Physics · Nuclei

Nuclear Fusion

Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus, releasing energy because the product is more tightly bound. Drawing on NCERT Class 12 §13.7.2–13.7.3 and NIOS §27.4, this note covers why fusion liberates energy, the Coulomb barrier and the high temperatures needed to overcome it, the proton-proton cycle that powers the Sun, and the deuterium-tritium fusion pursued in tokamaks. It is a recurring source of conceptual and Q-value questions in the NEET Nuclei chapter.

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.

Figure 1 A B A + B + Energy (MeV)
Two light nuclei A and B are forced together against their mutual repulsion; once close enough for the strong nuclear force to act, they fuse into a single, more tightly bound nucleus, releasing 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.

Figure 2 Mass number A → E_bn (MeV) peak ≈ A 56 ~8.75 MeV FUSION FISSION
Both fusion (climbing the curve from the light end) and fission (climbing it from the heavy end) move nuclei towards the binding-energy peak near A = 56, increasing binding energy per nucleon and releasing energy.
NEET Trap

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.

Figure 3 separation r → U(r) Coulomb barrier (~400 keV for p-p) nuclear well ~1/r repulsion
As two nuclei approach, Coulomb repulsion raises the potential energy to a peak — the barrier. Only nuclei with enough kinetic energy (supplied by high temperature) can cross it and fall into the deep attractive nuclear well, fusing.
Build the contrast

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 reactionProductsEnergy 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 $Q \approx 28.3 - 4.44 \approx 24\ \text{MeV}$.

Worked Example

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.

StepReactionEnergy
(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:

$4\,{}^{1}_{1}\text{H} \rightarrow {}^{4}_{2}\text{He} + 2e^{+} + 2\nu + 2\gamma + 26.7\ \text{MeV}$

Figure 4 p p p p ²H ²H ³He ³He ⁴He+ 2p 26.7 MeV
The proton-proton cycle: protons fuse pairwise into deuterons, which capture protons to make helium-3; two helium-3 nuclei then fuse into helium-4, returning two protons. The net burning of four hydrogen nuclei into one helium-4 releases 26.7 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.

NEET Trap

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).

FeatureNuclear fusionNuclear fission
ProcessTwo light nuclei combine into a heavier oneA heavy nucleus splits into intermediate fragments
Typical fuelHydrogen isotopes (deuterium, tritium)Heavy nuclei such as $^{235}_{92}\text{U}$
TriggerVery high temperature to cross the Coulomb barrierAbsorption of a (slow) neutron; no Coulomb barrier
Energy per event26.7 MeV for $4\,^{1}\text{H} \rightarrow {}^{4}\text{He}$≈ 200 MeV per fissioning uranium nucleus
Energy per nucleonHigher (≈ 6 MeV/nucleon, NIOS)Lower (≈ 0.83 MeV/nucleon, NIOS)
Occurs in natureCores of stars, including the SunReactors; rare natural occurrence
Quick Recap

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).

NEET PYQ Snapshot — Nuclear Fusion

The NEET Nuclei PYQ set carries no fusion-specific question; the cards below are concept checks built strictly from NCERT/NIOS values for this subtopic.

Concept

In the net proton-proton cycle of the Sun, four hydrogen nuclei combine to form one helium-4 nucleus. The total energy released is approximately:

  • (1) 0.42 MeV
  • (2) 3.27 MeV
  • (3) 26.7 MeV
  • (4) 200 MeV
Answer: (3) 26.7 MeV

NCERT §13.7.2: combining $2(\text{i})+2(\text{ii})+2(\text{iii})+(\text{iv})$ of the p-p cycle, four hydrogen atoms form one $^{4}_{2}\text{He}$ atom with a release of 26.7 MeV. The 200 MeV value belongs to fission, not fusion.

Concept

Why must the fuel in a fusion reaction be heated to very high temperatures (of order $10^{7}$–$10^{8}\ \text{K}$)?

  • (1) To melt the nuclei before they combine
  • (2) To give the positively charged nuclei enough kinetic energy to overcome the Coulomb barrier
  • (3) To split the heavy nuclei into fragments
  • (4) To slow neutrons so they are captured
Answer: (2)

Both fusing nuclei are positively charged and repel each other. They must approach within a few femtometres for the attractive nuclear force to act, which requires crossing the Coulomb barrier (≈ 400 keV for two protons, NCERT). High temperature supplies this kinetic energy — thermonuclear fusion. Option (4) describes fission moderation.

Concept

According to NIOS, the energy released per nucleon in deuteron-deuteron fusion compared with a fission event is approximately:

  • (1) The same
  • (2) About seven times larger in fusion
  • (3) About seven times larger in fission
  • (4) Negligible in both
Answer: (2)

NIOS §27.4: fusion releases about 6 MeV per nucleon, against about $200/238 \approx 0.83$ MeV per nucleon for fission — roughly seven times more. Per unit mass of fuel, fusion is the more energetic process.

FAQs — Nuclear Fusion

High-yield clarifications grounded in NCERT §13.7.2–13.7.3 and NIOS §27.4.

What is nuclear fusion?
Nuclear fusion is the process in which two light nuclei combine to form a heavier nucleus, with the release of energy. Because the larger product nucleus is more tightly bound — its binding energy per nucleon is higher than that of the light reactants — the surplus binding energy appears as released energy. Fusion of hydrogen nuclei into helium is the source of energy of all stars, including the Sun.
Why does nuclear fusion require very high temperatures?
Both fusing nuclei are positively charged, so they experience strong Coulomb repulsion as they approach. They must come close enough — within a few femtometres — for the short-range attractive nuclear force to act, and to do this they must overcome the Coulomb barrier. The barrier height for two protons is about 400 keV. Heating the fuel to temperatures of order 10⁷ K and above gives the nuclei enough kinetic energy to overcome this barrier. Fusion driven by high temperature is called thermonuclear fusion.
What is the proton-proton (p-p) cycle in the Sun?
The proton-proton cycle is the multi-step set of reactions by which hydrogen is burned into helium in the Sun's core. Two protons fuse to form a deuteron, a positron and a neutrino (releasing 0.42 MeV); the positron annihilates with an electron; a deuteron and proton fuse to give light helium-3 plus a gamma ray; finally two helium-3 nuclei fuse to ordinary helium-4 and two protons. The net effect is that four hydrogen nuclei combine to form one helium-4 nucleus with a release of 26.7 MeV of energy.
How much energy is released when four hydrogen nuclei fuse into helium in the Sun?
In the net proton-proton cycle, four hydrogen atoms combine to form one helium-4 atom with a release of 26.7 MeV of energy, accompanied by two positrons (which annihilate), neutrinos and gamma rays. This is the energy that ultimately sustains the Sun.
What is controlled thermonuclear fusion and why is it difficult?
Controlled thermonuclear fusion aims to generate steady power by heating nuclear fuel — typically deuterium and tritium — to temperatures in the range of 10⁸ K. At these temperatures the fuel becomes a plasma, a mixture of positive ions and electrons. The central difficulty is confining this plasma, since no material container can withstand such temperatures; magnetic confinement devices such as the tokamak are used. Several countries, including India, are developing these techniques.
Why does fusion produce more energy per nucleon than fission?
On the binding-energy-per-nucleon curve, light nuclei lie far below the peak near A = 56, so fusing them into heavier nuclei produces a large gain in binding energy per nucleon. According to NIOS, the energy released per nucleon in deuteron-deuteron fusion is about 6 MeV, nearly seven times the per-nucleon energy released in a fission event (about 0.83 MeV per nucleon). Per unit mass of fuel, fusion therefore releases more energy than fission.