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This free lesson on MarkScheme covers syllabus point 23.1 (Mass defect and nuclear binding energy) for Cambridge A-Level Physics. It includes visual revision, key points, and links to real past-paper questions with mark-scheme marking at markscheme.app/courses/9702/23-1-mass-defect-and-nuclear-binding-energy.

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23.1Physics25 min readPREMIUM

Mass defect and nuclear binding energy

Dive into the fascinating world of nuclear physics, where mass isn't always conserved! Discover the mass defect, a tiny difference in mass that reveals the powerful nuclear binding energy holding atomic nuclei together. We'll explore how Einstein's famous equation, $E=mc^2$ , unlocks the secrets of nuclear stability, fusion, and fission. This pilot aligns with Senpai Corner A Level notes (2025–2027) for topic 23.1.

BY THE END, YOU CAN…

exam checklist — tick these off

1Define mass defect and nuclear binding energy.
2Apply Einstein's mass-energy equivalence (E=mc²) to nuclear processes.
3Explain how binding energy per nucleon relates to nuclear stability and predict energy release in fusion and fission.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Mass defect and nuclear binding energy

Cambridge 9702 Paper 4 — Mass defect and nuclear binding energy (23.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.
2
Electronvolt (eV): The energy gained by an electron accelerated through a potential difference of 1 volt. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ . Nuclear energies are often expressed in Mega-electronvolts (MeV), where $1 \text{ MeV} = 10^6 \text{ eV}$ .
3
Energy-Mass Conversion: Using E=mc², the energy equivalent of 1 atomic mass unit can be calculated. It is a very useful conversion factor: $1 \text{ u} \approx 931.5 \text{ MeV}$ .

What this topic covers

The official Cambridge syllabus points this lesson works through.

23.1.1
Understand the equivalence between energy and mass as represented by $E = mc^2$ and recall and use this equation
23.1.2
Represent simple nuclear reactions by nuclear equations of the form $^{14}_7N + ^4_2He \rightarrow ^{17}_8O + ^1_1H$
23.1.3
Define and use the terms mass defect and binding energy
23.1.4
Sketch the variation of binding energy per nucleon with nucleon number
23.1.5
Explain what is meant by nuclear fusion and nuclear fission
23.1.6
Explain the relevance of binding energy per nucleon to nuclear reactions, including nuclear fusion and nuclear fission
23.1.7
Calculate the energy released in nuclear reactions using $E = c^2Δm$

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure Live interactive1 / 3

Loading simulation…

Fetching from 3JCN Physics Simulation by Thomas Nguyen…

Nuclear Fusion Principle

The fused nucleus has less mass than its parts, and the mass defect appears as energy.

If the embed does not load, use Open simulation.

3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Step-synced diagram — highlights what to look for in the simulation above.

Step 1

Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.

5 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

5 simulations · 4 to start with

Start herein this order — each one shows a different piece of the topic

PhETStart here · 19702 23.1
Build a Nucleus
Assemble nuclei and read off stability; follow decays on the nuclide chart.
Why this one: Add protons and neutrons and see which combinations are bound and stable.
Try this
1. Build helium-4, then iron-56 — note where each sits on the chart.
2. Add neutrons one at a time to a nucleus until it becomes unstable — what decay happens?
3. Follow a chain of decays back toward the stable band.
Look for Nuclei off the band of stability decay toward it; iron-56 region is most tightly bound.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 29702 23.1 · IB E.4
Nuclear Fission Principle
Fire a neutron at U-235 and see fission fragments and chain reaction
Why this one: Split uranium-235 and see the fragments carry away energy released by the mass defect.
Try this
1. Fire a neutron at the U-235 nucleus and watch the fragments.
2. Count the neutrons released and follow the chain reaction.
Look for Each fission releases energy and several neutrons, which can trigger further fissions.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhETStart here · 3Java · best on a laptop9702 23.1 · 23.2
Nuclear Fission
Fire a neutron at uranium-235 to split it, start a chain reaction, then control it with rods in a reactor.
Why this one: Start a chain reaction and control it with rods — each fission releases binding energy.
Try this
1. Fire one neutron at a single U-235 nucleus — watch it split and release neutrons.
2. On the Chain Reaction screen, add more U-235 and fire again.
3. On the Reactor screen, push the control rods in until the power steadies.
Look for Fission releases energy because the fragments have higher binding energy per nucleon than U-235.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 49702 23.1 · IB E.4
Nuclear Fission Reactor
Control rods and moderator in a fission reactor; manage the chain reaction
Why this one: Adjust control rods and moderator to keep a chain reaction steady.
Try this
1. Lower the control rods and watch the chain reaction slow.
2. Raise them and compare.
3. Remove the moderator and compare.
Look for Control rods absorb neutrons and the moderator slows them, together holding the reaction steady.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

