What Is Nuclear Fusion
Nuclear fusion is the process in which two light nuclei combine, or fuse, to form a single heavier nucleus. NCERT (§13.7.2) states it directly: when two light nuclei fuse to form a larger nucleus, energy is released, since the larger nucleus is more tightly bound. NIOS (§27.4) gives the same definition — the process in which two light nuclei combine to form a heavier nucleus is called nuclear fusion — and notes that the fusion of hydrogen nuclei into helium is the source of energy of all stars, including our Sun.
Fusion is, in a sense, the mirror image of fission. In fission, a single heavy nucleus splits into two intermediate-mass fragments; in fusion, two light nuclei merge upwards in mass. Both processes move nuclei towards the peak of the binding-energy-per-nucleon curve, and both release energy when they do so. Fusion, however, operates at the light end of the chart, taking nuclei such as hydrogen and its isotopes towards helium.
The contrast with chemical burning is stark. NIOS notes that one gram of deuterium yields about 100,000 kW·h of energy, and NCERT reminds us that nuclear processes release energies of the order of MeV per event, roughly a million times larger than the few electron-volts of a chemical reaction. The energy that has lit the Sun for some five billion years is fusion energy.
Why Fusion Releases Energy
The reason fusion liberates energy lies entirely in the binding-energy-per-nucleon curve. NCERT (§13.4.2, observation iv) puts it precisely: when two very light nuclei (A ≤ 10) join to form a heavier nucleus, the binding energy per nucleon of the fused heavier nucleus is more than that of the lighter nuclei. The final system is more tightly bound than the initial one, so energy is released.
The link between binding and energy release runs through the mass defect. The greater the binding energy of a bound system, the less its total mass. If light nuclei with relatively low total binding energy transform into a heavier nucleus with greater binding energy, the surplus appears as released energy — kinetic energy of products and radiation. This is why both fission of a heavy nucleus and fusion of light nuclei are exothermic: both end nearer the binding-energy peak at A = 56, where the curve maxes out at about 8.75 MeV per nucleon.
Fusion joins LIGHT nuclei; fission splits HEAVY ones
A common error is to assume any nuclear reaction that releases energy must be fission, or to apply fusion to mid/heavy nuclei. Energy release on the binding-energy curve only works towards the peak. Fusion is favourable for light nuclei (A below the peak, A < 56); fission is favourable for heavy nuclei (A above the peak, A > 170). Elements more massive than those near the peak cannot be synthesised by fusion — NCERT states this explicitly.
Remember: Fusion = light nuclei merge upward; per-nucleon energy released is higher than in fission; fusion powers the stars.
The Coulomb Barrier and High Temperature
For fusion to occur, the two nuclei must approach to within a few femtometres so that the short-range attractive nuclear force can act. The obstacle is that both nuclei are positively charged and therefore repel each other electrostatically. They must carry enough kinetic energy to overcome this Coulomb barrier. NCERT notes the barrier height depends on the charges and radii of the interacting nuclei; for two protons it is about 400 keV, and is higher for nuclei of higher charge. NIOS gives a comparable picture: the Coulomb barrier is about 3 MeV for carbon nuclei and 20 MeV for lead.
Where does this energy come from? In a star, it comes from heat. NCERT estimates the temperature at which protons in a gas would, on average, have enough thermal energy to clear the barrier by setting $\tfrac{3}{2}kT = K \simeq 400\ \text{keV}$, which gives $T \sim 3\times10^{9}\ \text{K}$. When fusion is achieved by raising the temperature so that particles acquire sufficient kinetic energy to overcome the Coulomb repulsion, it is called thermonuclear fusion.
Fusion needs a barrier crossing; fission is triggered by a neutron that feels no Coulomb barrier. See how the other half works in Nuclear Fission.
