Nuclear Reactions
2. Nuclear Fission
Learning outcomes
- I can describe nuclear fission.
- I can explain chain reactions.
- I can calculate simple energy changes.
- I can describe how nuclear reactors control fission.
- I can evaluate the advantages and disadvantages of fission.
What Is Nuclear Fission?
Nuclear fission is the splitting of a heavy atomic nucleus into two smaller nuclei.
This process usually also releases:
- neutrons
- gamma radiation
- a large amount of energy
A common example involves uranium-235.
One possible reaction is:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + energy
The exact fission products can vary, but the general pattern is:
heavy nucleus + neutron → two smaller nuclei + neutrons + energy
Why Can Heavy Nuclei Undergo Fission?
Very heavy nuclei contain many protons.
All protons repel one another because of the electromagnetic force.
The strong nuclear interaction holds nucleons together, but it acts only over very short distances.
As nuclei become very large:
- proton-proton repulsion becomes increasingly important
- the nucleus can become easier to deform
- some heavy nuclei become susceptible to splitting
A nucleus such as uranium-235 can absorb a neutron and become highly excited.
That excitation can cause the nucleus to stretch and split.
Fission of Uranium-235
Uranium-235 is especially important because it can undergo fission after absorbing a slow neutron.
The first step can be represented as:
²³⁵U + n → ²³⁶U*
The asterisk means that uranium-236 is in an excited state.
The excited nucleus can then split:
²³⁶U → fission fragments + neutrons + energy*
For example:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n + energy
Checking the Nuclear Equation
Mass numbers:
235 + 1 = 141 + 92 + 3
236 = 236
Atomic numbers:
92 = 56 + 36
92 = 92
So nucleon number and charge are conserved.
Where Does the Energy Come From?
The energy released during fission comes from a difference in nuclear binding energy.
Very heavy nuclei generally have a lower binding energy per nucleon than medium-mass nuclei.
When a heavy nucleus splits, the products move toward the more tightly bound middle region of the binding-energy curve.
Therefore:
fission products have greater binding energy per nucleon than the original heavy nucleus
The total mass of the products is slightly less than the total mass of the starting system.
This mass defect appears as released energy.
Mass-Energy in Fission
The energy released is calculated using:
E = Δmc²
where:
Δm = mass before − mass after
Even a very small mass difference can produce a large amount of energy because:
c² ≈ 9 × 10¹⁶ m²/s²
Example 1: Energy from a Mass Change
Suppose a fission reaction has a mass defect of:
3.5 × 10⁻²⁸ kg
Use:
E = Δmc²
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 from only one reaction.
That may seem tiny, but an enormous number of nuclei can undergo fission in a macroscopic sample.
Using Atomic Mass Units
Particle and nuclear masses are often given in atomic mass units.
Recall:
1 u c² ≈ 931.5 MeV
So:
Energy released in MeV = mass defect in u × 931.5
Example 2: Energy in MeV
Suppose the mass defect is:
0.210 u
Then:
E = 0.210 × 931.5
E ≈ 196 MeV
A single uranium-235 fission typically releases energy on the order of about 200 MeV.
Where Does the Fission Energy Go?
The released energy appears mainly as:
- kinetic energy of the fission fragments
- kinetic energy of emitted neutrons
- gamma radiation
- later radioactive decay energy from unstable fission products
Most of the immediate energy is carried by the two large fission fragments.
As these fragments move through surrounding material, collisions convert their kinetic energy into thermal energy.
Chain Reactions
One of the most important features of nuclear fission is that it can produce additional neutrons.
Suppose one fission produces three neutrons.
Those neutrons may strike other uranium-235 nuclei.
Each of those nuclei may also split.
This can produce still more neutrons.
The result is a chain reaction.
A Simple Chain Reaction
Imagine:
Generation 1
One fission produces:
3 neutrons
Generation 2
If all three cause fission:
3 fissions
Suppose each produces 3 more neutrons:
9 neutrons
Generation 3
Those could cause:
9 fissions
and produce:
27 neutrons
The number of reactions could increase very rapidly.
In reality, not every neutron causes another fission.
Some:
- escape
- are absorbed without causing fission
- lose energy
- interact with other nuclei
Criticality
A chain reaction can behave in three general ways.
Subcritical
On average, fewer than one neutron from each fission causes another fission.
The reaction gradually dies out.
Critical
On average, exactly one neutron from each fission causes another fission.
The reaction continues at a steady rate.
Supercritical
On average, more than one neutron from each fission causes another fission.
The reaction rate increases.
A power reactor is designed to operate close to a controlled critical condition.
The Multiplication Factor
Nuclear engineers often describe chain reactions using a multiplication factor called k.
Very simply:
k < 1 → subcritical
k = 1 → critical
k > 1 → supercritical
A reactor operating steadily aims for approximately:
k = 1
This means the fission rate remains roughly constant.
How a Nuclear Reactor Uses Fission
A nuclear reactor uses a controlled fission chain reaction to produce thermal energy.
The basic sequence is:
fission
↓
kinetic energy of fission products
↓
thermal energy in reactor fuel
↓
heat transferred to coolant
↓
steam produced, directly or indirectly
↓
turbine turns
↓
generator produces electricity
The reactor is therefore primarily a heat source.