More simulations1 more on this topic — core ones first

3JCN Physics9702 23.1 · IB E.5
Fusion Reactor
Confine a plasma in a tokamak fusion reactor
Try this
1. Confine the plasma in the tokamak.
2. Watch what holds the plasma away from the walls.
Look for Magnetic fields confine the hot plasma because no material wall could.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$E = mc^2$

Tap a symbol — great for exam definitions

KEY RELATION

$\Delta m = (Z \cdot m_p + N \cdot m_n) - M_{nucleus}$

Tap a symbol — great for exam definitions

KEY RELATION

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

Tap a symbol — great for exam definitions

KEY RELATION

$\frac{\text{Total Binding Energy}}{\text{Nucleon Number (A)}}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Einstein's Revolutionary Idea: Mass-Energy Equivalence

For centuries, mass and energy were considered entirely separate. Einstein's theory of relativity changed everything, revealing that mass and energy are two forms of the same fundamental entity. This profound insight is crucial in nuclear physics, where tiny changes in mass can correspond to enormous releases or absorptions of energy. It's the bedrock for understanding how stars burn and how nuclear power works.

$E = mc^2$ Where:

$E$ is energy (in Joules, J)
$m$ is mass (in kilograms, kg)
$c$ is the speed of light in a vacuum ( $3.00 \times 10^8 \text{ m s}^{-1}$ )

Not clear?

Important Units in Nuclear Physics

Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.
Electronvolt (eV): The energy gained by an electron accelerated through a potential difference of 1 volt. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ . Nuclear energies are often expressed in Mega-electronvolts (MeV), where $1 \text{ MeV} = 10^6 \text{ eV}$ .
Energy-Mass Conversion: Using E=mc², the energy equivalent of 1 atomic mass unit can be calculated. It is a very useful conversion factor: $1 \text{ u} \approx 931.5 \text{ MeV}$ .

Not clear?

The Missing Mass: Mass Defect

When protons and neutrons come together to form a nucleus, something unexpected happens: the total mass of the assembled nucleus is less than the sum of the individual masses of the protons and neutrons (also called nucleons) when they were separate. This 'missing' mass is called the mass defect ( $\Delta m$ ). It doesn't disappear; instead, it's converted into the energy that binds the nucleus together.

$\Delta m = (Z \cdot m_p + N \cdot m_n) - M_{nucleus}$ Where:

$Z$ = number of protons
$N$ = number of neutrons
$m_p$ = mass of a proton
$m_n$ = mass of a neutron
$M_{nucleus}$ = actual measured mass of the nucleus

Not clear?

Nuclear Binding Energy: The Glue that Holds it All

The nuclear binding energy is the minimum energy required to completely dismantle a nucleus into its individual, separate protons and neutrons. This energy is exactly equivalent to the energy associated with the mass defect. It represents the energy that was released when the nucleus formed, holding it together. A larger binding energy indicates a more stable nucleus, as more energy is needed to break it apart.

Binding Energy = $\Delta E = \Delta m c^2$

Not clear?

