Nuclear Fusion Explained: Concepts, Equations & Fusion vs Fission

Nuclear fusion is a fundamental process in physics where two light atomic nuclei combine to form a single heavier nucleus, with the simultaneous release of energy. This process is responsible for the vast amount of energy radiated by stars, including our Sun. The large energy output from fusion comes from the transformation of some nuclear mass into energy, governed by the binding energy of the nucleus.
Fusion reactions primarily occur between elements with low atomic numbers—mainly various forms of hydrogen. When these light nuclei interact at extremely high temperatures and pressures, the attractive nuclear force overcomes the repulsive electrostatic force between them, resulting in fusion and a considerable energy release.
Understanding nuclear fusion involves both theoretical knowledge and practical applications, especially in fields like astrophysics and the ongoing quest for clean energy production on Earth.

Detailed Explanation of Nuclear Fusion and Its Principles

The essence of nuclear fusion lies in the nucleus's binding energy. Binding energy is the energy required to separate a nucleus into its constituent protons and neutrons, or conversely, the energy released when these nucleons bind to form a nucleus. The higher the binding energy per nucleon, the more stable the nucleus.
For lighter elements than iron, fusing nuclei results in a higher binding energy per nucleon in the combined nucleus than in the original nuclei, so energy is released. Fusion of heavy elements, beyond iron, requires energy input and is not naturally exothermic.
The energy released in a fusion reaction can be calculated based on the difference in mass between the reactants and the products, applying Einstein’s mass-energy equivalence principle E = mc².

Binding Energy Formula

The binding energy (B) of a nucleus with Z protons and N neutrons (A = Z + N) is given by:

where:
A higher value of binding energy per nucleon means a more stable nucleus. Iron has the maximum binding energy per nucleon, which is a key reason behind the trends in both fusion and fission processes.

Key Fusion Reactions: Examples and Equations

In astrophysics and fusion research, two main fusion reactions have great significance:

• Deuterium-Tritium (D-T) Fusion:
  This reaction occurs between deuterium (²H) and tritium (³H), both heavy isotopes of hydrogen.
  Equation:
  D + T → He + n
  (Deuterium + Tritium → Helium + Neutron)
• Hydrogen-Hydrogen Fusion (Initiates Star Burning):
  The initial reaction within stars fuses two regular hydrogen nuclei (protons) to form deuterium, a positron, and a neutrino.
  Equation:
  H + H → D + β⁺ + ν
  (Hydrogen + Hydrogen → Deuterium + Positron + Neutrino)

Both reactions are exoergic, meaning they release energy.

Fusion Reaction Table

Reaction	Description	Energy Release	Where it Occurs
D + T → He + n	Deuterium & Tritium combining	Very high	Experimental fusion, stars
H + H → D + β+ + ν	Hydrogen nuclei fusing in stars	Lesser than D-T, but key for stars	Sun and other stars

Types of Fusion Reactions

Fusion reactions can be categorized into two main types:

• Reactions that preserve the number of protons and neutrons. These reactions, such as D + T → He + n, are crucial for practical fusion energy production.
• Reactions that convert protons to neutrons or vice versa, usually occurring in stellar environments to start the star “burning” phase, like H + H → D + β⁺ + ν.

Both types yield energy, but for practical energy on Earth, the D-T reaction is preferred due to its higher reaction rate and significantly larger energy output per reaction compared to the hydrogen-hydrogen process.

Step-by-Step Approach to Solving Fusion Problems

• Identify and write the nuclear reaction equation clearly.
• Determine the number of protons and neutrons on both sides to ensure balance.
• Calculate the mass difference (mass of reactants minus mass of products).
• Use the energy-mass equivalence formula, E = Δm c², where Δm is in kilograms and c is the speed of light.
• The calculated energy is the energy released during the fusion reaction.

Step	Description
1	Write the balanced fusion reaction equation.
2	Verify conservation of nucleon numbers.
3	Compute the mass defect (Δm).
4	Apply E = Δm c2 for released energy.
5	Interpret the result in the problem context.

Key Fusion Formulas

Formula	Description	Application
B = (Z mp + N mn − M) c2	Nuclear binding energy	Calculates binding energy per nucleus
E = Δm c2	Mass-energy equivalence	Finds energy released in fusion/fission

Practical Relevance and Applications

Nuclear fusion is the source of energy in all stars. The Sun, for example, sustains its radiance and thermal output via fusion of hydrogen nuclei into helium deep within its core. Attempts to harness fusion for clean energy on Earth focus on the D-T reaction due to its higher yield.
Understanding binding energy and the fusion process is also essential for explaining why elements lighter than iron release energy when fused, while heavier ones do not.
For a clear distinction between fusion and fission, visit the nuclear fission topic page.

Further Reading and Practice

For more detailed explanations, solved examples, and questions on related nuclear topics, check resources on:

• Nuclear Fusion
• Nuclear Fusion Reactor
• Source of Energy
• Binding Energy
• Nuclear Binding Energy
• Mass-Energy Equivalence

Continue your learning journey on related Physics topics including Atomic Physics, Isotopes, Nuclear Reactors, and more using Vedantu’s structured resources and practice questions.