Nuclear Energy
1. Nuclear Fission
Learning outcomes
- I can describe nuclear fission.
- I can explain how fission releases energy.
- I can describe a chain reaction.
- I can explain the role of neutrons in fission.
- I can identify fuels used in nuclear reactors.
Nuclear Fission
Nuclear fission is a nuclear reaction in which a heavy atomic nucleus splits into two smaller nuclei, releasing energy and usually several neutrons.
Fission is important because it is the process used to release energy in:
- nuclear power reactors
- some research reactors
Common fissile fuels include:
- uranium-235 (²³⁵U)
- plutonium-239 (²³⁹Pu)
Of these, uranium-235 is commonly used to introduce and explain the fission process.
The Atomic Nucleus
The nucleus of an atom contains:
- protons
- neutrons
These particles are collectively called:
nucleons
Protons and neutrons are held together by the:
strong nuclear interaction
At very short distances, this interaction helps hold the nucleus together despite the electrical repulsion between positively charged protons.
Very large nuclei contain many protons.
As nuclei become very large, maintaining stability becomes increasingly difficult.
Some heavy nuclei can therefore undergo:
fission
under suitable conditions.
Uranium-235
Uranium has several naturally occurring isotopes.
The most important for introductory nuclear fission is:
uranium-235
Its nucleus contains:
- 92 protons
- 143 neutrons
because:
235 − 92 = 143
Uranium-235 is fissile, meaning it can undergo fission after absorbing a neutron, including a slow neutron.
Starting Nuclear Fission
A typical fission event begins when a uranium-235 nucleus absorbs a neutron.
The process can be represented as:
²³⁵₉₂U + ¹₀n → ²³⁶₉₂U*
The asterisk indicates that the resulting uranium-236 nucleus is in an:
excited state
This excited nucleus is unstable.
It can deform and split into two smaller nuclei.
A Fission Reaction
One possible fission reaction is:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + energy
This represents uranium-235 splitting into:
- barium-141
- krypton-92
- three neutrons
plus energy.
This is only one possible fission pathway. Fission can produce many different combinations of daughter nuclei.
Checking the Nuclear Equation
Nuclear equations must conserve:
- nucleon number
- electric charge
For the example:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n
Check nucleon number:
Left:
235 + 1 = 236
Right:
141 + 92 + 3 = 236
Therefore:
nucleon number is conserved
Check atomic number:
Left:
92
Right:
56 + 36 = 92
Therefore:
charge is conserved
What Happens During Fission?
A simplified sequence is:
neutron approaches nucleus → neutron absorbed → unstable compound nucleus forms → nucleus deforms → nucleus splits → fission fragments + neutrons + energy
The products are called:
fission fragments
They are usually radioactive because they contain neutron-to-proton ratios that are not stable.
Why Does Fission Release Energy?
The total mass of the fission products is slightly less than the total mass of the original nucleus and absorbed neutron.
This difference is called the:
mass defect
The missing mass has been converted into other forms of energy.
Einstein's equation describes the relationship:
E = Δmc²
where:
- E = energy released
- Δm = decrease in mass
- c = speed of light
Because c² is extremely large, a very small change in mass can correspond to a substantial amount of energy.
Binding Energy
Another way to understand fission is through:
nuclear binding energy
Binding energy is the energy associated with holding a nucleus together.
Medium-mass nuclei are generally more tightly bound per nucleon than extremely heavy nuclei such as uranium.
When a heavy nucleus splits into medium-mass nuclei, the products are more tightly bound.
The difference in binding energy appears as released energy.
Binding Energy per Nucleon
A useful measure is:
binding energy per nucleon
This tells us how tightly, on average, each proton or neutron is bound inside a nucleus.
The binding energy per nucleon generally increases from very light nuclei toward nuclei around the iron/nickel region.
For very heavy nuclei, it is somewhat lower.
Therefore:
heavy nucleus → medium-sized nuclei
can move nucleons toward more tightly bound configurations.
The difference appears as released energy.
Where Does the Energy Go?
Most of the energy released in a fission event initially appears as:
kinetic energy of the fission fragments
The fragments move apart at high speeds.
They collide with surrounding atoms and transfer energy to them.
This increases the:
thermal energy
of the reactor fuel and surrounding material.
Energy is also carried by:
- emitted neutrons
- gamma radiation
- later radioactive decays of fission products
Energy Released per Fission
A typical uranium-235 fission releases approximately:
200 MeV
of energy.