Binding Energy Per Nucleon and Nuclear Stability

To compare the stability of different nuclei, we often look at the binding energy per nucleon. This is calculated by dividing the total binding energy of a nucleus by its nucleon number (the total count of protons and neutrons). Nuclei with a higher binding energy per nucleon are more stable because more energy is required to remove each individual proton or neutron.

Binding Energy Per Nucleon = $\frac{\text{Total Binding Energy}}{\text{Nucleon Number (A)}}$

Not clear?

The Binding Energy Curve: Fusion and Fission

The binding energy per nucleon curve is a vital graph in nuclear physics. It plots binding energy per nucleon against the nucleon number (A) for various isotopes. The shape of this curve is fundamental to understanding nuclear energy. It rises sharply for light nuclei, peaks around a nucleon number of A=56 (near Iron, Fe-56), and then slowly decreases for heavier nuclei. This peak represents the 'sweet spot' of nuclear stability. Any process that moves nuclei 'up the curve' towards higher binding energy per nucleon will release energy.

The curve peaks at Iron-56 (Fe-56), marking the most stable nuclei.
Nuclear fusion combines light nuclei to form heavier, more stable ones.
Fusion releases energy when products have higher binding energy per nucleon (lighter than Fe-56).
Nuclear fission splits heavy nuclei into lighter, more stable daughter nuclei.
Fission releases energy when products have higher binding energy per nucleon (heavier than Fe-56).
Energy is released when binding energy per nucleon increases in a reaction.

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

A nucleus of Helium-4 ( $^4_2\text{He}$ ) has an actual mass of $4.001506 \text{ u}$ . Given the mass of a proton is $1.007276 \text{ u}$ and a neutron is $1.008665 \text{ u}$ , calculate the mass defect and the binding energy of Helium-4 in MeV.

1
Identify components: Helium-4 has 2 protons (Z=2) and 2 neutrons (N=2).

EXAMPLE 2

Consider the fission of a Uranium-235 nucleus after it absorbs a slow neutron. One possible reaction is: $^1_0n + ^{235}_{92}U \rightarrow ^{141}_{56}Ba + ^{92}_{36}Kr + 3(^1_0n)$ Calculate the energy released in this reaction in MeV. Use the following data:

Mass of a neutron ( $^1_0n$ ) = 1.008665 u
Mass of a $^{235}_{92}U$ nucleus = 235.043930 u
Mass of a $^{141}_{56}Ba$ nucleus = 140.914411 u
Mass of a $^{92}_{36}Kr$ nucleus = 91.926156 u
1 u is equivalent to 931.5 MeV.

1
Calculate the total mass of the reactants (before fission):

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAMass defect and nuclear binding energy

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

mass defect: This 'missing' mass is called the mass defect ( $\Delta m$ ). It doesn't disappear; instead, it's converted into the energy that binds the nucleus together.
nuclear binding energy: The nuclear binding energy is the minimum energy required to completely dismantle a nucleus into its individual, separate protons and neutrons.
binding energy per nucleon: To compare the stability of different nuclei, we often look at the binding energy per nucleon. This is calculated by dividing the total binding energy of a nucleus by its nucleon number (the total count of protons and neutrons).
definition of mass: The difference between the total mass of individual, unbound protons and neutrons and the actual measured mass of the nucleus they form.
significance of "binding: It indicates the stability of a nucleus; a higher binding energy per nucleon means greater stability.
approximate energy: Approximately 931.5 MeV.
Nuclear fusion: The process where lighter nuclei combine to form a heavier, more stable nucleus, releasing energy.
Nuclear fission: The process where a heavy nucleus splits into lighter, more stable nuclei, releasing energy.
In a nuclear reaction: The total mass of the products is less than the total mass of the reactants. The 'lost' mass is converted into the released energy according to E = Δmc².

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

If you can explain it simply, you own it — gaps here are marks you’d lose.

Teach it back

Explain this topic as if teaching a friend. We name the gaps an examiner would still dock.