Fusion Reactions and Their Q-Values
NCERT (§13.7.2) lists several energy-liberating fusion reactions among hydrogen isotopes. In the first, two protons combine to form a deuteron and a positron; in the second, two deuterons combine to form light helium; in the third, two deuterons combine to give a triton and a proton. Each releases a definite Q-value of energy:
| Fusion reaction | Products | Energy released (Q) |
|---|---|---|
| $^{1}_{1}\text{H} + {}^{1}_{1}\text{H}$ | $^{2}_{1}\text{H} + e^{+} + \nu$ | 0.42 MeV |
| $^{2}_{1}\text{H} + {}^{2}_{1}\text{H}$ | $^{3}_{2}\text{He} + n$ | 3.27 MeV |
| $^{2}_{1}\text{H} + {}^{2}_{1}\text{H}$ | $^{3}_{1}\text{H} + {}^{1}_{1}\text{H}$ | 4.03 MeV |
These reactions all conserve the number of protons and the number of neutrons separately (with the proviso that a positron and neutrino accompany the conversion of a proton into a neutron). The released energy first appears as kinetic energy of the products. NIOS works the deuteron-deuteron route through binding energies, taking the binding energy of a deuteron as 2.22 MeV per nucleus, so that $^{2}_{1}\text{H} + {}^{2}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He}$ releases roughly $Q \approx 28.3 - 4.44 \approx 24\ \text{MeV}$.
Using NCERT's reaction $^{2}_{1}\text{H} + {}^{2}_{1}\text{H} \rightarrow {}^{3}_{2}\text{He} + n + 3.27\ \text{MeV}$, estimate how long a 100 W lamp could be kept glowing by fusing 2.0 kg of deuterium. (NCERT Exercise 13.8.)
Each reaction consumes 2 deuterium atoms and releases 3.27 MeV. The number of deuterium atoms in 2.0 kg is $N = \dfrac{2000}{2.0} \times 6.023\times10^{23} \approx 6.02\times10^{26}$. The number of fusion events is $N/2 \approx 3.01\times10^{26}$.
Total energy $E = 3.01\times10^{26} \times 3.27\ \text{MeV} \times 1.6\times10^{-13}\ \text{J/MeV} \approx 1.58\times10^{14}\ \text{J}$.
Time $t = \dfrac{E}{P} = \dfrac{1.58\times10^{14}}{100} \approx 1.58\times10^{12}\ \text{s} \approx 5\times10^{4}\ \text{years}$. The point is the sheer magnitude — a few kilograms of light fuel hold staggering energy.
Fusion in the Sun: the Proton-Proton Cycle
Thermonuclear fusion is the source of energy output in the interior of stars. NCERT notes the Sun's interior temperature is about $1.5\times10^{7}\ \text{K}$, which is in fact considerably less than the $\sim3\times10^{9}\ \text{K}$ estimated for protons of average energy to clear the barrier. Fusion in the Sun therefore proceeds through the rare protons whose energies sit far above the average, and through the high density of the core. The fuel of the Sun is the hydrogen in its core, burned into helium through a multi-step proton-proton (p, p) cycle.
| Step | Reaction | Energy |
|---|---|---|
| (i) | $^{1}_{1}\text{H} + {}^{1}_{1}\text{H} \rightarrow {}^{2}_{1}\text{H} + e^{+} + \nu$ | 0.42 MeV |
| (ii) | $e^{+} + e^{-} \rightarrow \gamma + \gamma$ | 1.02 MeV |
| (iii) | $^{2}_{1}\text{H} + {}^{1}_{1}\text{H} \rightarrow {}^{3}_{2}\text{He} + \gamma$ | 5.49 MeV |
| (iv) | $^{3}_{2}\text{He} + {}^{3}_{2}\text{He} \rightarrow {}^{4}_{2}\text{He} + {}^{1}_{1}\text{H} + {}^{1}_{1}\text{H}$ | 12.86 MeV |
For step (iv) to occur, the first three steps must each happen twice, so that two helium-3 nuclei are available to unite into ordinary helium-4. Combining $2(\text{i}) + 2(\text{ii}) + 2(\text{iii}) + (\text{iv})$, the net effect is that four hydrogen nuclei combine to form one $^{4}_{2}\text{He}$ nucleus with a release of 26.7 MeV:
$4\,{}^{1}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + 2e^{+} + 2\nu + 2\gamma + 26.7\ \text{MeV}$
Helium is not the only element a star can synthesise. NCERT explains that as the core hydrogen is depleted into helium, the core cools and begins to collapse under gravity, which raises its temperature. If the temperature reaches about $10^{8}\ \text{K}$, helium nuclei fuse into carbon, and this kind of process can build progressively heavier elements — though nothing more massive than those near the binding-energy peak can be produced by fusion. The age of the Sun is about $5\times10^{9}$ years, with enough hydrogen to keep it going for roughly another five billion years before it cools, collapses and swells into a red giant.
