PhysicsCBSE Class 12 · Nuclei

Nuclear Fission and Fusion Class 12: Energy from the Nucleus

Updated 15 October 2026 · Fact-checked

In nuclear fission, a heavy nucleus such as uranium-235, struck by a neutron, splits into two middle-sized nuclei and a few neutrons, releasing about 200 MeV. In nuclear fusion, light nuclei such as hydrogen isotopes join at very high temperatures. Both release energy because the products have higher binding energy per nucleon.

Fusion and fission both move nuclei up towards the peak near A = 56, where nucleons are bound most tightly, and the gain in binding energy is released.

Illustration drawn for QuestionBuddy.

Understand Nuclear Fission and Fusion

A kilogram of uranium in a power station gives as much energy as millions of kilograms of coal, and the Sun has shone for billions of years. Both are powered by nuclear reactions in which a little mass turns into a lot of energy.

Why energy is released. The binding energy per nucleon is about 7.6 MeV for very heavy nuclei, about 8.5 to 8.75 MeV for middle-mass nuclei, and much less for very light nuclei. Any reaction that moves nucleons towards the peak (near A = 56) binds them more tightly; the extra binding energy is released. Equivalently, the total mass of the products is less than that of the reactants, and the mass difference Δm appears as energy $Q = Δ m c^{2}$ (Δm in u × 931.5 MeV).

Nuclear fission. A slow neutron is absorbed by uranium-235, forming an excited uranium-236 nucleus that splits into two fragments of roughly equal mass plus two or three neutrons, for example:
$_{92}^{235}$ U + $_{0}^{1}$ n → $_{92}^{236}$ U* → $_{56}^{144}$ Ba + $_{36}^{89}$ Kr + 3 $_{0}^{1}$ n + energy.
Many different pairs of fragments are possible. In each, the mass number and charge balance. The energy released is about 200 MeV per fission: the binding energy per nucleon rises from about 7.6 MeV to about 8.5 MeV for 236 nucleons, giving roughly 0.9 × 236 ≈ 200 MeV, most of it as kinetic energy of the fragments. Because each fission releases more neutrons, these can cause further fissions: a chain reaction, which, if uncontrolled, releases enormous energy very quickly, and if controlled, can produce steady power.

Nuclear fusion. Two light nuclei combine to form a heavier one, for example deuterium and tritium:
$_{1}^{2}$ H + $_{1}^{3}$ H → $_{2}^{4}$ He + $_{0}^{1}$ n + 17.6 MeV.
Because the binding energy curve rises steeply for light nuclei, fusion releases more energy per unit mass than fission. But the nuclei are positively charged and repel each other strongly; they must approach within a few femtometres for the nuclear force to act. This needs enormous kinetic energies, i.e. temperatures of millions of kelvin, so fusion is called a thermonuclear reaction.

Energy of the Sun and stars. In the Sun's core (about 15 million K), hydrogen is fused into helium in a series of steps (the proton-proton cycle). The net effect is that four hydrogen nuclei become one helium-4 nucleus, releasing about 26.7 MeV. The Sun loses mass at a rate equal to its power output divided by c².

Comparing the two. Fission: heavy nucleus splits, triggered by a neutron, happens at ordinary temperatures, produces radioactive fragments. Fusion: light nuclei join, needs extremely high temperature, releases more energy per kilogram, and its main product (helium) is not radioactive. Controlled fusion for power remains a research goal.

Nuclear Fission and Fusion: formulas and key facts

Energy released (Q value): $Q = Δ m c^{2} = [Σ m_{r e a c t an t s} - Σ m_{p r o d u c t s}] \times 931.5 MeV$; Masses in u.
From binding energies: $Q = Σ E_{b} (products) - Σ E_{b} (reactants)$; Increase in total binding energy.
Typical fission of U-235: $_{92}^{235} U +_{0}^{1} n \to_{56}^{144} Ba +_{36}^{89} Kr + 3_{0}^{1} n + \approx 200 MeV$; Mass number and charge are conserved.
D-T fusion: $_{1}^{2} H +_{1}^{3} H \to_{2}^{4} He +_{0}^{1} n + 17.6 MeV$; Needs a very high temperature.
Number of reactions for a power P: $N = \frac{P}{Q}$; Q in joule per reaction.

How to solve Nuclear Fission and Fusion questions

Use this method for fission and fusion questions.

