Theme E — Nuclear and Quantum Physics
E.4.3 Chain Reactions from Fission — IB Physics HL Revision Notes & Topical Questions
5 min read 9 parts Lesson 34 of 45 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
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
Section 1 of 9The chain reaction
1
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.
Section 2 of 9Multiplication 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.
Section 3 of 9Critical mass
Critical 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.
Section 4 of 9What happens to the neutrons
1
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 |
Section 5 of 9Fast 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.
Section 6 of 9Controlling 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.
Section 7 of 9More 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.
Section 8 of 9Key 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. |
Section 9 of 9Exam technique
1
Thinking a critical reaction is a bomb — critical means steady, k = 1.
2
Believing k is the number of neutrons produced per fission — it is the number that cause further fission.
3
Assuming more mass always gives higher k with no limit — shape and leakage matter.
4
Forgetting that fast neutrons are poorly captured by uranium-235.
5
Confusing critical mass with the mass of the reactor — it is the minimum for k = 1.
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