PhysicsISC Class 12 · Nuclei

Nuclear Fission and the Nuclear Reactor: Energy Released, Chain Reaction and Reactor Parts

Updated 15 October 2026 · Fact-checked

Nuclear fission is the splitting of a heavy nucleus such as uranium-235, after it absorbs a slow neutron, into two middle-mass nuclei plus 2 or 3 neutrons, releasing about 200 MeV. The neutrons can cause further fissions (a chain reaction). In a reactor, a moderator slows neutrons and control rods absorb them to keep the reaction steady.

Understand Nuclear Fission and the Nuclear Reactor

Why fission releases energy. On the BE/A curve, heavy nuclei (A ≈ 240) have about 7.6 MeV per nucleon, while middle-mass nuclei (A ≈ 120) have about 8.5 MeV. When a heavy nucleus splits, its nucleons become more tightly bound, and the difference (roughly 0.9 MeV per nucleon, about 200 MeV per fission) is released, mainly as kinetic energy of the fragments.

A fission equation (any one is enough).
$_{92}^{235} U +_{0}^{1} n \to_{92}^{236} U^{*} \to_{56}^{141} Ba +_{36}^{92} Kr + 3_{0}^{1} n + Q, Q \approx 200 MeV .$
Mass number and charge are conserved (236 = 141 + 92 + 3; 92 = 56 + 36). Many other pairs of fragments are possible. Slow (thermal) neutrons are far more effective than fast ones in causing fission of U-235.

Chain reaction. Each fission releases 2 to 3 neutrons, each able to cause another fission. If on average more than one neutron from each fission causes a new fission, the number of fissions grows rapidly.

Uncontrolled chain reaction: the number grows explosively: the basis of the atom bomb.
Controlled chain reaction: on average exactly one neutron per fission causes another fission: steady power, the basis of a reactor.
Criticality (qualitative): the reactor is *critical* when the rate of fission stays constant (multiplication factor k = 1), *subcritical* when it dies away (k < 1), *supercritical* when it grows (k > 1). A minimum (critical) mass of fuel is needed, otherwise too many neutrons escape.

Main parts of a nuclear reactor and their functions.

Part	Function	Examples
Fuel elements	Fissile material that undergoes fission	Enriched uranium (U-235), plutonium-239
Moderator	Slows fast neutrons to thermal speeds so they cause fission efficiently	Heavy water, ordinary water, graphite
Control rods	Absorb neutrons to control the rate of fission (push in to slow, pull out to speed up, drop fully in to shut down)	Cadmium, boron
Coolant	Carries away the heat produced in the core to a heat exchanger	Water, heavy water, liquid sodium, CO₂ gas
Casing / shielding	Contains the core and stops radiation (neutrons, γ) escaping	Thick concrete, steel

Light nuclei make good moderators because a neutron loses much of its energy in each collision with a nucleus of similar mass.

Using the energy output (qualitative). Heat from the coolant makes steam that drives turbines to generate electricity. Reactors also produce radioisotopes for medicine, industry and agriculture, and provide neutrons for research.

Reactor versus bomb. A reactor uses a moderator and control rods to keep k = 1; a bomb assembles a supercritical mass of nearly pure fissile material very rapidly so that k > 1 and energy is released in microseconds. (Details of the chain reaction are not required.)

Nuclear Fission and the Nuclear Reactor: formulas and key facts

Fission example: $_{92}^{235} U +_{0}^{1} n \to_{56}^{141} Ba +_{36}^{92} Kr + 3_{0}^{1} n + Q$; A and Z conserved.
Q from masses: $Q = [m_{r e a c t an t s} - m_{p r o d u c t s}] \times 931 MeV$; Masses in u.
Q from BE/A: $Q = \sum (A \cdot \frac{B E}{A})_{p r o d u c t s} - (A \cdot \frac{B E}{A})_{p a r e n t}$; 240 → 2 × 120 gives ≈ 200 MeV.
Fission rate: $n = \frac{P}{E _{f i ss i o n}}$; P in W, E in J.
Energy per fission: $200 MeV = 3.2 \times 1 0^{- 11} J$; Typical value.

How to solve Nuclear Fission and the Nuclear Reactor questions

Fission numericals are either "Q of one fission" or "how many fissions for a given power".

