22.5.1 Nuclear Fusion | Nuclear Physics | Physics 12

What is Nuclear Fusion?

Nuclear fusion is the process in which two or more light nuclei combine to form a single, heavier, and more stable nucleus. This process releases a tremendous amount of energy.

$_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n + 17.6 MeV$

Fusion is the energy source of stars, including our Sun, where hydrogen nuclei fuse into helium through the proton-proton chain.

Why Does Fusion Release Energy?

The mass of the product nucleus is less than the sum of the masses of the reacting nuclei. This difference is called the mass defect ( $Δ m$ ).

According to Einstein's mass-energy equivalence:

$E = Δ m \cdot c^{2}$

This "missing" mass is converted into kinetic energy of the products, which manifests as heat and radiation.

Binding Energy and Fusion

The binding energy per nucleon (B.E./A) curve explains why fusion releases energy:

The curve peaks near iron-56 (~8.8 MeV/nucleon).
Light nuclei (low mass number $A$ ) have a lower B.E./A than nuclei near the peak.
When light nuclei fuse, the product has a higher B.E./A — meaning the nucleons are more tightly bound.
The system moves to a more stable configuration, releasing energy equal to the difference in total binding energies.

Key insight: Both fission (splitting heavy nuclei) and fusion (combining light nuclei) release energy because both processes move products toward the peak of the B.E./A curve.

Fusion vs. Fission: Energy per Nucleon

Process	Nuclei involved	Energy per nucleon
Fusion	Light (e.g., H, He)	Higher change in B.E./A
Fission	Heavy (e.g., U-235)	Lower change in B.E./A

Fusion typically releases more energy per nucleon than fission.

Conditions Required for Fusion

For two positively charged nuclei to fuse, they must overcome the Coulomb (electrostatic) repulsion between them. This requires:

Extremely high temperature — approximately $1 0^{7}$ K (tens of millions of kelvin). At these temperatures, nuclei have sufficient kinetic energy to approach each other close enough for the strong nuclear force to take over.
High pressure/density — to ensure frequent collisions between nuclei.

Because fusion requires such extreme heat, it is called a thermonuclear reaction.

The Deuterium–Tritium (D-T) Reaction

The most studied fusion reaction uses isotopes of hydrogen:

Deuterium ( $_{1}^{2} H$ ) — hydrogen with 1 neutron
Tritium ( $_{1}^{3} H$ ) — hydrogen with 2 neutrons

$_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n + 17.6 MeV$

Conservation checks:

Mass number: $2 + 3 = 4 + 1$ ✓
Atomic number: $1 + 1 = 2 + 0$ ✓

The 17.6 MeV of energy is released primarily as kinetic energy of the helium nucleus and neutron.

Calculating Energy Released

To calculate the energy released in a fusion reaction:

Find the mass defect: $Δ m = m_{reactants} - m_{products}$
Convert to energy: $E = Δ m \cdot c^{2}$
If $Δ m$ is in atomic mass units (u): use $1 u = 931.5 MeV / c^{2}$

$E (MeV) = Δ m (u) \times 931.5 MeV/u$

Worked Example

For the D-T reaction, given:

$m (_{1}^{2} H) = 2.01410 u$
$m (_{1}^{3} H) = 3.01605 u$
$m (_{2}^{4} He) = 4.00260 u$
$m (_{0}^{1} n) = 1.00867 u$

$Δ m = (2.01410 + 3.01605) - (4.00260 + 1.00867) = 0.01888 u$

$E = 0.01888 \times 931.5 \approx 17.6 MeV$

Fusion vs. Fission — Summary

Feature	Fusion	Fission
Nuclei involved	Light (H, He)	Heavy (U, Pu)
Energy source	Stars, H-bomb	Nuclear reactors, A-bomb
Conditions	$\sim 1 0^{7}$ K	Thermal neutrons + critical mass
Waste products	Helium (non-radioactive)	Radioactive fragments
Energy per nucleon	Higher	Lower

What is Nuclear Fusion?

