Nuclear Fusion
Nuclear fusion is a nuclear reaction in which two light atomic nuclei (typically isotopes of hydrogen — deuterium and tritium) combine to form a heavier nucleus, releasing an enormous amount of energy. The energy released greatly exceeds that of fission per unit mass, and the fuel (hydrogen isotopes) is abundant, making fusion the energy source of stars including the Sun. Fusion requires extremely high temperatures (tens of millions of kelvin) to overcome the Coulomb repulsion between positively charged nuclei, which is why sustaining controlled fusion on Earth for power generation remains a major technological challenge being pursued by projects such as ITER and NIF.
Key Formula
²H (D) + ³H (T) → ⁴He + n + 17.6 MeV
LaTeX: \text{D} + \text{T} \rightarrow \text{He-4} + n + 17.6 \text{ MeV}
| Symbol | Meaning | Unit |
|---|---|---|
| D (²H) | Deuterium nucleus (1 proton, 1 neutron) | atomic mass units (u) |
| T (³H) | Tritium nucleus (1 proton, 2 neutrons) | atomic mass units (u) |
| ⁴He | Helium-4 nucleus (alpha particle), 3.52 MeV kinetic energy | MeV |
| n | Fast neutron, 14.06 MeV kinetic energy | MeV |
| 17.6 MeV | Total energy released per fusion event | MeV |
Worked Example
Problem
Compare the energy density of D-T nuclear fusion with chemical combustion of hydrogen (H₂ + ½O₂ → H₂O releases 286 kJ/mol). How many times more energy per kg of fuel does fusion provide?
Solution
Step 1: D-T fusion releases 17.6 MeV per reaction. Molar mass of D + T ≈ 2 + 3 = 5 g/mol. Step 2: Energy per mole of D-T = 17.6 MeV × 6.022 × 10²³ / mol = 1.059 × 10²⁵ MeV/mol. Step 3: Convert to J/mol: 1.059 × 10²⁵ × 1.602 × 10⁻¹³ J = 1.697 × 10¹² J/mol. Step 4: Energy per kg of D-T = 1.697 × 10¹² J/mol / (5 × 10⁻³ kg/mol) = 3.39 × 10¹⁴ J/kg. Step 5: Hydrogen combustion: 286 kJ/mol, molar mass 2 g/mol → 1.43 × 10⁸ J/kg. Step 6: Ratio = 3.39 × 10¹⁴ / 1.43 × 10⁸ ≈ 2.37 × 10⁶.
Answer
D-T fusion releases ~2.4 million times more energy per kg than hydrogen combustion; 1 kg of D-T fuel ≈ 339 TJ
Key Nuclear Fusion Reactions and Their Energy Output
| Reaction | Reactants | Products | Energy Released | Ignition Temperature |
|---|---|---|---|---|
| D-T fusion | Deuterium + Tritium | ⁴He + neutron | 17.6 MeV | ~150 million K |
| D-D fusion | Deuterium + Deuterium | ³He + n or T + p | 3.27 or 4.03 MeV | ~400 million K |
| D-³He fusion | Deuterium + He-3 | ⁴He + proton | 18.3 MeV | ~600 million K |
| p-p chain | Proton + Proton (Sun) | ²H + e⁺ + ν_e | 1.44 MeV (step 1) | ~15 million K (Sun core) |
| CNO cycle | H via C/N/O catalysis | ⁴He + 2e⁺ + 2ν | ~26 MeV total | >20 million K |
| Li-6 + D | Lithium-6 + Deuterium | 2 ⁴He | 22.4 MeV | Used in H-bombs |
Interactive Tools
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Related Terms
Nuclear Fission
Nuclear fission is a nuclear reaction in which a heavy atomic nucleus (such as uranium-235 or plutonium-239) splits into two or more lighter nuclei, releasing a large amount of energy and typically two or three neutrons. The energy released comes from the binding energy difference between the original nucleus and the products, as described by Einstein's mass-energy equivalence (E = mc²). Controlled fission is the basis of nuclear power plants, while uncontrolled rapid fission is the mechanism of nuclear (fission) bombs.
Mass-Energy Equivalence
Mass-energy equivalence is the principle, derived from Einstein's special theory of relativity, stating that mass and energy are two forms of the same physical quantity and can be converted into each other. Expressed by the famous equation E = mc², it reveals that even a small amount of mass corresponds to an enormous amount of energy, since c² (the square of the speed of light) is approximately 9 × 10¹⁶ m²/s². This principle underlies the energy released in nuclear fission and fusion reactions, and explains the origin of stars' energy output.
Special Relativity
Special relativity is a physical theory proposed by Albert Einstein in 1905 that describes the relationship between space and time for objects moving at constant velocities, particularly near the speed of light. It is founded on two postulates: the laws of physics are identical in all inertial frames of reference, and the speed of light in a vacuum is constant for all observers regardless of their motion. The theory reveals that time, length, and mass are not absolute but depend on the relative motion between observer and object, unifying space and time into a single four-dimensional continuum called spacetime.
From Latin "fusio" (melting, pouring), from "fundere" (to pour, to melt). The term was adopted by analogy with metals melting together. The scientific concept of nuclear fusion as the energy source of stars was proposed by Arthur Eddington in 1920 and developed theoretically by Hans Bethe (Nobel Prize 1967) who described the proton-proton chain and CNO cycle in 1939.