Main Parts of a Nuclear Reactor
A simplified reactor includes:
- nuclear fuel
- moderator in many reactor designs
- control rods
- coolant
- reactor vessel/core
- heat exchanger or steam generator in many designs
- turbine
- generator
- containment structures
Nuclear Fuel
The fuel contains fissile material.
Common examples include fuels containing uranium, especially uranium-235.
The fuel is commonly formed into ceramic pellets and arranged in fuel rods.
The fuel rods are grouped into assemblies inside the reactor core.
The Moderator
In many thermal reactors, a moderator slows fast neutrons.
Why is this useful?
For uranium-235, slow or thermal neutrons are particularly effective at causing further fission.
Common moderator materials include:
- ordinary water
- heavy water
- graphite
The moderator does not stop the reaction. It changes neutron energies so that the chain reaction can be sustained efficiently.
Control Rods
Control rods absorb neutrons.
They can be inserted into or withdrawn from the reactor core.
If control rods are inserted farther:
more neutrons are absorbed
↓
fewer neutrons cause fission
↓
fission rate decreases
If control rods are withdrawn:
fewer neutrons are absorbed
↓
more neutrons remain available
↓
fission rate can increase
Control rods therefore help regulate reactor power.
Common Control-Rod Materials
Control rods use materials that absorb neutrons efficiently.
Examples include materials containing:
- boron
- cadmium
- hafnium
The exact materials depend on reactor design.
The Coolant
The coolant removes thermal energy from the reactor core.
Depending on reactor type, coolants may include:
- water
- heavy water
- gases
- liquid metals
- molten salts in some designs
The coolant transports energy from the core to another part of the power-generation system.
From Heat to Electricity
A nuclear power station does not generate electricity directly from the nucleus.
Instead:
nuclear energy → thermal energy → mechanical energy → electrical energy
The heat from fission ultimately produces steam or another working fluid.
The steam turns a turbine.
The turbine turns a generator.
The generator produces electrical energy.
Why Reactors Need Continuous Control
The power output of a reactor depends strongly on the neutron population.
If too many neutrons cause new fissions:
power rises
If too few do:
power falls
Reactor systems use:
- control rods
- neutron measurements
- temperature feedback
- coolant systems
- shutdown systems
to maintain safe operation.
Delayed Neutrons
Most neutrons from fission are emitted almost immediately.
However, a small fraction appear later from radioactive fission products.
These are called delayed neutrons.
Although they represent only a small fraction of the neutron population, they are extremely important because they make reactor chain reactions much easier to control over human and mechanical timescales.
Fission Products Are Often Radioactive
The smaller nuclei produced by fission are usually neutron-rich.
Many are unstable.
They undergo radioactive decay, often through beta decay.
Therefore, even after the chain reaction is stopped, radioactive fission products continue to release energy.
This is called decay heat.
Why Cooling Must Continue After Shutdown
Stopping the chain reaction does not instantly eliminate all heat production.
Radioactive fission products continue to decay.
Therefore:
reactor shutdown ≠ immediate zero heat
Cooling systems must continue removing decay heat.
This is one of the most important safety considerations in reactor design.
Advantages of Nuclear Fission
Nuclear fission has several major advantages as an energy source.
High Energy Density
A small amount of nuclear fuel can release a very large amount of energy.
This is because nuclear energy changes are much larger than ordinary chemical energy changes.
Low Direct Carbon Dioxide Emissions During Operation
A nuclear reactor does not burn fossil fuel during normal operation.
Therefore, direct carbon dioxide emissions from electricity generation are very low.
There are still lifecycle emissions from:
- construction
- mining
- fuel processing
- transport
- decommissioning
but overall lifecycle greenhouse-gas emissions are generally low compared with fossil-fuel generation.
Reliable Power Production
Nuclear power stations can produce large amounts of electricity continuously.
They are not directly dependent on:
- sunshine
- wind speed
- daily weather changes
This makes them useful for steady electricity generation.
Small Fuel Mass
Because nuclear fuel has very high energy density, relatively little fuel is required compared with coal, oil, or gas for the same amount of energy.
Disadvantages of Nuclear Fission
Fission also presents significant challenges.
Radioactive Waste
Fission produces radioactive materials.
Some waste remains hazardous for long periods.
It must be:
- contained
- shielded
- transported safely
- stored or disposed of securely
Accident Risk
Modern reactors include many safety systems, but severe accidents can have significant environmental, economic, and social consequences.
Safe reactor design therefore requires multiple independent protective systems.
High Construction Cost
Nuclear power stations are complex.
They require:
- extensive safety systems
- radiation shielding
- highly engineered components
- strict regulation
As a result, construction costs can be high.
Long Construction and Decommissioning Times
Large reactors can take years to plan and build.
At the end of their useful life, they must also be safely decommissioned.
This can be expensive and time-consuming.
Nuclear Material Security
Some nuclear materials and technologies can raise concerns involving:
- security
- theft
- diversion of nuclear material
- weapons proliferation
Civil nuclear programs therefore require strong safeguards and international oversight.
