Nuclear Fission

Overview

Nuclear Fission is the splitting of a heavy nucleus into two lighter nuclei. In reactor contexts, it is usually initiated when a fissile nucleus absorbs a neutron.

The essential H2 Physics idea is:

A heavy nucleus absorbs a neutron and forms an excited unstable nucleus. The nucleus undergoes fission into smaller daughter nuclei that are more tightly bound (higher binding energy per nucleon). The increase in total binding energy is released as energy, together with additional neutrons.

Fission is not simply “splitting releases energy”. Energy is released because the products have greater total binding energy and lower total mass than the reactants.

This topic links closely with:

• Nuclear Physics
• Nuclear Fusion
• Ionizing Radiation and Safety

Core Ideas

• A heavy nucleus may undergo fission after absorbing a neutron.
• The fission products are usually medium-mass nuclei, together with neutrons and released energy.
• Energy is released because the fission products have greater binding energy per nucleon and are therefore more tightly bound.
• The emitted neutrons may trigger further fission reactions, producing a chain reaction.
• Not all emitted neutrons continue the chain reaction; some escape or are absorbed without causing fission.
• Nuclear reactors use separate systems to control the neutron population and to remove thermal energy from the reactor core.

What Is Fission?

Fission occurs when a heavy nucleus splits into two medium-mass nuclei.

General features:

• often triggered by absorption of a neutron
• a short-lived unstable compound nucleus forms briefly
• daughter nuclei are produced
• additional neutrons are emitted
• energy is released, mainly as kinetic energy of the fission fragments and emitted neutrons

Fission differs from ordinary radioactive decay because the standard reactor example is an induced nuclear reaction initiated by neutron absorption, rather than spontaneous alpha, beta, or gamma decay.

Typical Example: Uranium-235

A common teaching example of fission is:

$${}_{92}^{235}\mathrm{U}+{}_0^1\mathrm{n}\to {}_{56}^{141}\mathrm{Ba}+{}_{36}^{92}\mathrm{Kr}+3{}_0^1\mathrm{n}+E$$

Here is a fission example that proceeds through an unstable uranium-236 compound nucleus:

$${}_0^1\mathrm{n}+{}_{92}^{235}\mathrm{U}\to {}_{92}^{236}{\mathrm{U}}^{\ast }\to {}_{54}^{140}\mathrm{Xe}+{}_{38}^{94}\mathrm{Sr}+2{}_0^1\mathrm{n}+\gamma +E$$

Many different fission product combinations are possible. The important general pattern is neutron absorption, formation of an unstable compound nucleus, splitting into medium-mass nuclei, emission of neutrons, and release of energy.

Figure: Neutron-induced fission of uranium-235 forms an unstable nucleus that splits into daughter nuclei, neutrons, and released energy.

Conservation Checks

In nuclear reactions:

• proton number is conserved
• nucleon number is conserved
• momentum is conserved
• total mass-energy is conserved

For the Ba-Kr example:

Quantity	Reactants	Products	Conserved?
Nucleon number	$235+1=236$	$141+92+3=236$	Yes
Proton number	$92+0=92$	$56+36+0=92$	Yes

Why Neutrons Are Used

Neutrons are useful because they carry no electric charge.

Therefore:

• they are not repelled by the positively charged nucleus
• they can approach and enter the nucleus more easily than charged projectiles
• in suitable fuels, they can induce fission

In many reactor contexts, slow thermal neutrons are especially effective at causing fission in uranium-235.

Why Energy Is Released

Mass Defect Explanation

The total mass after fission is less than the total mass before fission:

$$\Delta m=m_{\text{reactants}}-m_{\text{products}}$$

The missing mass appears as released energy:

$$E=\Delta m{c}^2$$

Binding Energy Explanation

Very heavy nuclei have lower binding energy per nucleon than many medium-mass nuclei.

After fission:

• the daughter nuclei are more tightly bound
• the total binding energy increases
• energy is released

So:

$$E=\text{total binding energy of products}-\text{total binding energy of reactants}$$

Do not say energy is released simply because the nucleus splits. The energy release is due to the increase in total binding energy, equivalently the mass defect.

Binding Energy Per Nucleon And Fission

The binding-energy-per-nucleon curve has a maximum near iron-56. Very heavy nuclei lie on the right side of the curve, where the binding energy per nucleon is lower.

When a very heavy nucleus splits into medium-mass nuclei closer to the peak:

• the products have greater binding energy per nucleon
• the products are more stable
• energy is released

Figure: Fission can release energy when a very heavy nucleus splits into products closer to the high-binding-energy region.

This figure is qualitative. It should not be used to read numerical binding energies.

Chain Reaction Overview

The extra neutrons from one fission event may trigger further fission events.

This is a chain reaction:

one fission -> emitted neutrons -> more fissions -> more emitted neutrons

However, not every emitted neutron continues the chain.

Possible neutron outcomes:

• causes another fission
• escapes the fuel
• is absorbed without causing fission
• is absorbed by control rods
• is slowed by a moderator before later causing fission

Figure: A fission chain reaction grows only if enough emitted neutrons cause further fissions; some neutrons are lost or absorbed.

For a fuller discussion of neutron multiplication, criticality, and reactor-component roles, see Chain Reactions and Reactors.

Criticality

Criticality describes whether enough neutrons continue the chain reaction.

