Nuclear Fission and Fusion ICSE Class 10: Equations, Chain Reaction and the Sun's Energy

What Nuclear Fission and Fusion is about

Weightage: CISCE publishes no chapter or unit weightage for ICSE Physics. Nuclear Fission and Fusion is in the 6. Modern Physics (ii) part of the 2027 syllabus and can be asked in both Section A and Section B of the 80-mark paper.Source: CISCE ICSE Physics (Science Paper 1) syllabus, examination year 2027

Key concepts

Nuclear fission

Nuclear fission is the splitting of a heavy nucleus into two nuclei of nearly equal (medium) mass, with the release of a large amount of energy and 2 or 3 neutrons.

Uranium-235 undergoes fission when it absorbs a slow (thermal) neutron; uranium-238, the more common isotope, does not do so readily. So U-235 is the fissionable isotope.

Typical equation:
${}_{92}^{235}\text{U}+{}_0^{1}n\to {}_{54}^{140}\text{Xe}+{}_{38}^{94}\text{Sr}+2{}_0^{1}n+\text{energy}$.

The products vary from fission to fission; each fission releases about 200 MeV of energy.

Worked example

Check that the fission equation above balances for mass number and atomic number.

Try it first, then show the solutionSolution

1. Mass numbers: $235+1=236$; $140+94+2\times 1=236$ ✓
2. Atomic numbers: $92+0=92$; $54+38+0=92$ ✓

Answer: Both balance: 236 and 92

Balancing nuclear equations

In every nuclear reaction:

• the sum of mass numbers (top) is the same on both sides;
• the sum of atomic numbers (bottom) is the same on both sides.

Remember that a neutron is ${}_0^{1}n$: it adds 1 to the mass total but 0 to the atomic total, and count every neutron (e.g. $3{}_0^{1}n$ adds 3). The absorbed neutron on the left adds 1 to the mass total too.

Worked example

Find $x$ and $y$: ${}_{92}^{235}\text{U}+{}_0^{1}n\to {}_{56}^x\text{Ba}+{}_y^{89}\text{Kr}+3{}_0^{1}n$.

Try it first, then show the solutionSolution

1. Mass: $236=x+89+3$, so $x=144$.
2. Atomic: $92=56+y$, so $y=36$.

Answer: x = 144, y = 36

Chain reaction

Each fission releases 2–3 neutrons. If at least one of them causes another fission, the process continues by itself: a chain reaction.

• Uncontrolled chain reaction: the number of fissions multiplies very rapidly, releasing huge energy in a fraction of a second (the principle of an atom bomb).
• Controlled chain reaction: in a nuclear reactor, neutrons are slowed by a moderator (such as heavy water or graphite) and their number is kept steady by control rods (such as cadmium or boron, which absorb neutrons), so energy is released steadily to generate electricity.

Worked example

If every fission produces 2 neutrons and each causes a new fission, how many fissions take place in the 10th generation, starting from one?

Try it first, then show the solutionSolution

1. Generations: 1, 2, 4, 8, … doubling each time.
2. 10th generation: $2^9=512$ fissions; the total up to then is $2^{10}-1=1023$.

Answer: 512 in the 10th generation (1023 in all)

Where the energy comes from: E = mc²

The total mass of the products of fission or fusion is slightly less than the mass of the reacting nuclei. This lost mass (mass defect) is converted into energy according to Einstein's relation
$E=m{c}^2$,
where $c=3\times 10^8$ m/s. Because $c^2$ is enormous, a tiny loss of mass releases a huge amount of energy.

Worked example

How much energy would be released if 1 g of mass were completely converted into energy? Express it in kW h.

Try it first, then show the solutionSolution

1. $E=0.001\times (3\times 10^8{)}^2=9\times 10^{13}$ J.
2. In kW h: $\frac{9\times 10^{13}}{3.6\times 10^6}=2.5\times 10^7$ kW h.

Answer: 9 × 10¹³ J = 2.5 × 10⁷ kW h

Nuclear fusion

Nuclear fusion is the joining of two light nuclei to form a heavier nucleus, with the release of a large amount of energy.