Nuclear fusion is the process in which two or more light nuclei combine to form a single, heavier, and more stable nucleus. This process releases a tremendous amount of energy.

$_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n + 17.6 MeV$

Fusion is the energy source of stars, including our Sun, where hydrogen nuclei fuse into helium through the proton-proton chain.

Why Does Fusion Release Energy?

The mass of the product nucleus is less than the sum of the masses of the reacting nuclei. This difference is called the mass defect ( $Δ m$ ).

According to Einstein's mass-energy equivalence:

$E = Δ m \cdot c^{2}$

This "missing" mass is converted into kinetic energy of the products, which manifests as heat and radiation.

Binding Energy and Fusion

The binding energy per nucleon (B.E./A) curve explains why fusion releases energy:

The curve peaks near iron-56 (~8.8 MeV/nucleon).
Light nuclei (low mass number $A$ ) have a lower B.E./A than nuclei near the peak.
When light nuclei fuse, the product has a higher B.E./A — meaning the nucleons are more tightly bound.
The system moves to a more stable configuration, releasing energy equal to the difference in total binding energies.

Key insight: Both fission (splitting heavy nuclei) and fusion (combining light nuclei) release energy because both processes move products toward the peak of the B.E./A curve.

Fusion vs. Fission: Energy per Nucleon

Process	Nuclei involved	Energy per nucleon
Fusion	Light (e.g., H, He)	Higher change in B.E./A
Fission	Heavy (e.g., U-235)	Lower change in B.E./A

Fusion typically releases more energy per nucleon than fission.

Conditions Required for Fusion

For two positively charged nuclei to fuse, they must overcome the Coulomb (electrostatic) repulsion between them. This requires:

Extremely high temperature — approximately $1 0^{7}$ K (tens of millions of kelvin). At these temperatures, nuclei have sufficient kinetic energy to approach each other close enough for the strong nuclear force to take over.
High pressure/density — to ensure frequent collisions between nuclei.

Because fusion requires such extreme heat, it is called a thermonuclear reaction.

The Deuterium–Tritium (D-T) Reaction

The most studied fusion reaction uses isotopes of hydrogen:

Deuterium ( $_{1}^{2} H$ ) — hydrogen with 1 neutron
Tritium ( $_{1}^{3} H$ ) — hydrogen with 2 neutrons

$_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n + 17.6 MeV$

Conservation checks:

Mass number: $2 + 3 = 4 + 1$ ✓
Atomic number: $1 + 1 = 2 + 0$ ✓

The 17.6 MeV of energy is released primarily as kinetic energy of the helium nucleus and neutron.

Calculating Energy Released

To calculate the energy released in a fusion reaction:

Find the mass defect: $Δ m = m_{reactants} - m_{products}$
Convert to energy: $E = Δ m \cdot c^{2}$
If $Δ m$ is in atomic mass units (u): use $1 u = 931.5 MeV / c^{2}$

$E (MeV) = Δ m (u) \times 931.5 MeV/u$

Worked Example

For the D-T reaction, given:

$m (_{1}^{2} H) = 2.01410 u$
$m (_{1}^{3} H) = 3.01605 u$
$m (_{2}^{4} He) = 4.00260 u$
$m (_{0}^{1} n) = 1.00867 u$

$Δ m = (2.01410 + 3.01605) - (4.00260 + 1.00867) = 0.01888 u$

$E = 0.01888 \times 931.5 \approx 17.6 MeV$

Fusion vs. Fission — Summary

Feature	Fusion	Fission
Nuclei involved	Light (H, He)	Heavy (U, Pu)
Energy source	Stars, H-bomb	Nuclear reactors, A-bomb
Conditions	$\sim 1 0^{7}$ K	Thermal neutrons + critical mass
Waste products	Helium (non-radioactive)	Radioactive fragments
Energy per nucleon	Higher	Lower