Theme E — Nuclear and Quantum Physics

E.4.3 Chain Reactions from Fission — IB Physics HL Revision Notes & Topical Questions

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E.4.3 Chain Reactions from Fission — IB PHYSICS SL notes: Explain how fission neutrons sustain a chain reaction and distinguish subcritical, critical and supercritical conditions.Each induced fission of uranium-235 releases two or three fast neutrons.Chain reaction = a process in…

Only thermal neutrons induce fission efficiently
The number of fissions per generation can stay the same, grow or fall
After n generations the number of fissions is Nn
In a reactor k is kept very close to 1
Critical mass
Small pieces lose many neutrons through the surface

Part 1 of 7The chain reaction

Each induced fission of uranium-235 releases two or three fast neutrons.

2Chain reaction

Chain reaction a process in which neutrons from one fission go on to cause further fissions.

Only one neutron per fission is needed to continue it.

3Only thermal neutrons induce fission efficiently

Only thermal neutrons induce fission efficiently neutrons with too much energy rebound from the uranium-235 nucleus.

4The number of fissions per generation can stay the same, grow or fall

The number of fissions per generation can stay the same, grow or fall depending on how the neutrons are used or lost.

Part 2 of 7Multiplication factor

k the average number of neutrons from one fission that cause another fission.

Value of k	Name	Result
k below 1	Subcritical	Each generation is smaller; the reaction dies away
k = 1	Critical	Steady chain reaction and constant power, as in a normal reactor
k above 1	Supercritical	Fissions grow exponentially; runaway reaction

1After n generations the number of fissions is Nn

N₀kⁿ — growth is very rapid even for k slightly above 1,

since generations last microseconds to milliseconds.

2In a reactor k is kept very close to 1

In a reactor k is kept very close to 1 in a bomb it is made much greater than 1.

Part 3 of 7Critical mass

Critical mass

Critical mass the minimum mass of fissile fuel that sustains a steady chain reaction (k = 1).

Small pieces lose many neutrons through the surface

Small pieces lose many neutrons through the surface volume, which makes neutrons, grows faster than surface area, which leaks them.

It depends on material, purity, shape, density and reflectors

It depends on material, purity, shape, density and reflectors a sphere has the smallest surface for its volume.

Less than critical mass (subcritical)

Less than critical mass (subcritical) the reaction eventually stops.

More than critical mass (supercritical)

More than critical mass (supercritical) a runaway reaction and eventually an explosion.

Part 4 of 7What happens to the neutrons

Of about 2.4 neutrons per fission, some are lost.

Leakage through the surface of the fuel.
Absorption by uranium-238, the moderator, coolant, control rods or structure without fission.

2Only the remainder cause fission

Only the remainder cause fission design must ensure one neutron per fission causes another.

Raises k	Lowers k
Higher enrichment	Absorbers such as boron or cadmium
Moderator slowing neutrons	Leakage
Reflectors returning neutrons	Impurities and uranium-238
Larger fuel mass	Smaller fuel mass

Part 5 of 7Fast and slow neutrons

Fast and slow neutrons

Fission neutrons emerge with energies of about 1 to 2 MeV

Fission neutrons emerge with energies of about 1 to 2 MeV but uranium-235 captures slow neutrons a few hundred times better.

A moderator slows neutrons without absorbing them

A moderator slows neutrons without absorbing them making a chain reaction possible in lightly enriched uranium.

Neutrons in uranium-238 lose energy by inelastic scattering

Neutrons in uranium-238 lose energy by inelastic scattering falling below its fission threshold, so it cannot sustain a chain reaction alone.

Part 6 of 7Controlling the reaction

Controlling the reaction

A reactor keeps k

1 — controlled with control rods, the moderator and coolant.

Delayed neutrons are emitted seconds after fission from some fragments

Delayed neutrons are emitted seconds after fission from some fragments about 0.65% of the total.
They stretch the effective generation time to about 0.1 s.
This gives operators time to move control rods.

A reactor is critical only with the help of delayed neutrons

A reactor is critical only with the help of delayed neutrons it is subcritical on prompt neutrons alone.

Part 7 of 7More from the specification

Fission product longevity over years

Fission product longevity over years sustained chain reactions produce radioactive caesium and strontium isotopes requiring monitored containment over hundreds of years.

Unstable nucleus

A nucleus with an imbalance of protons and neutrons that may decay.

Radioactive

Describes a nucleus that decays spontaneously and randomly.

Spontaneous

A process which cannot be influenced by environmental factors such as temperature or pressure.

Shielding

Material that absorbs radiation.

Specific energy

Energy released per unit mass of a fuel, in J kg⁻¹

Binding energy

The minimum energy required to separate the nucleons of a nucleus to infinity.

Radioactive waste

Unwanted material that emits ionising radiation.

Daughter nuclei

The smaller nuclei produced in fission.

High-level waste

Highly radioactive, heat-generating waste such as spent fuel.

Key terms

Term	Meaning
Chain reaction	Self-sustaining series of fissions caused by neutrons from earlier fissions.
Multiplication factor k	Average neutrons per fission that cause another fission.
Critical mass	Minimum mass of fissile material that sustains a chain reaction.
Subcritical	k less than 1; reaction dies away.
Supercritical	k greater than 1; reaction grows.
Delayed neutrons	Neutrons emitted after a delay by fission fragments.

Avoid these mistakes

Thinking a critical reaction is a bomb — critical means steady, k = 1.

Believing k is the number of neutrons produced per fission — it is the number that cause further fission.

Assuming more mass always gives higher k with no limit — shape and leakage matter.

Forgetting that fast neutrons are poorly captured by uranium-235.

Confusing critical mass with the mass of the reactor — it is the minimum for k = 1.

Last updated: 18 October 2026