Using:
1 eV = 1.60 × 10⁻¹⁹ J
then:
200 MeV = 200 × 10⁶ eV
Energy:
≈ 200 × 10⁶ × 1.60 × 10⁻¹⁹
≈ 3.2 × 10⁻¹¹ J
This seems extremely small for one nucleus.
However, a macroscopic amount of fuel contains an enormous number of nuclei.
Why Nuclear Fuel Contains So Much Energy
Suppose a very large number of uranium nuclei undergo fission.
Each releases approximately:
3.2 × 10⁻¹¹ J.
If:
10²⁰ nuclei
undergo fission:
Energy ≈ 10²⁰ × 3.2 × 10⁻¹¹
Energy ≈ 3.2 × 10⁹ J
This demonstrates why nuclear reactions can release enormous amounts of energy from relatively small quantities of fuel.
The Importance of Neutrons
Neutrons play a central role in nuclear fission.
A neutron can:
- enter a uranium-235 nucleus
- make the nucleus unstable
- trigger fission
- cause additional neutrons to be released
Those new neutrons may then strike other fissile nuclei.
This makes possible a:
chain reaction
Chain Reactions
A nuclear chain reaction occurs when neutrons produced by one fission event cause additional fission events.
A simplified pattern is:
1 fission → several neutrons → several possible fissions → more neutrons → more possible fissions
This creates a branching process.
A visual model of this branching process helps show why controlling the number of neutrons that cause further fissions is so important.
Multiplication of Fission Events
Imagine each fission releases three neutrons and every neutron successfully causes another fission.
Then theoretically:
First generation:
1 fission
Second generation:
3 fissions
Third generation:
9 fissions
Fourth generation:
27 fissions
Fifth generation:
81 fissions
The number could increase extremely rapidly.
In real systems, however, not every neutron causes another fission.
What Can Happen to a Neutron?
A neutron released during fission may:
- cause another fission
- be absorbed without causing fission
- escape from the material
- interact with other nuclei
- lose kinetic energy through collisions
Therefore, maintaining a chain reaction depends on how many neutrons successfully cause further fissions.
Subcritical Chain Reaction
A system is subcritical when, on average, fewer than one neutron from each fission produces another fission.
Therefore:
fission rate decreases
and the chain reaction eventually dies away.
Symbolically:
k < 1
where k represents the effective neutron multiplication factor.
Critical Chain Reaction
A system is critical when, on average, one neutron from each fission produces another fission.
Therefore:
fission rate remains approximately constant
and the chain reaction is self-sustaining.
Symbolically:
k = 1
This is the basic condition desired during steady reactor operation.
Supercritical Chain Reaction
A system is supercritical when, on average, more than one neutron from each fission produces another fission.
Therefore:
fission rate increases
Symbolically:
k > 1
A reactor may be slightly supercritical during controlled power increases, but reactor systems are designed to regulate neutron population carefully.
Comparing Chain Reaction Conditions
| Condition | Neutrons Causing Further Fission | Result |
|---|---|---|
| Subcritical | Less than 1 per fission on average | Reaction decreases |
| Critical | 1 per fission on average | Reaction remains steady |
| Supercritical | More than 1 per fission on average | Reaction increases |
The key idea is not simply how many neutrons are produced.
It is:
how many successfully produce another fission.
Neutron Energy
Neutrons released directly from fission are usually relatively fast.
For uranium-235, slower neutrons are particularly effective at causing further fission.
Many reactor designs therefore slow neutrons down using a:
moderator
Moderator
A moderator is a material that slows neutrons without absorbing too many of them.
Common moderator materials include:
- ordinary water
- heavy water
- graphite
Neutrons lose kinetic energy through collisions with nuclei in the moderator.
Slower neutrons can then have a greater probability of causing fission in uranium-235.
Why Water Is an Effective Moderator
Water contains hydrogen nuclei.
A hydrogen nucleus is a proton and has a mass similar to that of a neutron.
When a neutron collides with a particle of similar mass, it can transfer a significant fraction of its kinetic energy.
This makes hydrogen-containing materials effective at slowing neutrons.
Control Rods
Reactors must control the number of neutrons available to cause further fission.
This can be achieved using:
control rods
Control rods contain materials that absorb neutrons effectively.
Examples include materials containing:
- boron
- cadmium
- hafnium
The rods can be moved into or out of the reactor core.
How Control Rods Work
If control rods are inserted farther into the reactor:
more neutrons absorbed → fewer fissions → reactor power decreases
If control rods are withdrawn:
fewer neutrons absorbed → more neutrons available → fission rate can increase
Control rods therefore help regulate the chain reaction.