Your explanation — no notes

12Remember

Revision flashcards

Guess first, then flip — retrieval beats re-reading.

Your guess — write it before you look

1 / 13 · ← → space

Key takeaways

Review these before you close the topic — retrieval beats re-reading.

close the tab only after these stick

Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.
Electronvolt (eV): The energy gained by an electron accelerated through a potential difference of 1 volt. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ . Nuclear energies are often expressed in Mega-electronvolts (MeV), where $1 \text{ MeV} = 10^6 \text{ eV}$ .
Energy-Mass Conversion: Using E=mc², the energy equivalent of 1 atomic mass unit can be calculated. It is a very useful conversion factor: $1 \text{ u} \approx 931.5 \text{ MeV}$ .

Practice — then mark it

The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q9(a)

PhysicsMay/June 2024

(a)

State what is meant by the binding energy of a nucleus.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q9(b)(ii)

PhysicsMay/June 2024

(b) (ii)

the binding energy

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Extra simulations & links

PhET, GeoGebra and other curated tools — open in a new tab.

Frequently asked

Why is the mass of a nucleus always less than the sum of its individual protons and neutrons?

How does Einstein's E=mc² relate to mass defect and binding energy?

What is the most stable nucleus, and why is this important for nuclear reactions?

Checkpoint

One marked question is worth ten re-reads — close the loop before you move on.

Checkpoint

Reading it isn’t knowing it — prove it.

Before you move on: do 9702/42 · Q9(a) on paper, snap a photo, and get examiner-style feedback on exactly where you win and lose marks.

Attempt & get marked →Takes about a minute · you’ll land back on this lesson

← PREVIOUS22.4 Energy levels in atoms and line spectra NEXT →23.2 Radioactive decay

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Revise Mass defect and nuclear binding energy for Cambridge 9702 (23.1)

Looking for free Physics 9702 notes on Mass defect and nuclear binding energy? This A-Level lesson covers official syllabus point 23.1 on Paper 4: A Level Structured Questions. Use the visual steps, key terms, and quick checks below — then practise a real 9702 past-paper question with mark-scheme marking. Built for students searching "Mass defect and nuclear binding energy 9702 revision", "9702 23.1 notes", or a free alternative to paid note sites.

Full Physics 9702 course Mark a past paper →9702 subject hub

23.1Physics25 min readPREMIUM

Mass defect and nuclear binding energy

BY THE END, YOU CAN…

exam checklist — tick these off

1Define mass defect and nuclear binding energy.
2Apply Einstein's mass-energy equivalence (E=mc²) to nuclear processes.
3Explain how binding energy per nucleon relates to nuclear stability and predict energy release in fusion and fission.

STUDY MODE

READING

TYPEFACE

Literata — a reading serif made for e-books; set like a textbook, sits well beside maths.

SIZE

AIRY SPACING

Wider letter and line spacing. The one change with solid evidence for readers who lose their place — worth a try whoever you are.

Pick whatever reads fastest for you — it differs from person to person, by up to a third.

EXPLAIN SIMPLER

The same notes in plain English — no jargon. Key points and exam tips stay.

DIAGRAM NOTES

A small sketch beside each block of notes.

In simple terms

A friendly intro before the formal notes — no formulas yet.

Mass defect and nuclear binding energy

Cambridge 9702 Paper 4 — Mass defect and nuclear binding energy (23.1). Senpai Corner diagram-backed pilot with premium structure and live visuals.

1
Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.
2
Electronvolt (eV): The energy gained by an electron accelerated through a potential difference of 1 volt. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ . Nuclear energies are often expressed in Mega-electronvolts (MeV), where $1 \text{ MeV} = 10^6 \text{ eV}$ .
3
Energy-Mass Conversion: Using E=mc², the energy equivalent of 1 atomic mass unit can be calculated. It is a very useful conversion factor: $1 \text{ u} \approx 931.5 \text{ MeV}$ .

What this topic covers

The official Cambridge syllabus points this lesson works through.

