PhysicsICSE Class 10 · Nuclear Fission and Fusion

Nuclear Fission: U-235 Equations, Chain Reaction and the Nuclear Reactor (ICSE Class 10)

Updated 16 October 2026 · Fact-checked

Nuclear fission is the splitting of a heavy nucleus, such as uranium-235, into two medium nuclei after it absorbs a slow neutron. Each fission releases two or three neutrons and about 200 MeV of energy. The released neutrons can split more nuclei, giving a chain reaction, which a reactor keeps steady with control rods.

Understand Nuclear Fission and Chain Reaction

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

How it happens in uranium-235.
1. A slow (thermal) neutron is absorbed by a $_{92}^{235} U$ nucleus. Being uncharged, the neutron is not repelled by the nucleus.
2. This forms a very unstable nucleus, $_{92}^{236} U$ .
3. It splits at once into two medium nuclei (the fission fragments), giving out 2 or 3 fast neutrons and energy.

One possible fission:

$_{92}^{235} U +_{0}^{1} n \to_{56}^{139} Ba +_{36}^{94} Kr + 3_{0}^{1} n + energy$

Check: mass numbers $235 + 1 = 236$ and $139 + 94 + 3 = 236$ ; atomic numbers $92 = 56 + 36$ .

The fragments are different in different fissions (barium and krypton, xenon and strontium, caesium and rubidium, and so on), but every equation must balance.

Which nuclei are fissionable? U-235 splits with slow neutrons. U-238, which makes up over 99% of natural uranium, mostly absorbs slow neutrons without splitting. Plutonium-239 and uranium-233 are also fissionable.

Where the energy comes from. The total mass of the products is slightly less than the mass of $_{92}^{235} U$ plus the neutron. The lost mass $m$ is converted into energy $E = m c^{2}$ , with $c = 3 \times 1 0^{8}$ m/s. Each fission releases about 200 MeV, mostly as kinetic energy of the fragments, which becomes heat.

Chain reaction. Each fission releases 2 or 3 neutrons. If, on average, at least one of them causes another fission, the process keeps itself going: a chain reaction.

If more than one neutron per fission goes on to cause fission, the number of fissions multiplies every generation: an uncontrolled chain reaction, releasing enormous energy in a fraction of a second (atom bomb).
If exactly one neutron per fission goes on, the rate stays steady: a controlled chain reaction (nuclear reactor).
*Extension (beyond the syllabus wording):* in a small lump of uranium many neutrons escape through the surface, so a chain reaction needs a certain minimum mass, the critical mass.

The nuclear reactor.

Part	Example	Job
Fuel rods	enriched uranium (more U-235)	fission takes place here
Moderator	heavy water, graphite	slows fast neutrons so U-235 can capture them
Control rods	cadmium, boron	absorb neutrons; lowered to slow the reaction, raised to speed it up
Coolant	water, heavy water	carries heat to the boiler to make steam
Shield	thick concrete	stops radiation escaping

Enriched fuel and critical mass go a little beyond the syllabus wording ('basic introduction and equations'); learn them as extension.

Energy changes: nuclear → heat → mechanical (turbine) → electrical (generator).

Fission and radioactive decay are different. Decay is spontaneous and the nucleus throws out a small particle (α or β); fission is caused by a neutron and the nucleus breaks into two large pieces, with far more energy per event.

Problems. The fission fragments are themselves strongly radioactive, so spent fuel is dangerous radioactive waste for thousands of years. It must be stored and disposed of safely, and reactors need strict safety measures.

Nuclear Fission and Chain Reaction: formulas and key facts

A fission of U-235: $_{92}^{235} U +_{0}^{1} n \to_{56}^{139} Ba +_{36}^{94} Kr + 3_{0}^{1} n + energy$; Products vary; 2 or 3 neutrons.
Balancing: $235 + 1 = A_{1} + A_{2} + x, 92 = Z_{1} + Z_{2}$; x = number of neutrons released.
Energy from mass: $E = m c^{2}, c = 3 \times 1 0^{8} m/s$; m = mass lost, in kg.
Chain reaction: $fissions in generation n = N_{1} \times k^{n - 1}$; k = neutrons per fission that cause a new fission; k = 1 is steady.
Reactor parts: $Moderator: slows ∣ Control rods: absorb ∣ Coolant: carries heat ∣ Shield: stops radiation$; Graphite or heavy water; cadmium or boron.

How to solve Nuclear Fission and Chain Reaction questions

Fission questions are either equations to balance or explanations of the chain reaction and the reactor.