1Balance the reaction: total A and total Z must be the same on both sides.
2For Q, subtract the total mass of products from that of reactants (in u) and multiply by 931.5 MeV.
3Alternatively, use binding energies: Q = (binding energy of products) − (binding energy of reactants).
4For power problems, convert Q to joule (1 MeV = 1.6 × 10⁻¹³ J) and divide the power by it to get reactions per second.
5For energy per kilogram, divide Q by the mass of the reacting nuclei.
6Use the binding energy curve to explain why the process releases energy.

Nuclear Fission and Fusion in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Fuel use in a nuclear power station

Suppose a nuclear power station produces 3000 MW of heat from the fission of uranium-235, each fission releasing 200 MeV.

(a) How many fissions occur each second? (b) What mass of uranium-235 is used up in one day? (c) Why is the mass so small compared with the coal a coal station would burn?

Try it first, then show the solutionSolution

Energy per fission = 200 × 1.6 × 10⁻¹³ = 3.2 × 10⁻¹¹ J; fissions per second = 3 × 10⁹/3.2 × 10⁻¹¹ ≈ 9.4 × 10¹⁹.
Per day: 9.4 × 10¹⁹ × 86 400 ≈ 8.1 × 10²⁴ fissions; mass = 8.1 × 10²⁴ × 235 × 1.66 × 10⁻²⁷ kg ≈ 3.2 kg.
Each fission releases about 200 MeV, millions of times more than the few eV per molecule in burning coal.

Answer: (a) about 9.4 × 10¹⁹ per second; (b) about 3.2 kg per day; (c) nuclear energy per atom is millions of times larger.

Memory hook: A few kilograms of uranium a day do the work of trainloads of coal.

The Sun's mass loss

Imagine the Sun radiates power of about 3.8 × 10²⁶ W, all produced by fusing hydrogen into helium.

(a) Each conversion of four hydrogen nuclei into one helium-4 nucleus releases about 26.7 MeV. How many such conversions take place in the Sun each second? (b) Find the rate at which the Sun loses mass.

Try it first, then show the solutionSolution

Energy per conversion = 26.7 × 1.6 × 10⁻¹³ ≈ 4.27 × 10⁻¹² J; conversions per second = 3.8 × 10²⁶/4.27 × 10⁻¹² ≈ 8.9 × 10³⁷.
Mass loss rate = P/c² = 3.8 × 10²⁶/9 × 10¹⁶ ≈ 4.2 × 10⁹ kg/s, over four million tonnes every second.

Answer: (a) about 8.9 × 10³⁷ per second; (b) about 4.2 × 10⁹ kg/s.

Memory hook: Sunlight is the Sun's mass, turned into energy at four million tonnes a second.

Tricks to remember Nuclear Fission and Fusion

Short memory aids. Say each one aloud once, then use it on a question the same day.

Both roads lead to iron
Heavy nuclei split down, light nuclei fuse up, both towards the BE/A peak at A ≈ 56.
Use it when: Explaining energy release.
Fission: Few neutrons in, more out
One neutron in, two or three out: that is what makes a chain reaction possible.
Use it when: Chain reaction questions.
Fusion needs Fire
Light nuclei must be heated to millions of kelvin to beat their mutual repulsion.
Use it when: Why fusion is thermonuclear.
200 and 17.6
About 200 MeV per U-235 fission; 17.6 MeV per D-T fusion (but more per kilogram).
Use it when: Quick numbers.

Nuclear Fission and Fusion: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Fissions needed for a megawatt · 2 marks · Very short answerBoard level

Each fission of uranium-235 releases about 200 MeV. How many fissions per second are needed to produce a power of 1 MW?

Try it first, then show the solutionSolution

Energy per fission = 200 × 1.6 × 10⁻¹³ J = 3.2 × 10⁻¹¹ J. (1)
N = 10⁶/3.2 × 10⁻¹¹ ≈ 3.1 × 10¹⁶ fissions per second. (1)

Answer: About 3.1 × 10¹⁶ per second.

Example 2: Fission and fusion from the BE curve · 3 marks · Short answerBoard level

Using the binding energy per nucleon curve, explain why energy is released in (a) the fission of a heavy nucleus and (b) the fusion of light nuclei. Give one difference between the two processes.

Try it first, then show the solutionSolution

(a) A heavy nucleus (BE/A ≈ 7.6 MeV) splits into two middle-mass nuclei (BE/A ≈ 8.5 MeV); the nucleons become more tightly bound and the difference is released. (1)
(b) Light nuclei (low BE/A) join to form a heavier nucleus with higher BE/A, releasing the difference. (1)
Difference: fission is triggered by neutrons at ordinary temperatures; fusion needs extremely high temperatures (any one valid difference). (1)

Answer: Both move nucleons to higher BE/A; fission needs a neutron, fusion needs extreme temperature.