23.1.1
Understand the equivalence between energy and mass as represented by $E = mc^2$ and recall and use this equation
23.1.2
Represent simple nuclear reactions by nuclear equations of the form $^{14}_7N + ^4_2He \rightarrow ^{17}_8O + ^1_1H$
23.1.3
Define and use the terms mass defect and binding energy
23.1.4
Sketch the variation of binding energy per nucleon with nucleon number
23.1.5
Explain what is meant by nuclear fusion and nuclear fission
23.1.6
Explain the relevance of binding energy per nucleon to nuclear reactions, including nuclear fusion and nuclear fission
23.1.7
Calculate the energy released in nuclear reactions using $E = c^2Δm$

Explore the concept

Use the live diagram, PhET or GeoGebra sim, and synced steps — play it, drag controls, or tap a step.

Figure Live interactive1 / 3

Loading simulation…

Fetching from 3JCN Physics Simulation by Thomas Nguyen…

Nuclear Fusion Principle

The fused nucleus has less mass than its parts, and the mass defect appears as energy.

If the embed does not load, use Open simulation.

3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Step-synced diagram — highlights what to look for in the simulation above.

Step 1

Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.

5 more simulations for this topic — run them in the Simulations section below

Simulations

Every simulation here runs the real model — try the steps on a card, then check what you see against the notes.

5 simulations · 4 to start with

Start herein this order — each one shows a different piece of the topic

PhETStart here · 19702 23.1
Build a Nucleus
Assemble nuclei and read off stability; follow decays on the nuclide chart.
Why this one: Add protons and neutrons and see which combinations are bound and stable.
Try this
1. Build helium-4, then iron-56 — note where each sits on the chart.
2. Add neutrons one at a time to a nucleus until it becomes unstable — what decay happens?
3. Follow a chain of decays back toward the stable band.
Look for Nuclei off the band of stability decay toward it; iron-56 region is most tightly bound.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 29702 23.1 · IB E.4
Nuclear Fission Principle
Fire a neutron at U-235 and see fission fragments and chain reaction
Why this one: Split uranium-235 and see the fragments carry away energy released by the mass defect.
Try this
1. Fire a neutron at the U-235 nucleus and watch the fragments.
2. Count the neutrons released and follow the chain reaction.
Look for Each fission releases energy and several neutrons, which can trigger further fissions.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0
PhETStart here · 3Java · best on a laptop9702 23.1 · 23.2
Nuclear Fission
Fire a neutron at uranium-235 to split it, start a chain reaction, then control it with rods in a reactor.
Why this one: Start a chain reaction and control it with rods — each fission releases binding energy.
Try this
1. Fire one neutron at a single U-235 nucleus — watch it split and release neutrons.
2. On the Chain Reaction screen, add more U-235 and fire again.
3. On the Reactor screen, push the control rods in until the power steadies.
Look for Fission releases energy because the fragments have higher binding energy per nucleon than U-235.
Open on PhET
Simulation by PhET Interactive Simulations, University of Colorado Boulder · Licensed to MarkScheme (public licence CC BY-NC 4.0 since 2026-03-30)
3JCN PhysicsStart here · 49702 23.1 · IB E.4
Nuclear Fission Reactor
Control rods and moderator in a fission reactor; manage the chain reaction
Why this one: Adjust control rods and moderator to keep a chain reaction steady.
Try this
1. Lower the control rods and watch the chain reaction slow.
2. Raise them and compare.
3. Remove the moderator and compare.
Look for Control rods absorb neutrons and the moderator slows them, together holding the reaction steady.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

More simulations1 more on this topic — core ones first

3JCN Physics9702 23.1 · IB E.5
Fusion Reactor
Confine a plasma in a tokamak fusion reactor
Try this
1. Confine the plasma in the tokamak.
2. Watch what holds the plasma away from the walls.
Look for Magnetic fields confine the hot plasma because no material wall could.
Open on 3JCN Physics
3JCN Physics Simulation by Thomas Nguyen · CC BY 4.0

Key formulas

Tap any symbol to reveal exactly what it means and its units.