1Write the left side in full: $_{92}^{235} U +_{0}^{1} n$ , giving a mass total of 236 and an atomic total of 92.
2On the right, add up the mass numbers of the fragments and of all the neutrons ( $x$ neutrons add $x$ ).
3Solve for the unknown mass number, atomic number or number of neutrons from the two totals.
4For chain reactions, multiply generation by generation by the number of neutrons that actually cause fission.
5For reactor questions, say what each part does to neutrons or heat.
6For energy, convert the mass to kg and use $E = m c^{2}$ .

Nuclear Fission and Chain Reaction 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.

How much mass does a city use?

Suppose a nuclear power station supplies a city with 500 MW, all of it coming from mass converted into energy in its reactor (ignore losses).

How much mass is converted into energy in one day?

Try it first, then show the solutionSolution

Energy in a day: $E = P t = 5 \times 1 0^{8} \times 86400 = 4.32 \times 1 0^{13}$ J.
$m = \frac{E}{c ^{2}} = \frac{4.32 \times 1 0 ^{13}}{9 \times 1 0 ^{16}} = 4.8 \times 1 0^{- 4}$ kg.

Answer: About 0.48 g of mass per day.

Memory hook: Less than half a gram a day lights a city.

Falling dominoes

Imagine a row of dominoes where each falling domino knocks over two more.

How is this like an uncontrolled chain reaction, and what would make it like a controlled one?

Try it first, then show the solutionSolution

Each fission (domino) sets off more than one new fission, so the number doubles each step: uncontrolled.
If each domino could knock over exactly one more, the falls would continue at a steady rate.
In a reactor, control rods absorb the extra neutrons so that exactly one neutron per fission goes on.

Answer: More than one new fission each step: uncontrolled; exactly one: controlled.

Memory hook: One-for-one is steady; two-for-one is a bomb.

Tricks to remember Nuclear Fission and Chain Reaction

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

236 on the left
U-235 plus the neutron: always start with 236 on top and 92 below.
Use it when: Balancing fission equations.
Moderator Mellows, Control rods Capture
The moderator slows (mellows) neutrons; control rods capture them.
Use it when: Reactor parts.
k = 1 is calm
One neutron on per fission: steady reactor; more than one: runaway.
Use it when: Controlled and uncontrolled chain reactions.

Nuclear Fission and Chain Reaction: solved examples

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

Example 1: What fission does not give · 1 mark · MCQBoard level

Which of these is NOT a product of the fission of $_{92}^{235} U$ by a slow neutron?
(a) neutrons
(b) two nuclei of medium mass
(c) energy
(d) an α particle

Try it first, then show the solutionSolution

Fission gives two medium nuclei, 2 or 3 neutrons and energy; α particles come from radioactive decay.

Answer: (d) an α particle

Example 2: Counting the neutrons · 2 marks · Short answerBoard level

Find $x$ and $y$ :
$_{92}^{235} U +_{0}^{1} n \to_{58}^{146} Ce +_{y}^{87} Se + x_{0}^{1} n$

Try it first, then show the solutionSolution

Mass numbers: $235 + 1 = 146 + 87 + x$ , so $x = 3$ . (1)
Atomic numbers: $92 + 0 = 58 + y + 0$ , so $y = 34$ . (1)

Answer: x = 3, y = 34

Example 3: Fission of plutonium · 3 marks · Short answerHarder board level

Plutonium-239 also undergoes fission:
$_{94}^{239} Pu +_{0}^{1} n \to_{54}^{134} Xe +_{Z}^{A} X + 3_{0}^{1} n + energy$
(a) Find A and Z of X and name it, given that Z = 40 is zirconium.
(b) How many neutrons does X contain?

Try it first, then show the solutionSolution

(a) Mass: $239 + 1 = 134 + A + 3$ , so $A = 103$ . (1)
Atomic: $94 = 54 + Z$ , so $Z = 40$ : zirconium-103. (1)
(b) $N = 103 - 40 = 63$ . (1)

Answer: (a) ¹⁰³₄₀Zr (b) 63 neutrons

Example 4: Parts of a model reactor · 3 marks · Short answerHarder board level

A student builds a model of a nuclear reactor using: fuel rods, graphite blocks, boron rods, water pipes and a thick concrete wall. (a) State the job of each of the last four. (b) A friend suggests replacing the graphite blocks with more boron rods 'to make it safer'. Explain why the reactor would then stop working.

Try it first, then show the solutionSolution

(a) Graphite: moderator, slows fast neutrons. Boron rods: control rods, absorb neutrons. (1)
Water: coolant, carries heat to make steam. Concrete: shield, stops radiation escaping. (1)
(b) Without a moderator the neutrons stay fast and U-235 seldom captures them, and the extra boron absorbs even more neutrons, so fewer than one neutron per fission causes a new fission and the chain reaction dies out. (1)

Answer: (a) Moderator, control rods, coolant, shield (b) No moderator and more absorption: the chain reaction dies out.