1Balance the equation: total A and total Z must match on both sides; the remainder is neutrons.
2Q from masses: (left side − right side) in u × 931 MeV.
3Q from BE/A: total BE of products − total BE of parent (neutrons have zero BE).
4Power problems: fissions per second $= \frac{P}{200 \times 1.6 \times 1 0 ^{- 13}}$ .
5Mass of fuel: fissions ÷ $N_{A}$ × 235 g.
6Reactor questions: name the part, then its function in one line (and an example).

Nuclear Fission and the Nuclear Reactor 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.

A household's monthly electricity

Suppose a home uses 300 kWh of electrical energy in a month, and imagine it all came directly from fission of U-235 at 200 MeV per fission (ignoring losses).

How much U-235 would undergo fission?

Try it first, then show the solutionSolution

Energy $= 300 \times 3.6 \times 1 0^{6} = 1.08 \times 1 0^{9}$ J.
Fissions $= \frac{1.08 \times 1 0 ^{9}}{3.2 \times 1 0 ^{- 11}} \approx 3.38 \times 1 0^{19}$ .
Mass $= \frac{3.38 \times 1 0 ^{19}}{6.02 \times 1 0 ^{23}} \times 235$ g ≈ 0.013 g.

Answer: About 13 mg of uranium-235 a month (a real plant needs about three times more because of conversion losses).

Memory hook: A grain of uranium lights a home.

Emergency shutdown

Imagine an earthquake sensor at a nuclear power station triggers a shutdown.

What happens inside the reactor, and why does the coolant keep running afterwards?

Try it first, then show the solutionSolution

All control rods drop fully into the core; they absorb so many neutrons that fewer than one neutron per fission causes another fission (subcritical), and the chain reaction stops.
Fission products in the fuel are still radioactive and keep producing heat, so the coolant must keep circulating.

Answer: Control rods make the reactor subcritical; cooling continues to remove leftover heat.

Memory hook: Rods in, reaction down; cooling stays on.

Tricks to remember Nuclear Fission and the Nuclear Reactor

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

Fuel, Moderator, Control, Coolant, Casing
"Fat Monkeys Climb Coconut Columns": five parts in order.
Use it when: Listing reactor parts.
Moderator slows, rods swallow
Moderator slows neutrons; control rods absorb them.
Use it when: Avoiding the 2024 mix-up.
Two hundred MeV
One fission ≈ 200 MeV ≈ $3.2 \times 1 0^{- 11}$ J.
Use it when: Power problems.
k = 1 is calm
k < 1 dies, k = 1 steady, k > 1 runaway.
Use it when: Criticality.

Nuclear Fission and the Nuclear Reactor: solved examples

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

Example 1: Job of the moderator · 1 mark · MCQBoard level

In a nuclear reactor, the moderator is used to:
(a) absorb neutrons
(b) slow down fast neutrons
(c) cool the core
(d) shield against radiation

Try it first, then show the solutionSolution

Slow (thermal) neutrons cause fission of U-235 more efficiently, so the moderator slows them.

Answer: (b).

Example 2: Fissions for one watt · 2 marks · Short answerBoard level

Each fission of U-235 releases 200 MeV. How many fissions per second produce a power of 1 W?

Try it first, then show the solutionSolution

200 MeV = $200 \times 1.6 \times 1 0^{- 13}$ J = $3.2 \times 1 0^{- 11}$ J. (1)
Fissions per second $= \frac{1}{3.2 \times 1 0 ^{- 11}} \approx 3.1 \times 1 0^{10}$ . (1)

Answer: ≈ $3.1 \times 1 0^{10}$ per second.

Example 3: Reactor parts · 3 marks · Long answerHarder board level

Name the main parts of a nuclear reactor and state the function of each, giving one material used for the moderator and for the control rods.

Try it first, then show the solutionSolution

Fuel elements (enriched U-235) undergo fission; casing/shielding (concrete) stops radiation. (1)
Moderator (heavy water or graphite) slows fast neutrons; control rods (cadmium or boron) absorb neutrons to control the fission rate. (1)
Coolant (water, liquid sodium) carries heat from the core to the heat exchanger to make steam. (1)

Answer: Fuel, moderator, control rods, coolant, shielding, with functions as above.

