Nuclear Fusion

Nuclear fusion is the process by which two light atomic nuclei collide with enough energy to overcome their mutual electrostatic repulsion and merge into a single, heavier nucleus. The product nucleus has slightly less mass than the sum of the original nuclei, and that missing mass — called the mass defect — is converted into an enormous burst of energy according to Einstein's mass-energy equivalence, E = mc². Fusion is the engine powering every star in the universe, including our Sun, where roughly 600 million tonnes of hydrogen are fused into helium every second. To appreciate why fusion releases energy, think of nuclear binding energy as a kind of 'savings account'. Light nuclei like hydrogen have relatively little binding energy per nucleon, meaning their nucleons are not held together very tightly. When they fuse to form helium, the product sits much higher on the binding-energy-per-nucleon curve, meaning each nucleon is now in a more stable, lower-energy state. The difference in that 'account balance' is paid out as kinetic energy of the products and, ultimately, as radiation. Iron (Fe-56) sits at the peak of this curve — fusing anything heavier than iron actually costs energy rather than releasing it. On Earth, controlled fusion has been pursued as a potential clean energy source for decades. Experimental reactors like ITER (under construction in France) aim to fuse deuterium and tritium — two heavy isotopes of hydrogen — at temperatures exceeding 150 million °C, held in place by powerful magnetic fields. Unlike nuclear fission, fusion produces no long-lived radioactive waste and uses fuel derived from seawater, making it one of the most exciting frontiers in modern energy research.

Key takeaways

The Coulomb Barrier
The Proton–Proton Chain (in Stars)
Mass Defect and Energy Release
D–T Fusion: The Practical Terrestrial Reaction

The Coulomb Barrier

Two protons both carry positive charge, so they repel each other electrostatically. To fuse, they must be brought within about 1 femtometre (10⁻¹⁵ m) of each other — the range of the strong nuclear force. The electrostatic potential energy at that separation is on the order of 1 MeV, which corresponds to temperatures above 10 billion Kelvin classically. Stars manage to fuse at 'only' 15 million K because of quantum tunnelling: protons have a small but non-zero probability of tunnelling through the Coulomb barrier without having enough classical energy to surmount it.

The Proton–Proton Chain (in Stars)

The dominant fusion pathway in Sun-like stars is the proton–proton (pp) chain. In the first step, two protons fuse: ¹H + ¹H → ²H + e⁺ + νₑ (a deuteron, a positron, and a neutrino are produced). Next, ²H + ¹H → ³He + γ. Finally, two helium-3 nuclei combine: ³He + ³He → ⁴He + 2¹H. The net reaction is 4¹H → ⁴He + 2e⁺ + 2νₑ + 2γ, releasing about 26.7 MeV per cycle. The neutrinos escape the Sun almost instantly, while the gamma rays diffuse outward over thousands of years before emerging as sunlight.

Mass Defect and Energy Release

The mass of a helium-4 nucleus (4.0015 u) is less than the mass of four separate protons (4 × 1.00728 u = 4.02912 u). The mass defect is Δm = 4.02912 − 4.0015 = 0.02762 u. Converting: 1 atomic mass unit = 931.5 MeV/c², so the energy released is 0.02762 × 931.5 ≈ 25.7 MeV (the remainder goes to neutrinos that escape). This is about 7 million times the energy released by burning the equivalent mass of chemical fuel.

D–T Fusion: The Practical Terrestrial Reaction

For man-made reactors, the easiest fusion reaction to achieve is deuterium–tritium (D–T) fusion: ²H + ³H → ⁴He + n + 17.6 MeV. This reaction has the highest cross-section (reaction probability) at achievable temperatures (~150 million K). The 17.6 MeV is split between the alpha particle (3.5 MeV) and the neutron (14.1 MeV). The alpha particle heats the plasma to sustain the reaction; the neutron's energy is absorbed by a surrounding 'blanket' to generate steam and electricity. Tritium itself is rare and must be bred from lithium inside the reactor: ⁶Li + n → ⁴He + ³H.

The Key Equation

E = \Delta m \, c^2 = (m_{\text{reactants}} - m_{\text{products}})c^2

E — Energy released (Joules (J) or MeV): The energy liberated as kinetic energy of products and gamma-ray photons.
\Delta m — Mass defect (kilograms (kg) or atomic mass units (u)): The difference between the total rest mass of the reactant nuclei and the total rest mass of the product nuclei.
c — Speed of light (m s⁻¹): Approximately 3 × 10⁸ m s⁻¹. Because c² ≈ 9 × 10¹⁶ m² s⁻², even a tiny mass defect releases enormous energy.

Worked Example

Problem. In the D–T fusion reaction ²₁H + ³₁H → ⁴₂He + ¹₀n, the exact nuclear masses are: deuterium = 2.01355 u, tritium = 3.01550 u, helium-4 = 4.00151 u, neutron = 1.00867 u. Calculate the energy released in MeV. (1 u = 931.5 MeV/c²)

E = 0.01887 \, \text{u} \times 931.5 \, \frac{\text{MeV}}{\text{u}} \approx 17.6 \, \text{MeV}

Answer. Approximately 17.6 MeV is released per D–T fusion event.

Figure

Diagram

Origins · 1 minHans Bethe and how this was discovered

Hans Bethe

1906–2005 · German-American

Hans Bethe worked out the detailed nuclear reaction cycles powering the stars. In 1938–1939 he identified two primary mechanisms: the proton–proton chain (dominant in stars like the Sun) and the CNO cycle (dominant in more massive, hotter stars), explaining quantitatively why stars shine. This work earned him the 1967 Nobel Prize in Physics. Bethe was still publishing original research papers on stellar physics and supernovae well into his 90s, making him one of the most productive physicists of any age in history.

Nuclear Fission — Fission is the splitting of heavy nuclei and is the conceptual counterpart to fusion. Both release energy via mass defect but from opposite ends of the binding-energy curve.
Nuclear Binding Energy — The binding energy per nucleon curve directly explains why fusion of light nuclei releases energy — understanding it is essential to understanding why fusion works.
Mass–Energy Equivalence (E = mc²) — All fusion energy calculations depend on converting mass defect into energy via Einstein's famous relation.
Radioactive Decay — Tritium, the fuel in D–T fusion, is radioactive and decays by beta emission — understanding decay is needed to handle fusion fuel safely.