Example 5: Growth of a chain reaction · 3 marks · Short answerHarder board level

Suppose 5 fissions take place in the first generation, and each fission releases 3 neutrons, of which 2 go on to cause new fissions. Find (a) the number of fissions in the 4th generation, (b) the total number of fissions in the first four generations. (c) Is this chain reaction controlled?

Try it first, then show the solutionSolution

(a) Each generation doubles: 5, 10, 20, 40. So 40 fissions. (1)
(b) Total $= 5 + 10 + 20 + 40 = 75$ . (1)
(c) No: more than one neutron per fission causes a new fission, so it grows without limit. (1)

Answer: (a) 40 (b) 75 (c) Uncontrolled

Example 6: Keeping a reactor steady · 3 marks · Short answerHOTS / competency

Suppose in a reactor each fission releases on average 2.5 neutrons.
(a) For the power to stay steady, how many neutrons per fission must be absorbed by the control rods or escape?
(b) What fraction of the neutrons is this?
(c) What happens if the control rods are pulled out a little?

Try it first, then show the solutionSolution

(a) Exactly one neutron per fission must cause a new fission, so $2.5 - 1 = 1.5$ must be removed. (1)
(b) $\frac{1.5}{2.5} \times 100 = 60%$ . (1)
(c) Fewer neutrons are absorbed, so more than one per fission causes fission: the rate and the power rise. (1)

Answer: (a) 1.5 (b) 60% (c) The reaction speeds up.

Example 7: Case study: energy from a small mass · 4 marks · Case-basedHOTS / competency

In a nuclear power station, the mass of the products is slightly less than the mass of the uranium and neutrons that react.
(a) What is this lost mass converted into?
(b) Find the energy released when 4 mg of mass is lost.
(c) For how long would this energy keep a 100 MW station running?
(d) State the energy changes from the reactor to the electricity supply.

Try it first, then show the solutionSolution

(a) Energy, according to $E = m c^{2}$ . (1)
(b) $E = 4 \times 1 0^{- 6} \times 9 \times 1 0^{16} = 3.6 \times 1 0^{11}$ J. (1)
(c) $t = \frac{3.6 \times 1 0 ^{11}}{1 \times 1 0 ^{8}} = 3600$ s = 1 hour. (1)
(d) Nuclear energy → heat → mechanical energy of the turbine → electrical energy from the generator. (1)

Answer: (a) Energy (b) 3.6 × 10¹¹ J (c) 1 hour (d) Nuclear → heat → mechanical → electrical

Where students lose marks in Nuclear Fission and Chain Reaction

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

Mistake: Ignoring the neutrons on the right
CISCE examiners' comments, 2024 Q3(v): completing a fission equation, candidates wrote the wrong mass number for barium and ignored the 3 neutrons, so the atomic number of krypton also went wrong.
Wrong working
Treating '3 ¹₀n' as adding 1 (or nothing) to the mass total.
Right working
3 ¹₀n adds 3 to the mass total and 0 to the atomic total.
Do this: Multiply each particle by its coefficient before adding.
Usually costs: 1–2 marks.
Mistake: Forgetting the absorbed neutron
CISCE examiners' comments, 2025 Q8(ii): candidates wrote the intermediate uranium nucleus as 235, forgetting to add the neutron's mass, and gave the neutron in the wrong notation.
Wrong working
U-235 + n → U-235
Right working
U-235 + ¹₀n → ²³⁶₉₂U, which then splits.
Do this: The left side totals 236.
Usually costs: 1 mark.
Mistake: Calling fission 'fusion' or just 'chain reaction'
CISCE examiners' comments, 2025 Q8(ii): shown a neutron splitting U-235, candidates named it nuclear fusion, radioactive reaction or only 'chain reaction', and called the missing product 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 Q7(ii): asked which uranium isotope is more fissionable, candidates wrote U-238 or both.
Do this: U-235 splits with slow neutrons.
Usually costs: 1 mark.

Exam tips

Write the neutron as $_{0}^{1} n$ and show both totals (top and bottom) when balancing.
Name the process exactly: 'nuclear fission', not just 'chain reaction'.
For reactor parts, say what each does to neutrons: moderator slows, control rods absorb.
In energy questions, change mg or g to kg before using $E = m c^{2}$ .