Example 4: Q of a fission from masses · 3 marks · Short answerHarder board level

Find the energy released in $^{235}$ U + n → $^{141}$ Ba + $^{92}$ Kr + 3n. (Atomic masses: ²³⁵U 235.043930 u, ¹⁴¹Ba 140.914411 u, ⁹²Kr 91.926156 u, n 1.008665 u; 1 u = 931 MeV)

Try it first, then show the solutionSolution

Reactants: 235.043930 + 1.008665 = 236.052595 u. (1)
Products: 140.914411 + 91.926156 + 3 × 1.008665 = 235.866562 u; Δm = 0.186033 u. (1)
Q = 0.186033 × 931 ≈ 173 MeV. (1)

Answer: ≈ 173 MeV.

Example 5: An unequal split · 3 marks · Short answerHOTS / competency

A nucleus with A = 236 and BE/A = 7.59 MeV splits into fragments of A = 140 (BE/A = 8.38 MeV) and A = 94 (BE/A = 8.59 MeV) with two free neutrons. Estimate the energy released and explain its origin.

Try it first, then show the solutionSolution

BE of parent = 236 × 7.59 ≈ 1791.2 MeV; BE of fragments = 140 × 8.38 + 94 × 8.59 ≈ 1173.2 + 807.5 = 1980.7 MeV (free neutrons have no BE). (1)
Q ≈ 1980.7 − 1791.2 ≈ 189 MeV. (1)
The fragments' nucleons are more tightly bound; the extra binding energy appears as kinetic energy of the fragments and neutrons. (1)

Answer: ≈ 189 MeV.

Example 6: A 10 MW research reactor · 4 marks · Case-basedHOTS / competency

Suppose a research reactor whose core sits in a pool of water runs at a thermal power of 10 MW, with 200 MeV per fission.
(i) Find the number of fissions per second. (1 mark)
(ii) Find the mass of U-235 used per day ( $N_{A} = 6.02 \times 1 0^{23}$ ). (1 mark)
(iii) What happens if the control rods are withdrawn too far? (1 mark)
(iv) Give two jobs the pool water does. (1 mark)

Try it first, then show the solutionSolution

(i) $\frac{1 0 ^{7}}{3.2 \times 1 0 ^{- 11}} \approx 3.13 \times 1 0^{17}$ per second.
(ii) Per day: $3.13 \times 1 0^{17} \times 86400 \approx 2.7 \times 1 0^{22}$ fissions; mass ≈ $\frac{2.7 \times 1 0 ^{22}}{6.02 \times 1 0 ^{23}} \times 235 \approx 10.5$ g.
(iii) Too few neutrons are absorbed; the reactor becomes supercritical (k > 1) and power rises.
(iv) Moderator (slows neutrons) and coolant (removes heat); it also shields radiation.

Answer: (i) ≈ $3.1 \times 1 0^{17}$ s⁻¹; (ii) ≈ 10.5 g; (iii) supercritical, power rises; (iv) moderator and coolant.

Where students lose marks in Nuclear Fission and the Nuclear Reactor

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

Mistake: Mixing up moderator and control rods
The ISC 2024 examiners (Q7(ii)) saw graphite rods called control rods, and cadmium described as a moderator.
Do this: Moderator (graphite, heavy water) slows neutrons; control rods (cadmium, boron) absorb them.
Usually costs: 1 mark each.
Mistake: Naming a material instead of the term
In 2025 Q19(ii) candidates wrote "water" or "graphite" when asked the name for a material that slows neutrons.
Do this: The answer is "moderator".
Usually costs: 1 mark.
Mistake: Vague control answers
Also 2025: "turn off the reactor" or "remove the fuel" instead of control rods.
Do this: Say "by inserting or withdrawing control rods".
Usually costs: 1 mark.
Mistake: Missing the use of a reactor
2025: the use of a reactor was wrong or left out.
Do this: Electric power generation; also radioisotopes, research, neutron source.
Usually costs: 1 mark.

Exam tips

Balance mass numbers and charges in every fission equation.
For each reactor part, give function and an example material.
Use the BE/A curve to explain why fission releases energy.
Keep all reactor answers qualitative unless numbers are given.