Controlled Thermonuclear Fusion
The natural thermonuclear process in a star is replicated, on the ground, in a thermonuclear fusion device. NCERT (§13.7.3) describes the goal of a controlled fusion reactor: to generate steady power by heating the nuclear fuel to a temperature in the range of $10^{8}\ \text{K}$. The favoured fuel is a mixture of deuterium and tritium. At these temperatures the fuel is no longer an ordinary gas but a plasma — a mixture of positive ions and electrons.
The central engineering challenge is confinement. No material container can withstand a temperature of $10^{8}\ \text{K}$, so the plasma must be held away from any wall, typically by strong magnetic fields in a doughnut-shaped device called a tokamak. NIOS adds the further difficulty that maintaining such high temperatures continuously, while keeping the reactants together, has not yet been fully solved. NCERT notes that several countries, including India, are developing these techniques, and that successful fusion reactors would hopefully supply almost unlimited power to humanity, since deuterium is abundant in the oceans.
Temperature figures: Sun's core vs reactor vs barrier estimate
Three different temperatures are easy to confuse. The Sun's core is about $1.5\times10^{7}\ \text{K}$ (NCERT) — lower than the $\sim3\times10^{9}\ \text{K}$ that NCERT estimates for average-energy protons to clear the barrier. A ground-based controlled reactor aims for about $10^{8}\ \text{K}$. NIOS quotes around 10–20 million kelvin for the deuteron-deuteron reaction to start.
Anchor value: Sun's interior ≈ $1.5\times10^{7}\ \text{K}$; controlled fusion reactor target ≈ $10^{8}\ \text{K}$.
Fusion Versus Fission
NEET frequently asks students to distinguish the two great energy-releasing nuclear processes. Both move towards the binding-energy peak and both release MeV-scale energy, but they differ in fuel, mechanism and per-nucleon yield. NIOS makes the per-nucleon point quantitatively: energy released per nucleon in deuteron-deuteron fusion is about 6 MeV, nearly seven times the per-nucleon energy of a fission event (about $200/238 \approx 0.83$ MeV per nucleon).
| Feature | Nuclear fusion | Nuclear fission |
|---|---|---|
| Process | Two light nuclei combine into a heavier one | A heavy nucleus splits into intermediate fragments |
| Typical fuel | Hydrogen isotopes (deuterium, tritium) | Heavy nuclei such as $^{235}_{92}\text{U}$ |
| Trigger | Very high temperature to cross the Coulomb barrier | Absorption of a (slow) neutron; no Coulomb barrier |
| Energy per event | 26.7 MeV for $4\,^{1}\text{H} \rightarrow {}^{4}\text{He}$ | ≈ 200 MeV per fissioning uranium nucleus |
| Energy per nucleon | Higher (≈ 6 MeV/nucleon, NIOS) | Lower (≈ 0.83 MeV/nucleon, NIOS) |
| Occurs in nature | Cores of stars, including the Sun | Reactors; rare natural occurrence |
Nuclear Fusion in one screen
- Definition: two light nuclei combine into a heavier, more tightly bound nucleus, releasing energy.
- Why energy: binding energy per nucleon increases towards the peak (≈ A 56); the surplus binding energy is released.
- Coulomb barrier: ≈ 400 keV for two protons; nuclei need high kinetic energy to cross it — hence very high temperature (thermonuclear fusion).
- In the Sun: the proton-proton cycle burns hydrogen to helium; net $4\,^{1}\text{H} \rightarrow {}^{4}\text{He}$ releases 26.7 MeV. Core temperature ≈ $1.5\times10^{7}\ \text{K}$.
- Controlled fusion: deuterium-tritium plasma heated to ≈ $10^{8}\ \text{K}$; confinement (tokamak) is the main challenge.
- Vs fission: fusion uses light nuclei and releases more energy per nucleon (≈ 6 MeV vs ≈ 0.83 MeV, NIOS).