Moderator vs Control Rod
These components have very different functions.
Moderator
slows neutrons
It helps make neutrons more effective at producing fission in thermal-reactor fuels such as uranium-235.
Control rods
absorb neutrons
They reduce the number of neutrons available to produce additional fission.
Do not confuse the two.
Nuclear Reactor Fuel
Nuclear reactors require material containing nuclei capable of sustaining fission.
Important fuels include:
Uranium-235
The most important fissile isotope in conventional uranium fuel.
Plutonium-239
A fissile isotope that can be produced from uranium-238 in reactors and can be used as reactor fuel.
Some reactor fuels contain mixtures of uranium and plutonium.
Uranium-238
Natural uranium consists mostly of:
uranium-238
with a much smaller proportion of:
uranium-235
Uranium-238 is not fissile with slow neutrons in the same way as uranium-235.
However, it is important because it can absorb a neutron and, through subsequent nuclear transformations, contribute to the production of:
plutonium-239
Uranium-238 is therefore described as:
fertile
rather than fissile in this context.
Fissile vs Fertile
Fissile material
can sustain a chain reaction using suitable neutrons.
Examples:
- uranium-235
- plutonium-239
Fertile material
can be converted into fissile material through nuclear reactions.
Example:
- uranium-238
This distinction is important in nuclear reactor physics.
Natural Uranium
Natural uranium contains approximately:
- 99.3% uranium-238
- 0.7% uranium-235
Some reactor designs can use natural uranium.
Many others use:
enriched uranium
in which the proportion of uranium-235 has been increased.
Enriched Uranium
Uranium enrichment increases the proportion of uranium-235 relative to uranium-238.
Commercial reactor fuel in many reactor designs uses uranium enriched to a few percent uranium-235.
The remaining uranium is mostly uranium-238.
The exact enrichment depends on reactor design and fuel requirements.
Fuel Rods
Nuclear fuel is commonly manufactured into small ceramic pellets.
These pellets are placed inside:
fuel rods
Many fuel rods are grouped into:
fuel assemblies
which form part of the reactor core.
The Reactor Core
The reactor core contains the nuclear fuel where fission occurs.
Depending on reactor design, the core may contain:
- fuel rods
- moderator
- control rods
- coolant
The core is designed so that the chain reaction can be carefully controlled.
Coolant
Fission produces thermal energy in the reactor core.
A coolant carries this thermal energy away.
Different reactor designs use different coolants, including:
- water
- gases
- liquid metals
In many power reactors, water acts as both:
coolant and moderator
From Fission to Electricity
A nuclear power station converts nuclear energy into electrical energy through several stages.
A simplified energy pathway is:
nuclear energy → thermal energy → kinetic energy → electrical energy
More specifically:
fission → heats coolant/water → steam produced → turbine rotates → generator produces electricity
Fission Heats the Reactor
The fission fragments produced inside the fuel move at high speed.
They collide with atoms in the fuel.
Their kinetic energy becomes:
thermal energy
The fuel becomes hot.
A coolant transfers this energy away from the reactor core.
Producing Steam
In many nuclear power stations, the thermal energy is ultimately used to produce:
steam
The steam flows through a turbine.
The moving steam causes the turbine blades to rotate.
This converts:
thermal energy → kinetic/mechanical energy
Generator
The rotating turbine is connected to a:
generator
The generator converts mechanical energy into:
electrical energy
Therefore, the reactor itself does not directly produce electricity.
The reactor provides the:
thermal energy source
Nuclear vs Fossil-Fuel Power Stations
Nuclear and fossil-fuel power stations can have similar later stages.
Both may use:
heat → steam → turbine → generator
The major difference is the source of thermal energy.
Fossil-fuel station
Chemical combustion releases energy.
Nuclear station
Nuclear fission releases energy.
Controlled Chain Reaction
A power reactor requires a:
controlled chain reaction
The objective is to maintain the fission rate at the level needed to produce the desired thermal power.
If too few neutrons cause further fission:
power decreases
If too many cause further fission:
power increases
Control systems regulate the neutron population.
Criticality
A reactor operating steadily is approximately:
critical
This does not mean:
dangerous or about to explode
In reactor physics, critical simply means:
the chain reaction is self-sustaining at a steady level
This is an important use of the word "critical" that differs from its everyday meaning.
Delayed Neutrons
Most fission neutrons are released almost immediately.
However, a small fraction are released later by certain radioactive fission products.
