Fission chain reactions

Distinguish emitted neutrons from successful fission triggers, calculate a simple next-generation count and compare moderator, control-rod and coolant roles.

GCE A-Level H2 Physics 2027

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This optional supporting lesson explains how neutrons from one fission can cause later fissions. First study Nuclear fission for the equation and energy of one event. Here the new question is: how many events follow it?

Emitted does not mean successful

A fission chain reaction occurs when neutrons from fission induce further fissions. Not every emitted neutron does this. Some escape; others are absorbed without causing fission. Counting all emitted neutrons as successful triggers would overestimate the next generation.

For a simplified generation model, let k be the mean number of new fissions caused by each current fission. Then

Nₙₑₓₜ = kN_current.

These are expected counts. The model assumes the same k for that generation and says nothing about its duration.

Effective multiplier	Expected next generation	Interpretation in this model
k < 1	Fewer fissions	The chain decreases
k = 1	The same number	The chain is sustained
k > 1	More fissions	The chain grows

For example, 100 current fissions with k = 0.8 give 80 expected next-generation fissions. With k = 1.2, they give 120. The number of neutrons emitted per fission alone does not determine k.

Independent transfer

Each fission releases three neutrons on average, but in a simplified reactor model only two neutrons per fission trigger another fission; the rest escape or are absorbed. How many new fissions are expected in the next generation after 10 initial fissions?

Try this before viewing the solution

Next-generation fissions

Unit: fissions

Hints

Hint 1: use the effective multiplier

Each initial fission produces two successful triggers for the next generation.

Show solution step by step

Identify the effective factor
Method
The next-generation multiplication factor in this model is two.
Reason
Only two of the three emitted neutrons cause further fission.
Working
k = 2 new fissions per fission
Apply one generation
Method
The model predicts 20 new fissions on average.
Reason
Multiply the ten initial fissions by the effective factor.
Working
Nₙₑₓₜ = 2(10) = 20

Try next

Attempt why slow neutrons can be effective at inducing fission independently.

Separate the roles of moderator, control rods and coolant

In a typical light-water reactor using uranium fuel, water slows neutrons and carries heat away. Slower neutrons are more effective at inducing fission in uranium-235 in this context. Control rods absorb neutrons to alter how many remain available for further fission. See the US Department of Energy’s light-water reactor explanation.

Role	What it changes	What it does not establish by itself
Moderator	Neutron energies, mainly by scattering	How many neutrons cause further fission
Control rods	Neutron availability through absorption	Energy released by an individual fission
Coolant	Heat transfer from the reactor	Whether the chain is sustained

A material can serve more than one role: water may be both moderator and coolant. Slowing and absorbing neutrons are different processes. Absorption need not produce fission.

Mind stretcher 1: Are slow neutrons always required?Extension

A learner says every fission reactor must slow its neutrons. What is the missing qualification?

Compare your explanation

Slow, or thermal, neutrons are useful for inducing uranium-235 fission in thermal reactors. This is not a rule for every fuel and reactor. Fast reactors use fast neutrons and do not use a moderator. The relevant probability depends on the isotope and neutron energy; neutron absorption and fission are not identical outcomes. See the Department of Energy’s fast-reactor explanation.

Mind stretcher 2: Why absorb some neutrons?Extension

In the simplified model, explain why control rods can help keep the expected next-generation fission count equal to the current count.

Compare your reasoning

Absorbing some neutrons reduces the number available to cause new fissions. For a sustained chain, the mean successful triggers per current fission must be one, after allowing for escape and other absorptions. This means k = 1 in the model; it does not mean only one neutron is emitted. Real reactor control also depends on timing and changing conditions.

Try the model without a worked sequence

A model predicts 60 fissions in a generation, with a mean of three emitted neutrons per fission. One sixth of the emitted neutrons cause a next-generation fission. Calculate the expected next count and decide whether the chain grows or decreases.

Check your next generation

The effective multiplier is k = 3(1/6) = 0.5. The expected next count is 60(0.5) = 30 fissions, so the chain decreases. Using all 180 emitted neutrons as new fissions would ignore the stated losses.

Summary

A chain depends on successful subsequent fissions, not simply emitted neutrons. Distinguish moderation, absorption and heat removal. To calculate the energy released by a given event count, return to Nuclear fission.

Optional videos

Syllabus and review details

GCE A-Level H2 Physics 2027 · 2027
Content Overview, PDF pages 9–10; Subject Content, PDF pages 11–30