Physics 001.002.019 Fission Chain Reaction
Alignment
Learning Intentions
By the end of the lesson, students will be able to:
- Explain how one neutron-induced fission reaction can trigger further fission reactions.
- Describe the role of extra neutrons in sustaining a fission chain reaction.
- Distinguish between uncontrolled, controlled and subcritical fission chain reactions.
- Use simple nuclear equations and diagrams to represent a fission chain reaction.
Success Criteria
By the end of the lesson, students have successfully:
- Identified the reactant neutron, fissile nucleus, fission fragments, released energy and extra neutrons in a fission event.
- Explained that a chain reaction occurs when released neutrons cause further fission reactions.
- Described the conditions for a sustained chain reaction, including neutron availability and sufficient fissile material.
- Compared subcritical, critical and supercritical chain reactions.
- Interpreted a simple diagram of a fission chain reaction.
Syllabus Reference
- Unit 1: Thermal, Nuclear and Electrical Physics
- Topic 2: Ionising Radiation and Nuclear Reactions
- Energy and Mass Defect
- Explain a fission chain reaction.
Phenomenon
A single neutron strikes a uranium-235 nucleus. The nucleus becomes unstable, splits into two smaller nuclei, releases energy, and emits several more neutrons. These new neutrons can strike other uranium-235 nuclei, causing more fission reactions. Very quickly, one event can become many events.
This is the physical basis of a fission chain reaction.
Key Idea
A fission chain reaction occurs when neutrons released from one fission reaction cause further fission reactions. Each fission reaction can release energy and additional neutrons, allowing the process to continue.
Concept
In neutron-induced nuclear fission, a neutron is absorbed by a large unstable or fissile nucleus such as uranium-235. The nucleus becomes more unstable and splits into two smaller nuclei called fission fragments. Energy is released because the products have less total mass than the reactants. The missing mass has been transformed into energy.
A typical example is:
The important feature is that extra neutrons are produced. These neutrons can go on to cause further fission reactions:
This rapid increase is an example of exponential growth.
A chain reaction is sustained when, on average, at least one neutron from each fission event causes another fission event.
Convention
The key conventions associated with fission chain reactions are below.
- Neutrons are represented as
. - Uranium-235 is represented as
. - Nuclear equations must conserve nucleon number and proton number.
- The mass number
is conserved across a nuclear equation. - The atomic number
is conserved across a nuclear equation. - Energy is shown as a product because fission releases energy.
- Not all released neutrons necessarily cause further fission.
- Some neutrons escape the material or are absorbed without causing fission.
- A controlled chain reaction keeps the average number of successful fission-causing neutrons close to
. - An uncontrolled chain reaction allows the number of fission events to grow rapidly.
Misconceptions
Common misconceptions students have regarding the concept when applying to various situations and solving problems. It could be a conceptual, mathematical or logical misconception.
- A chain reaction does not mean one nucleus splits into endless pieces. It means neutrons from one fission event trigger fission in other nuclei.
- Every neutron released does not necessarily cause another fission reaction.
- Fission and radioactive decay are not the same process. Fission is the splitting of a nucleus, often induced by neutron absorption.
- A chain reaction does not always explode. Nuclear reactors use controlled chain reactions.
- Energy is not created from nothing. Energy is released because some mass is transformed into energy according to mass-energy equivalence.
Further Reading
- Nuclear fission in uranium-235
- Neutron-induced nuclear reactions
- Critical mass
- Controlled nuclear reactors
- Nuclear safety and control rods
Explicit Instruction
A fission chain reaction can be explained in stages.
- A neutron is absorbed by a fissile nucleus.
- The newly formed nucleus is unstable.
- The nucleus undergoes fission.
- Extra neutrons are released.
These neutrons may:
- cause further fission reactions
- escape the material
- be absorbed by other nuclei without causing fission
- If enough neutrons cause further fission, a chain reaction occurs.
The chain reaction can be described using the neutron multiplication factor
If
If
If
In a nuclear reactor, the aim is usually to maintain
Worked Examples
Worked Example 1
A uranium-235 fission reaction produces three neutrons. Explain how this can lead to a chain reaction.
