutrons, plus gamma radiation.
Chain Reaction
The 2–3 neutrons released in each fission can cause further fissions, creating a chain reaction.
Critical mass: The minimum amount of fissile material needed to sustain a chain reaction. Below this, too many neutrons escape without causing fission.
Controlling the chain reaction in a nuclear reactor:
- Moderator (e.g., water, graphite): slows neutrons to thermal speeds so they are more likely to be absorbed by U-235 (slow neutrons have a much larger fission cross-section)
- Control rods (e.g., boron, cadmium): absorb neutrons to control the reaction rate
- Coolant (e.g., water, CO₂): transfers thermal energy away from the reactor core to produce steam for turbines
Reactor Components
| Component | Material | Purpose |
|---|---|---|
| Fuel rods | Enriched uranium (3–5% U-235) | Fissile material |
| Moderator | Water or graphite | Slow neutrons to thermal speeds |
| Control rods | Boron or cadmium | Absorb neutrons, control rate |
| Coolant | Water, heavy water, or CO₂ | Remove heat |
| Shielding | Concrete + steel | Absorb radiation |
Nuclear Fusion
Fusion is the joining of light nuclei to form a heavier nucleus. It is the process that powers stars.
Hydrogen fusion in stars (the proton-proton chain):
4¹₁H → ⁴₂He + 2⁰₁e + 2νₑ + energy
The overall mass defect: 4 × 1.007825 u − 4.002603 u = 0.02870 u
Energy released: 0.02870 × 931.5 = 26.7 MeV per helium-4 nucleus formed
Why Fusion is Difficult on Earth
To fuse, nuclei must overcome their electrostatic (Coulomb) repulsion. This requires:
1. Extremely high temperatures (~10⁷ to 10⁸ K) so nuclei have enough kinetic energy to approach closely — at these temperatures, matter exists as plasma
2. High density to increase the probability of collisions
3. Sufficient confinement time to allow enough fusions to occur
The Lawson criterion specifies the minimum product of density × confinement time for net energy gain.
Confinement Methods
- Magnetic confinement (e.g., tokamak): Plasma is contained by powerful magnetic fields in a doughnut-shaped (toroidal) chamber. ITER is a major international tokamak project.
- Inertial confinement: Powerful lasers compress a fuel pellet so rapidly that fusion occurs before the plasma can expand. The National Ignition Facility achieved net energy gain from fusion in 2022.
Comparing Fission and Fusion
| Feature | Fission | Fusion |
|---|---|---|
| Process | Heavy nucleus splits | Light nuclei join |
| Fuel | U-235, Pu-239 | Deuterium, tritium |
| Energy per nucleon | ~0.9 MeV | ~6.7 MeV (much more per unit mass) |
| Products | Radioactive fission fragments | Helium (non-radioactive) |
| Conditions | Moderate (needs neutron moderation) | Extreme temperature (~10⁸ K) |
| Waste | Long-lived radioactive waste | Minimal radioactive waste |
| Current status | Widely used in power stations | Not yet commercially viable |
| Weapons | Atomic bomb (A-bomb) | Hydrogen bomb (H-bomb, uses fission trigger) |
Worked Example — Energy from Fusion
Calculate the energy released when two deuterium nuclei fuse:
²₁H + ²₁H → ³₂He + ¹₀n
Masses: ²₁H = 2.01410 u, ³₂He = 3.01603 u, ¹₀n = 1.00867 u
Mass of reactants = 2 × 2.01410 = 4.02820 u
Mass of products = 3.01603 + 1.00867 = 4.02470 u
Δm = 4.02820 − 4.02470 = 0.00350 u
Energy = 0.00350 × 931.5 = 3.26 MeV
Stellar Nucleosynthesis
- Main sequence stars (like the Sun): fuse hydrogen to helium via the proton-proton chain
- Red giants: fuse helium to carbon (triple-alpha process) and heavier elements up to iron
- Supernovae: the extreme temperatures and pressures create elements heavier than iron (endothermic fusion, powered by gravitational collapse energy)
This explains why iron is relatively abundant in the universe and why elements heavier than iron are rarer — they can only be made in the most violent stellar events.
Safety and Environmental Considerations
Fission waste: High-level waste remains dangerously radioactive for thousands of years and must be stored in deep geological repositories. Spent fuel can be reprocessed to extract usable plutonium and uranium.
Fusion advantages: Fuel (deuterium from seawater) is virtually unlimited; no long-lived radioactive waste; no risk of meltdown (plasma simply disperses if containment fails); no carbon emissions.
Fusion challenges: Sustaining plasma at >100 million °C; achieving net energy gain; materials that can withstand intense neutron bombardment; scaling to commercial power output.