Practice questions on Nuclear Fission and Chain Reaction

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
In a nuclear reactor, the coolant:
(a) slows down the neutrons
(b) absorbs extra neutrons
(c) carries heat from the core to the boiler
(d) stops radiation escaping
Hint
Think of steam.
Answer
(c) carries heat from the core to the boiler
Q2 · 1 mark · Very short answerBoard level
Why is a neutron, rather than a proton, used to split a uranium nucleus?
Hint
Charge.
Answer
A neutron has no charge, so it is not repelled by the positively charged nucleus and can enter it easily.
Q3 · 2 marks · Short answerBoard level
Complete: ${}^{235}_{92}\text{U} + {}^{1}_{0}n \to {}^{133}_{51}\text{Sb} + {}^{101}_{?}\text{Nb} + ?\,{}^{1}_{0}n
Hint
236 on top, 92 below.
Answer
Nb: $Z = 92 - 51 = 41$ ; neutrons: $236 - 133 - 101 = 2$ .
Q4 · 2 marks · Short answerBoard level
Give two differences between nuclear fission and radioactive decay.
Hint
Cause and products.
Answer
Fission is caused by a neutron; decay is spontaneous. Fission splits the nucleus into two medium nuclei; decay emits a small particle (α or β). (Also: fission releases far more energy per event.)
Q5 · 2 marks · Short answerHarder board level
Find the number of neutrons released: $_{92}^{233} U +_{0}^{1} n \to_{56}^{138} Ba +_{36}^{93} Kr + x_{0}^{1} n$ . Check the atomic numbers as well.
Hint
The left total is 234, not 236.
Answer
$233 + 1 = 138 + 93 + x$ , so $x = 3$ . Atomic: $92 = 56 + 36$ ✓.
Q6 · 2 marks · Short answerHarder board level
(Extension) Why can a very small lump of uranium-235 not sustain a chain reaction?
Hint
Surface.
Answer
In a small lump, most of the released neutrons escape through the surface before they meet another U-235 nucleus, so on average fewer than one neutron per fission causes a new fission. The mass must exceed the critical mass.
Q7 · 2 marks · Short answerHarder board level
In the fission $_{92}^{235} U +_{0}^{1} n \to_{53}^{A} I +_{39}^{94} Y + 3_{0}^{1} n$ , find A and the number of neutrons in the iodine nucleus.
Hint
Count all three neutrons on the right.
Answer
$236 = A + 94 + 3$ , so $A = 139$ ; neutrons in I $= 139 - 53 = 86$ .
Q8 · 2 marks · Short answerHarder board level
Spent fuel taken out of a reactor is far more radioactive than the fresh uranium fuel put in. Explain, and state one way it is disposed of safely.
Hint
What do the fragments do?
Answer
Fission produces medium nuclei that are unstable and strongly radioactive. Spent fuel is sealed in thick containers and stored, then buried deep underground in stable rock away from groundwater.
Q9 · 3 marks · Short answerHOTS / competency
In one fission, uranium-235 splits into tellurium-134 (Z = 52) and zirconium-100 (Z = 40). (a) How many neutrons are released? (b) Suppose exactly two of these cause new fissions each time. Starting with one fission, how many fissions occur in the 5th generation?
Hint
Balance first, then double each generation.
Answer
(a) $236 - 134 - 100 = 2$ neutrons (and $52 + 40 = 92$ ✓). (b) 1, 2, 4, 8, 16: 16 fissions.
Q10 · 2 marks · Short answerHOTS / competency
(Extension) Natural uranium is over 99% U-238. Explain why fuel for many reactors is 'enriched' with extra U-235.
Hint
Which isotope splits with slow neutrons?
Answer
U-235 splits with slow neutrons, but U-238 mostly absorbs them without splitting. With too little U-235, too many neutrons are lost to U-238 for the chain reaction to continue, so the U-235 content is raised.

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.Particle that starts the fission of U-235?Show answer
A slow (thermal) neutron.
2.Nucleus formed when U-235 absorbs a neutron?Show answer
U-236 (unstable).
3.Energy per fission of U-235?Show answer
About 200 MeV.
4.Material for control rods?Show answer
Cadmium or boron.
5.Condition for a steady chain reaction?Show answer
Exactly one neutron per fission causes a new fission.

Nuclear Fission and Chain Reaction: frequently asked questions

Why do fission fragments differ from one fission to another?

The U-236 nucleus can split in many ways. Barium and krypton, xenon and strontium, or caesium and rubidium are common pairs; each equation must still balance in mass number and atomic number.

Can a nuclear reactor explode like an atom bomb?

No. Reactor fuel is only slightly enriched, and the control rods keep exactly one neutron per fission going on. A serious accident can release heat and radioactive material, which is why strict safety measures are needed, but not a nuclear explosion like a bomb.

Is the critical mass in the ICSE syllabus?

The syllabus asks for a basic introduction to fission with equations. Knowing that a minimum mass is needed for a chain reaction helps in explaining chain reactions.