These are called:
delayed neutrons
Although they represent only a small fraction of the total neutron population, they are extremely important in conventional reactor control because they make changes in reactor power much slower and therefore manageable by control systems.
Fission Products
The nuclei produced by fission are called:
fission products
Many are unstable and radioactive.
They may undergo:
- beta decay
- gamma emission
until they eventually reach more stable nuclear configurations.
These radioactive fission products are one reason spent nuclear fuel remains radioactive after it is removed from a reactor.
Decay Heat
Even after the chain reaction is stopped, radioactive fission products continue to decay.
Their radioactive decay releases energy.
This produces:
decay heat
Therefore:
shutting down the chain reaction does not instantly eliminate heat production.
Cooling must continue after shutdown.
This is an important reactor-safety concept.
Spent Nuclear Fuel
After being used in a reactor, nuclear fuel contains:
- remaining uranium
- fission products
- newly produced isotopes
- transuranic elements
This material is highly radioactive and must be:
- cooled
- shielded
- securely stored
- carefully managed
Why Fission Products Are Radioactive
Fission produces nuclei with neutron-to-proton ratios that are often unstable.
Many therefore undergo:
beta-minus decay
A neutron changes into a proton, producing an electron and an antineutrino.
Through chains of radioactive decay, fission products eventually move toward more stable nuclei.
Energy Density
Nuclear fuel has an extremely high:
energy density
This means a relatively small mass of nuclear fuel can release a very large amount of energy.
This occurs because nuclear reactions involve changes in nuclear binding energy rather than chemical bonds between atoms.
Chemical vs Nuclear Energy
Chemical reactions involve:
electrons and chemical bonds
Nuclear fission involves:
atomic nuclei
The energy released per reaction in nuclear processes is typically vastly larger than in ordinary chemical reactions.
This is why small amounts of nuclear fuel can provide large amounts of energy.
Fission vs Radioactive Decay
Fission and radioactive decay are related nuclear processes, but they are not the same.
Radioactive decay
An unstable nucleus spontaneously changes.
Examples include:
- alpha decay
- beta decay
- gamma emission
Induced fission
A heavy nucleus such as uranium-235 absorbs a neutron and then splits.
A major difference is that fission releases additional neutrons that can produce:
a chain reaction
Fission vs Fusion
Fission should also not be confused with:
nuclear fusion
Fission
large nucleus → smaller nuclei
Example:
uranium splitting.
Fusion
small nuclei → larger nucleus
Example:
hydrogen nuclei combining in stars.
Both can release energy because the products have greater binding energy per nucleon than the starting nuclei.
Conservation in Fission
Nuclear fission obeys conservation laws.
Quantities conserved include:
- electric charge
- total energy
- momentum
- nucleon number in the usual nuclear-equation accounting
Mass by itself is not separately conserved in the classical sense because some rest mass can be converted into other forms of energy.
Instead:
mass-energy is conserved
Worked Nuclear Equation
Consider:
²³⁵₉₂U + ¹₀n → ¹⁴⁴₅₆Ba + X + 3¹₀n
Find X.
Mass numbers:
236 = 144 + A + 3
A = 89
Atomic numbers:
92 = 56 + Z
Z = 36
Element 36 is krypton.
Therefore:
X = ⁸⁹₃₆Kr
Worked Energy Calculation
Suppose a fission event has a mass defect of:
3.5 × 10⁻²⁸ kg
Use:
E = Δmc²
with:
c = 3.0 × 10⁸ m/s
Then:
E = (3.5 × 10⁻²⁸)(3.0 × 10⁸)²
E = (3.5 × 10⁻²⁸)(9.0 × 10¹⁶)
E = 3.15 × 10⁻¹¹ J
This is the energy released by a single nuclear event.
Worked Chain-Reaction Example
Suppose each fission produces three neutrons, but on average only one neutron successfully causes another fission.
Then:
Generation 1: 1 fission
Generation 2: 1 fission
Generation 3: 1 fission
Generation 4: 1 fission
The average fission rate remains constant.
The system is:
critical
with:
k = 1
Common Mistakes
Mistake: Saying fission means two atoms collide.
Fission is the splitting of a heavy nucleus.
Mistake: Saying the neutron splits in fission.
The neutron is absorbed by the heavy nucleus, which then becomes unstable and splits.
Mistake: Saying uranium-235 always produces exactly the same two fission fragments.
Many different fission-product combinations are possible.
Mistake: Saying all neutrons released cause another fission.
Some escape or are absorbed without causing fission.
Mistake: Saying a moderator absorbs neutrons.