Example 3: Estimating fission energy · 3 marks · Short answerHarder board level

Estimate the energy released when a ²³⁶U nucleus (BE/A ≈ 7.6 MeV) splits into two fragments with BE/A ≈ 8.5 MeV. Why is the actual value close to this estimate?

Try it first, then show the solutionSolution

Binding energy before ≈ 236 × 7.6 MeV; after ≈ 236 × 8.5 MeV (the number of nucleons is unchanged). (1)
Q ≈ 236 × (8.5 − 7.6) ≈ 212 MeV, about 200 MeV. (1)
The small mismatch comes from the few free neutrons (unbound) and from rounding the BE/A values; the method captures the main effect. (1)

Answer: About 200 MeV.

Example 4: Energy from D-T fusion · 3 marks · Short answerHarder board level

Find the energy released in the reaction ²H + ³H → ⁴He + n. Masses: ²H = 2.014102 u, ³H = 3.016049 u, ⁴He = 4.002603 u, n = 1.008665 u.

Try it first, then show the solutionSolution

Mass before = 2.014102 + 3.016049 = 5.030151 u; after = 4.002603 + 1.008665 = 5.011268 u. (1)
Δm = 0.018883 u. (1)
Q = 0.018883 × 931.5 ≈ 17.6 MeV. (1)

Answer: About 17.6 MeV.

Example 5: Fission versus fusion per kilogram · 5 marks · Long answerHOTS / competency

(a) Find the energy released per kilogram of fuel in (i) the fission of U-235 (200 MeV per fission) and (ii) D-T fusion (17.6 MeV per reaction of 5 u of fuel). (3)
(b) Suppose burning petrol gives 4.5 × 10⁷ J/kg. How many kilograms of petrol match 1 kg of U-235? (1)
(c) Why is fusion still not used in power stations? (1)

Try it first, then show the solutionSolution

(a)(i) Mass per fission = 235 × 1.66 × 10⁻²⁷ kg; energy per kg = 3.2 × 10⁻¹¹/(3.9 × 10⁻²⁵) ≈ 8.2 × 10¹³ J/kg. (1)
(ii) Energy per kg = (17.6 × 1.6 × 10⁻¹³)/(5 × 1.66 × 10⁻²⁷) ≈ 3.4 × 10¹⁴ J/kg. (1)
Fusion gives about 4 times more energy per kilogram. (1)
(b) 8.2 × 10¹³/4.5 × 10⁷ ≈ 1.8 × 10⁶ kg of petrol. (1)
(c) The fuel must be held at many millions of kelvin long enough for fusion to occur, and no material container can withstand this; controlling it is still a research challenge. (1)

Answer: (a) about 8.2 × 10¹³ J/kg and 3.4 × 10¹⁴ J/kg; (b) about 1.8 million kg; (c) the extreme temperatures are very hard to contain.

Example 6: A fission reaction · 4 marks · Case-basedHarder board level

Read the passage and answer.

A slow neutron is absorbed by ²³⁵₉₂U, which splits into ¹⁴⁴₅₆Ba, ⁸⁹₃₆Kr and some neutrons.
(a) How many neutrons are released? (1)
(b) Check that the charge balances. (1)
(c) Why can this reaction lead to a chain reaction? (1)
(d) In what form does most of the released energy appear immediately? (1)

Try it first, then show the solutionSolution

(a) Mass numbers: 235 + 1 = 144 + 89 + x, so x = 3 neutrons. (1)
(b) Charges: 92 + 0 = 56 + 36 + 0 = 92. (1)
(c) Each fission releases about three neutrons, each of which can cause another fission, so the number of fissions can multiply. (1)
(d) As kinetic energy of the fission fragments (which becomes heat). (1)

Answer: (a) 3; (b) 92 = 56 + 36; (c) more neutrons are released than absorbed; (d) kinetic energy of the fragments.

Where students lose marks in Nuclear Fission and Fusion

The slips examiners see most often, and what to write instead.

Mistake: Unbalanced nuclear equations.
Forgetting the extra neutrons.
Do this: Check that total A and total Z are equal on both sides.
Usually costs: 1 mark.
Mistake: Saying fission releases energy because heavy nuclei are unstable 'by nature'.
No reasoning from binding energy.
Do this: Explain with BE/A: products are more tightly bound than the parent.
Usually costs: 1 mark.
Mistake: Forgetting to convert MeV to joule in power problems.
Unit slip.
Do this: 1 MeV = 1.6 × 10⁻¹³ J.
Usually costs: The answer mark.
Mistake: Describing a nuclear reactor in detail.
Older notes include it.
Do this: The nuclear reactor is not in the 2026-27 syllabus; describe fission, fusion and the chain reaction idea only.
Usually costs: Time.