Evaluating Fission Fairly
Whether nuclear fission is considered a good energy option depends on several factors.
These include:
- electricity demand
- available alternatives
- local geography
- cost
- climate goals
- grid reliability
- waste-management plans
- reactor technology
- public acceptance
A strong evaluation considers both advantages and disadvantages rather than treating nuclear power as simply "good" or "bad."
Comparing Fission with Fossil Fuels
| Nuclear Fission | Fossil Fuels |
|---|---|
| Very high energy density | Lower energy density |
| Low direct CO₂ during operation | Large CO₂ emissions when burned |
| Produces radioactive waste | Produces greenhouse gases and air pollutants |
| High construction cost | Often lower initial construction cost |
| Requires radioactive-material management | Requires continuous fuel extraction and combustion |
| Can provide steady output | Can also provide controllable steady output |
Fission and Renewable Energy
Nuclear and renewable technologies are not necessarily direct opposites.
A low-carbon electricity system can potentially combine:
- nuclear power
- solar
- wind
- hydroelectricity
- storage
- other low-carbon technologies
The best mixture depends on the needs and resources of a particular region.
Example 3: Chain Reaction Reasoning
Suppose each fission produces an average of:
2.5 neutrons
But only:
40%
of those neutrons cause another fission.
Average successful neutrons per fission:
2.5 × 0.40 = 1.0
So:
k ≈ 1
The chain reaction would be approximately critical and could continue at a steady rate.
Example 4: Subcritical Reaction
Suppose each fission produces:
2.4 neutrons
and only:
30%
cause another fission.
Then:
2.4 × 0.30 = 0.72
Since:
k < 1
the reaction is subcritical.
The chain reaction will decrease.
Example 5: Supercritical Reaction
Suppose each fission produces:
3 neutrons
and:
50%
cause another fission.
Then:
3 × 0.50 = 1.5
Since:
k > 1
the neutron population increases.
The reaction is supercritical.
Nuclear Fission and Conservation Laws
A fission reaction must conserve:
- electric charge
- nucleon number
- energy
- momentum
- angular momentum
Consider:
²³⁵₉₂U + ¹₀n → ¹⁴¹₅₆Ba + ⁹²₃₆Kr + 3¹₀n
Nucleon number:
235 + 1 = 141 + 92 + 3
Charge:
92 = 56 + 36
Both are conserved.
The small difference in rest mass appears as released energy.
Did You Know?
Most of the energy released in a fission event does not come directly from the emitted neutrons.
A large fraction appears as kinetic energy of the two heavy fission fragments.
These positively charged fragments move rapidly through the surrounding fuel and collide with other atoms.
Their motion is converted into thermal energy.
This is how microscopic nuclear energy ultimately becomes the heat used to generate electricity.
Connecting the Ideas
Nuclear fission links several ideas from this course:
Heavy nucleus absorbs neutron
↓
Excited compound nucleus forms
↓
Nucleus splits
↓
Smaller nuclei + neutrons produced
↓
Products have greater binding energy per nucleon
↓
Mass decreases slightly
↓
E = Δmc²
↓
Energy released
↓
Released neutrons can trigger more fissions
↓
Chain reaction
↓
Control rods and reactor systems regulate the process
Fission is therefore a direct application of nuclear stability, binding energy, mass defect, mass-energy equivalence, and conservation laws.
Key Terms
Nuclear fission – The splitting of a heavy nucleus into smaller nuclei, usually with the release of neutrons and energy.
Fission fragment – One of the smaller nuclei produced during fission.
Chain reaction – A sequence in which neutrons from one fission cause additional fissions.
Critical – A condition in which the chain reaction continues at a steady rate.
Subcritical – A condition in which the chain reaction decreases.
Supercritical – A condition in which the chain reaction increases.
Moderator – Material used in many reactors to slow neutrons.
Control rod – A neutron-absorbing component used to regulate a reactor.
Coolant – Material that transfers heat away from a reactor core.
Fissile material – Material capable of sustaining fission after absorbing appropriate neutrons.
Decay heat – Heat produced by radioactive decay of fission products after the main chain reaction has stopped.
Key Takeaways
- Nuclear fission is the splitting of a heavy nucleus into smaller nuclei.
- Fission typically releases neutrons and a large amount of energy.
- Uranium-235 can undergo fission after absorbing a neutron.
- Fission releases energy because the products are generally more tightly bound per nucleon than the original heavy nucleus.
- The small loss of rest mass is converted to energy according to E = Δmc².
- One fission releases energy on the order of hundreds of MeV.
- Neutrons released by fission can trigger further fissions, producing a chain reaction.
- A steady reactor aims to maintain approximately k = 1.
- Control rods absorb neutrons and help regulate the reaction.
- A moderator slows neutrons in many reactor designs.
- A coolant transfers thermal energy away from the reactor core.
- Radioactive fission products continue producing decay heat even after shutdown.
- Fission offers very high energy density and low direct operational carbon emissions, but it also produces radioactive waste and requires strict safety and security systems.
- A fair evaluation of nuclear fission must consider both its benefits and limitations.