The primary purpose of a moderator is to slow neutrons.
Mistake: Saying control rods slow neutrons.
Control rods primarily absorb neutrons.
Mistake: Thinking "critical reactor" means an emergency.
Critical means the chain reaction is self-sustaining at a steady level.
Mistake: Saying nuclear reactors directly create electricity.
Fission produces thermal energy, which is ultimately used to drive generators.
Mistake: Saying a reactor immediately becomes cold when fission stops.
Radioactive fission products continue producing decay heat.
Mistake: Confusing fission and fusion.
Fission splits heavy nuclei; fusion combines light nuclei.
Key Terms
Nuclear fission — splitting of a heavy nucleus into smaller nuclei with the release of energy and neutrons.
Fissile — capable of sustaining a nuclear fission chain reaction with suitable neutrons.
Fission fragment — one of the smaller nuclei produced when a heavy nucleus undergoes fission.
Chain reaction — process in which neutrons from one fission cause additional fissions.
Criticality — condition describing whether a fission chain reaction decreases, remains steady, or increases.
Multiplication factor (k) — measure of how the neutron population changes from one generation to the next.
Subcritical — condition where k < 1 and the chain reaction decreases.
Critical — condition where k = 1 and the chain reaction remains steady.
Supercritical — condition where k > 1 and the chain reaction increases.
Moderator — material used to slow neutrons.
Control rod — neutron-absorbing component used to regulate a reactor chain reaction.
Nuclear fuel — material containing nuclei used to sustain nuclear reactions.
Uranium-235 — important fissile isotope used in nuclear reactors.
Plutonium-239 — fissile isotope that can be used as nuclear fuel.
Uranium-238 — fertile isotope that can contribute to production of plutonium-239.
Enriched uranium — uranium in which the proportion of uranium-235 has been increased.
Mass defect — difference in rest mass associated with a nuclear reaction or nuclear binding.
Binding energy — energy associated with holding a nucleus together.
Decay heat — thermal energy produced by radioactive decay after the fission chain reaction has been reduced or stopped.
Key Takeaways
- Nuclear fission is the splitting of a heavy atomic nucleus.
- Uranium-235 is an important fissile isotope.
- Fission can begin when uranium-235 absorbs a neutron.
- The resulting excited uranium-236 nucleus can split into smaller nuclei.
- Fission produces fission fragments, neutrons and energy.
- Different fission events can produce different combinations of daughter nuclei.
- A typical uranium-235 fission releases roughly 200 MeV.
- Fission releases energy because the products have greater binding energy per nucleon than the original heavy nucleus.
- A small amount of mass corresponds to released energy according to E = Δmc².
- Most fission energy initially appears as kinetic energy of the fission fragments.
- Neutrons released during fission can trigger further fissions.
- This produces a nuclear chain reaction.
- A subcritical reaction decreases.
- A critical reaction remains approximately steady.
- A supercritical reaction increases.
- Moderators slow neutrons.
- Control rods absorb neutrons.
- Uranium-235 and plutonium-239 are important fissile fuels.
- Uranium-238 is primarily fertile rather than fissile with slow neutrons.
- Many reactors use enriched uranium.
- Nuclear power stations convert nuclear → thermal → mechanical → electrical energy.
- Fission products are often radioactive.
- Radioactive fission products continue producing decay heat after reactor shutdown.
- Nuclear fuel has a much greater energy density than ordinary chemical fuels.
- Fission splits heavy nuclei, whereas fusion combines light nuclei.
Check Your Understanding
- Define nuclear fission.
- Name two fissile isotopes that can be used as nuclear fuel.
- How many protons and neutrons are present in uranium-235?
- Explain what happens when uranium-235 absorbs a neutron.
- What are fission fragments?
- Write a word description of a typical uranium-235 fission reaction.
- Explain why nuclear fission releases energy.
- What is meant by mass defect?
- State the equation connecting mass and energy.
- Approximately how much energy is released by a typical uranium-235 fission?
- Explain the role of neutrons in a fission chain reaction.
- What can happen to a neutron after it is released during fission?
- Distinguish between subcritical, critical and supercritical chain reactions.
- What does k = 1 mean?
- Explain the purpose of a moderator in a nuclear reactor.
- Explain the purpose of control rods.
- What is the difference between fissile and fertile material?
- Why is uranium sometimes enriched before being used as reactor fuel?
- Describe the energy transformations that occur from nuclear fission to electricity generation.
- Explain why a nuclear reactor continues producing some heat even after the fission chain reaction has been stopped.