Exam tips

Fission and fusion questions appeared in 2025 (55/1/1 Q27 and 55/7/1 Q21) and in the 2025 and 2026 sample papers.
Always link the explanation to the binding energy per nucleon curve.
Balance A and Z in any equation you write.
Keep the Q-value method (mass before minus mass after × 931.5 MeV) ready for numericals.
Radioactivity and nuclear reactors are not in the 2026-27 syllabus.

Practice questions on Nuclear Fission and Fusion

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · MCQBoard level
The energy released in the fission of one uranium-235 nucleus is about
(a) 2 MeV (b) 20 MeV (c) 200 MeV (d) 2000 MeV
Hint
Remember the standard figure.
Answer
(c) 200 MeV.
Q2 · 2 marks · Very short answerBoard level
Why does nuclear fusion require a very high temperature?
Hint
Like charges.
Answer
The nuclei are positively charged and repel each other strongly. They must come within a few femtometres for the attractive nuclear force to act, which needs very high kinetic energies, i.e. temperatures of millions of kelvin.
Q3 · 1 mark · Very short answerHarder board level
Complete the reaction ²³⁵₉₂U + ¹₀n → ¹⁴⁰₅₄Xe + ⁹⁴₃₈Sr + x ¹₀n and find x.
Hint
Balance mass numbers.
Answer
236 = 140 + 94 + x gives x = 2 (charge check: 92 = 54 + 38).
Q4 · 2 marks · Very short answerHarder board level
Find the energy released by the complete fission of 5 g of U-235 (200 MeV per fission).
Hint
Number of nuclei = mass/(235 u).
Answer
Nuclei = 5 × 10⁻³/(235 × 1.66 × 10⁻²⁷) ≈ 1.28 × 10²²; energy ≈ 1.28 × 10²² × 3.2 × 10⁻¹¹ ≈ 4.1 × 10¹¹ J.
Q5 · 1 mark · Assertion-reasonHarder board level
Assertion (A): Fusion of light nuclei releases more energy per kilogram of fuel than fission of heavy nuclei.
Reason (R): The binding energy per nucleon rises steeply for light nuclei.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Hint
Gain in BE/A for light nuclei.
Answer
(a).
Q6 · 2 marks · Very short answerHOTS / competency
Why can neither fission nor fusion of iron-56 release energy?
Hint
Position on the BE curve.
Answer
Iron-56 is at the peak of the binding energy per nucleon curve. Splitting it or fusing it with another nucleus would produce nuclei with lower binding energy per nucleon, which would absorb energy rather than release it.
Q7 · 1 mark · Very short answerHOTS / competency
How many fissions are needed to release 1 J of energy (200 MeV per fission)?
Hint
1/(3.2 × 10⁻¹¹).
Answer
About 3.1 × 10¹⁰ fissions.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Energy per U-235 fission?Show answer
About 200 MeV.
2.What triggers fission of U-235?Show answer
Absorption of a slow neutron.
3.Energy released in D-T fusion?Show answer
About 17.6 MeV.
4.Why is fusion called thermonuclear?Show answer
It needs extremely high temperatures.
5.Net reaction powering the Sun?Show answer
Four hydrogen nuclei fuse into one helium-4 nucleus, releasing about 26.7 MeV.
6.What makes a chain reaction possible?Show answer
Each fission releases two or three neutrons that can cause further fissions.

Nuclear Fission and Fusion: frequently asked questions

What is the difference between nuclear fission and fusion?

Fission splits a heavy nucleus into two middle-mass nuclei, usually triggered by a neutron. Fusion joins light nuclei into a heavier one and needs very high temperatures. Both release energy by increasing binding energy per nucleon.

Where does the energy in fission come from?

The products are more tightly bound and have less total mass than the original nucleus plus neutron. The lost mass appears as energy, mostly the kinetic energy of the fragments.

Why does the Sun shine?

In its very hot core, hydrogen nuclei fuse into helium, converting a little mass into a great deal of energy, which eventually leaves the Sun as light and heat.

Is the nuclear reactor in the 2026-27 syllabus?

No. The syllabus covers nuclear fission and fusion; the nuclear reactor and radioactivity are listed as not to be assessed.

Why does fusion give more energy per kilogram than fission?

The binding energy per nucleon rises very steeply for the lightest nuclei, so each nucleon gains more binding energy in fusion than in fission, and the fuel nuclei are light.