Practice questions on Nuclear Fission and the Nuclear Reactor

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
Fission of uranium-235 is caused most effectively by:
(a) fast neutrons
(b) slow (thermal) neutrons
(c) protons
(d) alpha particles
Hint
Why reactors need a moderator.
Answer
(b).
Q2 · 1 mark · Short answerBoard level
Write one nuclear equation for the fission of U-235 by a neutron.
Hint
Balance A and Z.
Answer
$_{92}^{235}$ U + $_{0}^{1}$ n → $_{56}^{141}$ Ba + $_{36}^{92}$ Kr + 3 $_{0}^{1}$ n + energy (about 200 MeV).
Q3 · 1 mark · Assertion-reasonHarder board level
Assertion (A): The chain reaction in a nuclear reactor can be kept steady.
Reason (R): Control rods absorb enough neutrons that, on average, one neutron per fission causes another fission.
(a) Both true, R explains A. (b) Both true, R does not explain A. (c) A true, R false. (d) A false, R true.
Hint
k = 1.
Answer
(a).
Q4 · 1 mark · Short answerHarder board level
In $_{92}^{235}$ U + $_{0}^{1}$ n → $_{54}^{140}$ Xe + $_{38}^{94}$ Sr + x $_{0}^{1}$ n, find x and check the charge balance.
Hint
236 on the left.
Answer
x = 2; 92 = 54 + 38.
Q5 · 2 marks · Short answerHarder board level
Distinguish between subcritical, critical and supercritical states of a reactor.
Hint
Neutrons per fission causing new fission.
Answer
Subcritical: fewer than one, reaction dies out. Critical: exactly one on average, steady rate. Supercritical: more than one, rate grows.
Q6 · 3 marks · Short answerHOTS / competency
Estimate the energy released by complete fission of 1 g of U-235 (200 MeV per fission) and how many kilograms of coal (about $3 \times 1 0^{7}$ J/kg) would give the same energy.
Hint
Nuclei in 1 g = $\frac{N _{A}}{235}$ .
Answer
≈ $2.56 \times 1 0^{21}$ nuclei; ≈ $8.2 \times 1 0^{10}$ J; about 2700 kg of coal.
Q7 · 2 marks · Short answerHOTS / competency
Why is heavy water a better moderator than ordinary water, even though both contain light nuclei?
Hint
Absorption of neutrons.
Answer
Both slow neutrons well, but ordinary hydrogen absorbs neutrons appreciably; deuterium absorbs far fewer, so more neutrons survive to cause fission, and natural uranium can be used.
Q8 · 4 marks · Case-basedHOTS / competency
Case study: Suppose a class debates "a reactor is just a slow bomb".
(i) What does a reactor have that a bomb lacks? (1 mark)
(ii) What is the value of k in each? (1 mark)
(iii) Why can a reactor not explode like a bomb? (1 mark)
(iv) Name one useful product of a reactor besides electricity. (1 mark)
Hint
Control and fuel enrichment.
Answer
(i) A moderator, control rods and coolant. (ii) Reactor k = 1; bomb k > 1. (iii) Reactor fuel is not enriched enough or assembled fast enough for an explosive supercritical mass, and control rods keep k at 1. (iv) Radioisotopes for medicine and industry (or neutrons for research).

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 fission of U-235?Show answer
About 200 MeV.
2.Function of control rods?Show answer
Absorb neutrons to control the fission rate.
3.Common moderators?Show answer
Heavy water, ordinary water, graphite.
4.Critical state means?Show answer
Steady chain reaction, k = 1.
5.Neutrons released per fission?Show answer
2 to 3.

Nuclear Fission and the Nuclear Reactor: frequently asked questions

Why do slow neutrons work better than fast ones?

A slow neutron spends longer near a U-235 nucleus and is much more likely to be captured, triggering fission.

Where does the 200 MeV go?

Mostly into the kinetic energy of the two fragments, which heats the fuel; the rest goes to neutrons, γ rays and later radioactive decay.

What is enriched uranium?

Uranium in which the proportion of fissile U-235 has been raised above the natural 0.7%.

What does the ISC 2027 syllabus need here?

Any one fission equation, Q ≈ 200 MeV from the BE/A graph (A = 240 into two A = 120), controlled and uncontrolled chain reactions, the reactor and the bomb, and the main parts of a reactor with their functions, criticality and use of the energy output, all qualitative.

How was this asked recently?

ISC 2024 Q7(ii) (2 marks) asked the use of the moderator and control rods; ISC 2025 Q19(ii)(a) asked the use of a reactor, the name for a neutron-slowing material and how a reactor can be shut down in an emergency.