Example (isotopes of hydrogen, deuterium and tritium):
${}_1^2\text{H}+{}_1^3\text{H}\to {}_2^4\text{He}+{}_0^{1}n+\text{energy}$.
Also ${}_1^2\text{H}+{}_1^2\text{H}\to {}_2^3\text{He}+{}_0^{1}n+\text{energy}$.

Fusion needs extremely high temperatures (millions of kelvin) and pressures, so that the positively charged nuclei move fast enough to overcome their repulsion: hence the name thermonuclear reaction.

The Sun and stars shine because hydrogen nuclei fuse into helium in their cores. The hydrogen bomb is an uncontrolled fusion reaction; controlled fusion for power is still being developed.

Worked example

Complete: ${}_1^2\text{H}+{}_1^2\text{H}\to {}_2^3\text{He}+{}_{?}^{?}X$. Name X.

Try it first, then show the solutionSolution

1. Mass: $2+2=3+A$, so $A=1$.
2. Atomic: $1+1=2+Z$, so $Z=0$: a neutron.

Answer: ¹₀n (a neutron)

Fission and fusion compared

• Process: fission splits a heavy nucleus; fusion joins light nuclei.
• Conditions: fission needs slow neutrons and a critical amount of fuel; fusion needs extremely high temperature and pressure.
• Fuel: fission: uranium-235, plutonium-239; fusion: hydrogen isotopes (deuterium from sea water).
• Products: fission gives radioactive waste; fusion gives mainly helium (far less radioactive waste).
• Energy per unit mass of fuel: fusion releases more.
• Use today: fission in nuclear power stations; fusion in the Sun and stars (power stations still experimental).

Worked example

Give two differences between nuclear fission and nuclear fusion.

Try it first, then show the solutionSolution

1. Fission splits a heavy nucleus; fusion combines light nuclei.
2. Fission occurs with slow neutrons at ordinary temperatures; fusion needs millions of kelvin.

Answer: Splitting vs joining; neutrons vs very high temperature

Nuclear power and safety

In a nuclear power station, the heat from controlled fission boils water into steam, which drives turbines and generators: nuclear → heat → mechanical → electrical energy.

Advantages: very large energy from little fuel; no carbon dioxide from burning.
Disadvantages: radioactive waste that stays dangerous for a very long time; risk of accidents and radioactive fallout.

Safety: strong shielding around the reactor; strict control of the chain reaction; safe, long-term disposal of waste (sealed and buried deep underground); careful monitoring of workers' radiation doses.

Worked example

State the energy changes in a nuclear power station and one problem it creates.

Try it first, then show the solutionSolution

1. Nuclear energy → heat → mechanical (turbine) → electrical.
2. Problem: long-lived radioactive waste that must be stored safely.

Answer: Nuclear → heat → mechanical → electrical; radioactive waste

Physics in real life: Nuclear Fission and Fusion

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.

Topics in this chapter

• Nuclear Fission and Chain Reaction
• Nuclear Fusion and the Energy of the Sun

Nuclear Fission and Fusion formula sheet

A fission reaction

${}_{92}^{235}\text{U}+{}_0^{1}n\to {}_{54}^{140}\text{Xe}+{}_{38}^{94}\text{Sr}+2{}_0^{1}n+\text{energy}$

Products vary; 2–3 neutrons released.

A fusion reaction

${}_1^2\text{H}+{}_1^3\text{H}\to {}_2^4\text{He}+{}_0^{1}n+\text{energy}$

Needs millions of kelvin.

Mass–energy relation

$E=m{c}^2$

c = 3 × 10⁸ m/s; m = mass defect.

Balancing rule

$\Sigma A_{\text{left}}=\Sigma A_{\text{right}},\Sigma Z_{\text{left}}=\Sigma Z_{\text{right}}$

Neutron: ¹₀n.

Energy per fission

$\approx 200\text{MeV}\approx 3.2\times 10^{-11}\text{J}$

1 MeV = 1.6 × 10⁻¹³ J.

Nuclear Fission and Fusion: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the board asks Nuclear Fission and Fusion

The question patterns to expect, and the method that works for each.