KEY RELATION

$E = mc^2$

Tap a symbol — great for exam definitions

KEY RELATION

$\Delta m = (Z \cdot m_p + N \cdot m_n) - M_{nucleus}$

Tap a symbol — great for exam definitions

KEY RELATION

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

Tap a symbol — great for exam definitions

KEY RELATION

$\frac{\text{Total Binding Energy}}{\text{Nucleon Number (A)}}$

Full topic notes

Formal explanation with the rigour you need for the exam.

Einstein's Revolutionary Idea: Mass-Energy Equivalence

$E = mc^2$ Where:

$E$ is energy (in Joules, J)
$m$ is mass (in kilograms, kg)
$c$ is the speed of light in a vacuum ( $3.00 \times 10^8 \text{ m s}^{-1}$ )

Not clear?

Important Units in Nuclear Physics

Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.
Electronvolt (eV): The energy gained by an electron accelerated through a potential difference of 1 volt. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ . Nuclear energies are often expressed in Mega-electronvolts (MeV), where $1 \text{ MeV} = 10^6 \text{ eV}$ .
Energy-Mass Conversion: Using E=mc², the energy equivalent of 1 atomic mass unit can be calculated. It is a very useful conversion factor: $1 \text{ u} \approx 931.5 \text{ MeV}$ .

Not clear?

The Missing Mass: Mass Defect

$\Delta m = (Z \cdot m_p + N \cdot m_n) - M_{nucleus}$ Where:

$Z$ = number of protons
$N$ = number of neutrons
$m_p$ = mass of a proton
$m_n$ = mass of a neutron
$M_{nucleus}$ = actual measured mass of the nucleus

Not clear?

Nuclear Binding Energy: The Glue that Holds it All

Binding Energy = $\Delta E = \Delta m c^2$

Not clear?

Binding Energy Per Nucleon and Nuclear Stability

Binding Energy Per Nucleon = $\frac{\text{Total Binding Energy}}{\text{Nucleon Number (A)}}$

Not clear?

The Binding Energy Curve: Fusion and Fission

The curve peaks at Iron-56 (Fe-56), marking the most stable nuclei.
Nuclear fusion combines light nuclei to form heavier, more stable ones.
Fusion releases energy when products have higher binding energy per nucleon (lighter than Fe-56).
Nuclear fission splits heavy nuclei into lighter, more stable daughter nuclei.
Fission releases energy when products have higher binding energy per nucleon (heavier than Fe-56).
Energy is released when binding energy per nucleon increases in a reaction.

Not clear?

Worked examples

See the formulas applied — reveal one step at a time, like the exam.

reveal slowly — mark each step

EXAMPLE 1

1
Identify components: Helium-4 has 2 protons (Z=2) and 2 neutrons (N=2).

EXAMPLE 2

Mass of a neutron ( $^1_0n$ ) = 1.008665 u
Mass of a $^{235}_{92}U$ nucleus = 235.043930 u
Mass of a $^{141}_{56}Ba$ nucleus = 140.914411 u
Mass of a $^{92}_{36}Kr$ nucleus = 91.926156 u
1 u is equivalent to 931.5 MeV.

1
Calculate the total mass of the reactants (before fission):

How it all connects

The big idea sits in the middle — tap a linked idea to explore the link.

MAIN IDEAMass defect and nuclear binding energy

Tap a linked idea to see how it connects back to the main topic — that connection is what examiners reward.