State	Meaning	Result
Subcritical	Too few useful neutrons continue	Reaction rate decreases
Critical	Just enough useful neutrons continue	Reaction rate steady
Supercritical	More than enough useful neutrons continue	Reaction rate increases

In reactor operation, “critical” can mean steady controlled power. It does not automatically mean an explosion.

Controlled vs Uncontrolled Fission

Controlled Fission

Controlled fission occurs in nuclear reactors.

• reaction rate is regulated
• heat is removed continuously
• power output is kept steady
• control rods adjust the neutron population

Uncontrolled Fission

Uncontrolled fission occurs when the chain reaction grows rapidly.

• reaction rate increases very fast
• energy is released in a short time

Keep the comparison qualitative; detailed weapons engineering is outside this topic.

Nuclear Reactor Overview

A nuclear reactor uses a controlled fission chain reaction to generate heat, which is then used to produce electricity.

Main sequence:

1. fission releases energy in the reactor core
2. a coolant transfers thermal energy away from the core
3. the thermal energy produces steam directly or indirectly
4. the steam drives a turbine
5. the turbine drives a generator

Reactor Components and Roles

Figure: Fuel fissions, moderator slows neutrons, control rods absorb neutrons, coolant removes heat, and shielding reduces radiation exposure.

Component	Main Role	Common Confusion
Fuel	Provides fissile nuclei such as uranium-235 or plutonium-239	Not the same as moderator
Moderator	Slows fast neutrons into thermal neutrons	Does not mainly absorb neutrons
Control rods	Absorb neutrons to regulate reaction rate	Do not remove heat directly
Coolant	Transfers heat away from the core	Does not control neutrons directly
Shielding	Reduces radiation exposure	Does not carry heat away

Advantages of Nuclear Fission

• very large energy output from a small mass of fuel
• low direct carbon dioxide emissions during operation
• reliable base-load electricity generation
• relatively small fuel transport volume compared with fossil fuels

Disadvantages and Challenges

• radioactive waste disposal
• accident risk if cooling or containment fails
• high construction and decommissioning cost
• security and proliferation concerns
• possible thermal pollution

Safety and Waste Overview

Fission reactors require:

• shielding
• emergency shutdown systems
• cooling systems
• containment structures
• secure spent-fuel management

Spent fuel and some reactor materials remain radioactive and require careful long-term handling.

See Ionizing Radiation and Safety.

Short Worked Examples

Example 1: Why Use Neutrons Rather Than Protons?

Neutrons are uncharged, so they are not repelled by the positively charged nucleus.

Example 2: Why Does Fission Release Energy?

The products have greater total binding energy and lower total mass. The mass defect is released as energy according to:

$$E=\Delta m{c}^2$$

Example 3: Why Are Control Rods Needed?

Control rods absorb neutrons. Inserting them reduces the number of neutrons available to continue the chain reaction.

Example 4: Why Do Some Reactors Need Moderators?

Fast neutrons from fission are slowed by a moderator. Slow neutrons can be more effective at inducing further fission in fuels such as uranium-235.

Example 5: Estimating Energy Released From Binding Energy Per Nucleon

For the reaction:

$${}_{92}^{235}\mathrm{U}+{}_0^1\mathrm{n}\to {}_{56}^{141}\mathrm{Ba}+{}_{36}^{92}\mathrm{Kr}+3{}_0^1\mathrm{n}$$

suppose the binding energy per nucleon values are:

Nucleus	Binding energy per nucleon
${}^{235}\mathrm{U}$	$7.6\mathrm{MeV}$
${}^{141}\mathrm{Ba}$	$8.25\mathrm{MeV}$
${}^{92}\mathrm{Kr}$	$8.75\mathrm{MeV}$

The approximate energy released is:

$$E=\left(141\times 8.25+92\times 8.75\right)-\left(235\times 7.6\right)$$ $$E\approx 181\mathrm{MeV}$$

The free neutrons are not included in this binding-energy calculation because a free neutron is not bound inside a nucleus.

Exam Relevance

Students should be able to:

• describe a typical neutron-induced fission reaction
• explain energy release using mass defect and binding energy
• explain why neutrons are useful in fission
• distinguish subcritical, critical, and supercritical behavior qualitatively
• distinguish moderator, control rods, coolant, and shielding
• explain why not all emitted neutrons continue the chain reaction

Formula / Relationship Summary

Mass-Energy

$$E=\Delta m{c}^2$$

Binding-Energy Method

$$E=\text{total B.E. of products}-\text{total B.E. of reactants}$$

Fission Pattern

$$\text{heavy nucleus}+\text{neutron}\to \text{daughter nuclei}+\text{neutrons}+E$$

Common Exam Traps Overview

Students often confuse:

• fission with radioactive decay
• moderator with control rods
• coolant with shielding
• energy release with “nucleus splits, so energy appears”
• chain reaction with every neutron always causing another fission
• critical reactor operation with a bomb reaction

See Nuclear Fission Common Exam Traps.

Quick Revision Summary

• fission splits a heavy nucleus into medium-mass nuclei
• reactor fission is usually neutron-induced
• energy release comes from mass defect and increased total binding energy
• emitted neutrons can sustain a chain reaction
• not all neutrons continue the chain
• moderator slows neutrons
• control rods absorb neutrons
• coolant removes heat
• shielding reduces radiation exposure

Links

• Nuclear Physics
• Mass Defect and Binding Energy
• Chain Reactions and Reactors
• Nuclear Fusion
• Ionizing Radiation and Safety
• Nuclear Fission Common Exam Traps