Tricks to remember Nuclear Fission and Fusion

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

• Fission = fissure

  Fission splits (like a fissure, a crack); fusion fuses together.

  Use it when: Naming the process.

• Count the neutrons

  Add 1 for the absorbed neutron on the left and 1 for each neutron on the right.

  Use it when: Balancing fission equations.

• 235 breaks, 238 takes

  U-235 splits with slow neutrons; U-238 mostly just absorbs them.

  Use it when: Which isotope is fissionable.

• Sun = fusion

  Stars fuse hydrogen into helium.

  Use it when: Source of solar energy.

Nuclear Fission and Fusion: board-level solved questions

Ordered from board level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section B style)

Read the situation, then answer every part. In the board paper this is a 10-mark question split into 3 + 3 + 4 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in Nuclear Fission and Fusion

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

• ✗Mistake: Ignoring emitted neutrons

  CISCE examiners' comments, 2024: completing a fission equation, candidates gave the wrong mass number for barium and ignored the 3 neutrons, so the atomic number of krypton was wrong too.

  ✓Do this: Count every neutron: 3 ¹₀n adds 3 to the mass total and 0 to the atomic total.

  Usually costs: 1 to 2 marks.

• ✗Mistake: Forgetting the absorbed neutron

  CISCE examiners' comments, 2025: candidates wrote X as 235 instead of adding the absorbed neutron's mass, and gave the neutron in wrong notation.

  ✓Do this: U-235 + ¹₀n gives a total mass number of 236 on the left.

  Usually costs: 1 mark.

• ✗Mistake: Naming the process wrongly

  CISCE examiners' comments, 2025: shown a fission diagram, candidates named it nuclear fusion, radioactive reaction, or only 'chain reaction'; some identified the missing product as α, β or γ.

  ✓Do this: A heavy nucleus split by a neutron is nuclear fission; the extra products are neutrons.

  Usually costs: 1 mark each.

• ✗Mistake: Choosing U-238

  CISCE examiners' comments, 2024: asked which uranium isotope is more fissionable, candidates answered U-238 or named both.

  ✓Do this: U-235 is fissionable with slow neutrons.

  Usually costs: 1 mark.

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.

1. Q1 · 1 mark · MCQBoard level

   The process that produces the energy of the Sun is:
   (a) nuclear fission
   (b) nuclear fusion
   (c) radioactive decay
   (d) chemical burning

   Hint

   Hydrogen to helium.

   Answer

   (b)

2. Q2 · 1 mark · MCQBoard level

   In a nuclear reactor, the chain reaction is controlled by:
   (a) the moderator
   (b) control rods that absorb neutrons
   (c) the coolant
   (d) the turbine

   Hint

   Cadmium or boron.

   Answer

   (b)

3. Q3 · 1 mark · MCQHarder board level

   In the reaction ${}_{92}^{235}\text{U}+{}_0^{1}n\to {}_{56}^{144}\text{Ba}+{}_{36}^{89}\text{Kr}+x{}_0^{1}n$, the value of $x$ is:
   (a) 1
   (b) 2
   (c) 3
   (d) 4

   Hint

   236 = 144 + 89 + x.

   Answer

   (c)

4. Q4 · 1 mark · Assertion-reasonBoard level

   Assertion (A): A large amount of energy is released in nuclear fission.
   Reason (R): The total mass of the products is slightly less than that of the reactants, and the lost mass appears as energy.
   (a) (A) is true and (R) is false.
   (b) (A) is false and (R) is true.
   (c) Both (A) and (R) are true, and (R) is the correct explanation for (A).
   (d) Both (A) and (R) are true, but (R) is not the correct explanation for (A).

   Hint

   Mass defect.

   Answer

   (c)

5. Q5 · 2 marks · Very short answerHarder board level

   Complete: ${}_1^2\text{H}+{}_1^2\text{H}\to {}_1^3\text{H}+{}_{?}^{?}\text{X}$, and name X.

   Hint

   Balance A and Z.

   Answer

   ${}_1^1\text{H}$: a proton.