Glossary

Key terms for this topic — skim now; the Check step will test them.

mass defect: This 'missing' mass is called the mass defect ( $\Delta m$ ). It doesn't disappear; instead, it's converted into the energy that binds the nucleus together.
nuclear binding energy: The nuclear binding energy is the minimum energy required to completely dismantle a nucleus into its individual, separate protons and neutrons.
binding energy per nucleon: To compare the stability of different nuclei, we often look at the binding energy per nucleon. This is calculated by dividing the total binding energy of a nucleus by its nucleon number (the total count of protons and neutrons).
definition of mass: The difference between the total mass of individual, unbound protons and neutrons and the actual measured mass of the nucleus they form.
significance of "binding: It indicates the stability of a nucleus; a higher binding energy per nucleon means greater stability.
approximate energy: Approximately 931.5 MeV.
Nuclear fusion: The process where lighter nuclei combine to form a heavier, more stable nucleus, releasing energy.
Nuclear fission: The process where a heavy nucleus splits into lighter, more stable nuclei, releasing energy.
In a nuclear reaction: The total mass of the products is less than the total mass of the reactants. The 'lost' mass is converted into the released energy according to E = Δmc².

10Apply

Quick check

Write your answer first, then compare it with the model one — the gap is what you would have lost.

0 of 6 answered

11Understand

Teach it back

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12Remember

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Atomic Mass Unit (u): Defined as 1/12th the mass of a neutral carbon-12 atom. $1 \text{ u} = 1.661 \times 10^{-27} \text{ kg}$ . It's a convenient unit for the tiny masses of subatomic particles.
Electronvolt (eV): The energy gained by an electron accelerated through a potential difference of 1 volt. $1 \text{ eV} = 1.60 \times 10^{-19} \text{ J}$ . Nuclear energies are often expressed in Mega-electronvolts (MeV), where $1 \text{ MeV} = 10^6 \text{ eV}$ .
Energy-Mass Conversion: Using E=mc², the energy equivalent of 1 atomic mass unit can be calculated. It is a very useful conversion factor: $1 \text{ u} \approx 931.5 \text{ MeV}$ .

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The whole point: a real Cambridge question, marked mark-by-mark.

Question 1 of 29702/42 · Q9(a)

PhysicsMay/June 2024

(a)

State what is meant by the binding energy of a nucleus.

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

Question 2 of 29702/42 · Q9(b)(ii)

PhysicsMay/June 2024

(b) (ii)

the binding energy

Do it on paper → mark itMARKED MARK-BY-MARK · B1 / M1 / A1 · OFFICIAL SCHEME

9702/42/M/J/24

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Frequently asked

Why is the mass of a nucleus always less than the sum of its individual protons and neutrons?

How does Einstein's E=mc² relate to mass defect and binding energy?

What is the most stable nucleus, and why is this important for nuclear reactions?

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Revise Mass defect and nuclear binding energy for Cambridge 9702 (23.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Build a Nucleus

Nuclear Fission Principle

Nuclear Fission

Nuclear Fission Reactor

Fusion Reactor

Key formulas

Full topic notes

Einstein's Revolutionary Idea: Mass-Energy Equivalence

Important Units in Nuclear Physics

The Missing Mass: Mass Defect

Nuclear Binding Energy: The Glue that Holds it All

Binding Energy Per Nucleon and Nuclear Stability

The Binding Energy Curve: Fusion and Fission

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Mass defect and nuclear binding energy

Revise Mass defect and nuclear binding energy for Cambridge 9702 (23.1)

In simple terms

What this topic covers

Explore the concept

Simulations

Build a Nucleus

Nuclear Fission Principle

Nuclear Fission

Nuclear Fission Reactor

Fusion Reactor

Key formulas

Full topic notes

Einstein's Revolutionary Idea: Mass-Energy Equivalence

Important Units in Nuclear Physics

The Missing Mass: Mass Defect

Nuclear Binding Energy: The Glue that Holds it All

Binding Energy Per Nucleon and Nuclear Stability

The Binding Energy Curve: Fusion and Fission

Worked examples

How it all connects

Glossary

Quick check

Teach it back

Revision flashcards

Key takeaways

Practice — then mark it

Extra simulations & links

Frequently asked

Checkpoint

Reading it isn’t knowing it — prove it.

Discuss Mass defect and nuclear binding energy