Solution:
One neutron causes one uranium-235 nucleus to split.
The three released neutrons can each strike another uranium-235 nucleus. If each neutron successfully causes another fission reaction, then three new fission reactions occur.
Those three fission reactions may release:
Those nine neutrons may then cause further fission reactions.
Therefore, the number of reactions can increase rapidly because each fission event releases neutrons that can trigger more fission events.
Worked Example 2
A chain reaction has
Solution:
The neutron multiplication factor is:
Since
This means the reaction is sustained at a steady rate.
Worked Example 3
A fission reaction releases
Solution:
Generation
Generation
Generation
Generation
Generation
So, after four generations, there could be
The total number of fission events from generation
Therefore,
Check for Understanding
Check 1
Question:
Why are extra neutrons important in a fission chain reaction?
Expected answer:
Extra neutrons are important because they can strike other fissile nuclei and cause further fission reactions. This allows the reaction to continue.
Check 2
Question:
A fission reaction releases three neutrons, but only one causes another fission reaction. Is the chain reaction increasing, steady, or decreasing?
Expected answer:
It is steady if, on average, one neutron from each fission event causes another fission event. This corresponds to
Check 3
Question:
Explain why a fission chain reaction may stop.
Expected answer:
A fission chain reaction may stop if too many neutrons escape or are absorbed without causing fission. If fewer than one neutron per fission event causes another fission event on average, then
Investigation (Alternative to Explicit)
Hypothesis
If each fission event produces more than one neutron that causes further fission, then the number of fission events will increase rapidly over successive generations.
Data Collection
Use a safe classroom model such as counters, dominoes, marbles or a spreadsheet simulation.
Example model:
- One counter represents one fission event.
- Each fission event produces three “neutrons”.
- Roll a die for each neutron.
- If the die shows
, or , the neutron causes another fission event. - If the die shows
, or , the neutron escapes or is absorbed.
Record the number of fission events in each generation.
| Generation | Number of fission events |
|---|---|
| 0 | 1 |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 |
Analysis
Students calculate the multiplication factor for each generation.
Students decide whether the reaction is:
- subcritical if
- critical if
- supercritical if
Students graph fission events against generation number and describe the trend.
Evaluation
Students discuss limitations of the model.
Possible limitations:
- Real neutrons move in three dimensions.
- Real fission fragments and neutron energies vary.
- Not all nuclei in a sample are fissile.
- Control rods, moderators and geometry affect real chain reactions.
- The model does not represent the energy released by fission.
Problems
The following problems are designed to practise explaining and applying fission chain reactions.
-
Define a fission chain reaction.
-
Explain why uranium-235 can support a fission chain reaction.
-
Complete the explanation:
A neutron is absorbed by a uranium-235 nucleus. The nucleus becomes unstable and splits into two smaller nuclei. During this process, energy and extra __________ are released. These can cause further __________ reactions.
-
A fission reaction releases three neutrons. In the next generation, only two neutrons cause fission. Explain why the reaction can still grow.
-
A sample has
fission events in one generation and in the next generation. Calculate and classify the chain reaction. -
A sample has
fission events in one generation and in the next generation. Calculate and classify the chain reaction. -
A sample has
fission events in one generation and in the next generation. Calculate and classify the chain reaction. -
Explain the difference between a controlled and uncontrolled fission chain reaction.
-
Explain why a chain reaction requires enough fissile material.
-
In a reactor, control rods absorb neutrons. Explain how this helps control the chain reaction.
-
A chain reaction starts with one fission event. Each fission event causes two further fission events. Calculate the number of fission events in generation
. -
Explain why the number of fission events may not increase exactly as predicted in a real material.
Followup
Self-check
Students should be able to answer these questions.
- Can I explain how one fission event can trigger another?
- Can I describe the role of neutrons in a fission chain reaction?
- Can I classify a chain reaction as subcritical, critical or supercritical?
- Can I explain why real chain reactions depend on neutron loss and neutron absorption?
- Can I distinguish between a controlled reactor chain reaction and an uncontrolled chain reaction?
Next Topic
The next topic is:
Describe the concepts of mass defect, binding energy and binding energy per nucleon.