6. Q6 · 2 marks · Short answerHarder board level

   State the role of (a) the moderator, (b) the control rods in a nuclear reactor.

   Hint

   Slow down; absorb.

   Answer

   (a) Slows fast neutrons so they can cause fission. (b) Absorb neutrons to control the rate of the chain reaction.

7. Q7 · 3 marks · Long answerBoard level

   (a) What is nuclear fusion? (b) Write one fusion equation. (c) Why is a very high temperature needed?

   Hint

   Repulsion.

   Answer

   (a) Joining of light nuclei into a heavier nucleus with release of energy. (b) ${}_1^2\text{H}+{}_1^3\text{H}\to {}_2^4\text{He}+{}_0^{1}n$ + energy. (c) To give the positive nuclei enough speed to overcome their mutual repulsion.

8. Q8 · 3 marks · Long answerHarder board level

   In the fission ${}_{92}^{235}\text{U}+{}_0^{1}n\to {}_{55}^a\text{Cs}+{}_b^{93}\text{Rb}+2{}_0^{1}n$, find $a$ and $b$, showing the balancing.

   Hint

   236 on the left.

   Answer

   $236=a+93+2$, so $a=141$; $92=55+b$, so $b=37$.

9. Q9 · 3 marks · Long answerHOTS / competency

   If each fission in a chain reaction releases 2 neutrons, each causing another fission, find the number of fissions in the 10th generation and the total in the first 10 generations. Why does an uncontrolled chain reaction release energy so fast?

   Hint

   Doubling.

   Answer

   10th generation: $2^9=512$; total $2^{10}-1=1023$. The number of fissions grows geometrically, and each generation takes a tiny fraction of a second.

10. Q10 · 3 marks · Long answerHarder board level

    Give two advantages and two disadvantages of nuclear power stations.

    Hint

    Energy vs waste.

    Answer

    Advantages: very large energy from a small mass of fuel; no CO₂ from burning fuel. Disadvantages: long-lived radioactive waste; risk of accidents and radioactive fallout.

11. Q11 · 1 mark · MCQHOTS / competency

    In nuclear reactions, which quantity is converted into the energy released?
    (a) charge
    (b) a small part of the mass
    (c) the number of protons
    (d) the number of neutrons

    Hint

    E = mc².

    Answer

    (b)

12. Q12 · 4 marks · Long answerHOTS / competency

    (a) A fission releases about $3.2\times 10^{-11}$ J. How many fissions are needed to release $3.2\times 10^{10}$ J? (b) Using $E=m{c}^2$, what mass is converted to release $9\times 10^{13}$ J? (c) Explain why fusion of hydrogen gives more energy per kilogram of fuel than fission of uranium.

    Hint

    Divide; m = E/c².

    Answer

    (a) $\frac{3.2\times 10^{10}}{3.2\times 10^{-11}}=10^{21}$ fissions. (b) $m=\frac{9\times 10^{13}}{9\times 10^{16}}=10^{-3}$ kg = 1 g. (c) In fusion a larger fraction of the fuel's mass is converted into energy, so each kilogram of hydrogen fuel releases more energy.

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. 1.Define nuclear fission.Show answer

   Splitting of a heavy nucleus into two medium nuclei with release of energy and neutrons.

2. 2.Define nuclear fusion.Show answer

   Joining of light nuclei into a heavier nucleus with release of energy.

3. 3.Which uranium isotope is fissionable?Show answer

   U-235.

4. 4.Source of the Sun's energy?Show answer

   Nuclear fusion of hydrogen into helium.

5. 5.Role of control rods?Show answer

   To absorb neutrons and control the chain reaction.

6. 6.Einstein's mass–energy relation?Show answer

   E = mc²

7. 7.Why is fusion called thermonuclear?Show answer

   It needs extremely high temperatures.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you balance fission and fusion equations, counting all neutrons?
• ☐Can you explain a chain reaction and its control?
• ☐Can you use E = mc²?
• ☐Can you give four differences between fission and fusion?
• ☐Do you know U-235 is the fissionable isotope?

Nuclear Fission and Fusion: frequently asked questions