What is mass defect in nuclear physics?

Mass defect refers to the difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons. This discrepancy arises because some mass is converted into binding energy, which holds the nucleus together. Understanding mass defect is crucial for Cambridge International A Levels Physics students studying nuclear physics.

How is nuclear binding energy related to mass defect?

Nuclear binding energy is the energy required to disassemble a nucleus into its constituent protons and neutrons. It is directly related to mass defect through Einstein's equation, E=mc², where E represents the binding energy, m is the mass defect, and c is the speed of light. This concept is essential for students learning about nuclear stability in Cambridge International A Levels Physics.

Why is mass defect important in understanding nuclear reactions?

Mass defect is important because it explains the energy changes in nuclear reactions. When a nucleus forms, the mass defect results in the release of energy, which is the binding energy. This principle is fundamental in nuclear physics, helping Cambridge International A Levels students comprehend processes like nuclear fission and fusion.

How do you calculate the mass defect of a nucleus?

To calculate the mass defect, subtract the actual mass of the nucleus from the sum of the masses of its individual protons and neutrons. This calculation is crucial for Cambridge International A Levels Physics students to understand the energy dynamics within a nucleus and is often used in problems involving nuclear stability and reactions.

What role does nuclear binding energy play in nuclear stability?

Nuclear binding energy is a measure of a nucleus's stability; the higher the binding energy, the more stable the nucleus. It indicates how much energy is needed to break the nucleus apart. For Cambridge International A Levels Physics students, understanding this concept is key to analyzing why certain isotopes are stable while others are radioactive.

Why is "Confusing binding energy sign" a common mistake in Mass defect and nuclear binding energy?

Why it happens: Energy released when nucleus assembles vs. work needed to separate. How to avoid it: BE is POSITIVE in 9702 — energy needed to separate; equivalently, energy released on formation. Source: 9702 Examiner Reports 2022-2024

Why is "Misplacing the BE/A peak" a common mistake in Mass defect and nuclear binding energy?

Why it happens: Forgetting the location of the peak on the curve. How to avoid it: Peak near A 56 (iron region). Fusion releases energy below peak; fission releases above.

Cambridge International A Levels Physics (9702)

Mass defect and nuclear binding energy

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Short Notes - Mass defect and nuclear binding energy

Detailed Study Notes

Detailed notes on Nuclear Physics for Cambridge International A Levels Physics, covering key concepts, explanations, examples, and exam-focused revision points.

Mass Defect & Binding Energy Study Notes — Cambridge International A Level Physics 9702 (2025-2027 syllabus)

Mass-energy equivalence; nuclear binding; the BE/A curve and stability.

At a glance

$E = mc^2$ .
1 u $\leftrightarrow$ 931.5 MeV.
$\Delta m =$ (free nucleon mass) − (nuclear mass).
BE peaks near $^{56}\text{Fe}$ .
Fusion below peak, fission above.

What you’ll learn

Mapped to the Cambridge International A Level 9702 syllabus (2025-2027).

23.1.1 — State mass-energy equivalence.
23.1.2 — Calculate mass defect and binding energy.
23.1.3 — Interpret the BE per nucleon curve.

Mass-energy equivalence

$E = mc^2$ .

Einstein's relation: $E = mc^2$ — mass and energy are interchangeable.

Atomic mass unit: 1 u = $1.661 \times 10^{-27}$ kg. Energy equivalent: 1 u $c^2 \approx 931.5$ MeV.

Figure 1 — Two routes from mass defect to binding energy

Either work in kilograms and joules throughout, or stay in u and MeV and use the 931.5 MeV per u conversion.

Cambridge tip. Use 931.5 MeV/u for quick conversion.

$E = mc^2$ .
1 u $\leftrightarrow$ 931.5 MeV.

Mass defect and binding energy

$\Delta m$ and BE.

Mass defect: $\Delta m = Zm_p + Nm_n - m_{\text{nucleus}}$ . The bound nucleus has LESS mass than its separated constituents.

Figure 2 — Mass defect: a bound nucleus weighs less than its parts

The nucleons lose mass when they bind. That missing mass, the mass defect, is exactly the binding energy divided by c².

Binding energy: $E_B = \Delta m c^2$ . Energy needed to completely dismantle the nucleus.

Figure 3 — Binding energy seen as an energy gap

Binding energy is the size of this gap. It is released when the nucleus forms and must be put back to dismantle it.

BE per nucleon (BE/A). Measure of stability. Curve rises sharply from H, peaks near $^{56}\text{Fe}$ (~8.8 MeV/nucleon), then decreases for heavy nuclei.

Implications.

Fusion (light → heavier, below peak) RELEASES energy.
Fission (heavy → lighter, above peak) RELEASES energy.

Figure 4 — Binding energy per nucleon against nucleon number

Binding energy per nucleon peaks near ⁵⁶Fe at about 8.8 MeV. Note the helium-4 bump on the way up, and the slow decline towards uranium.

Mass defect and binding energy at a glance.

Quantity	How to find it	What it means
Mass defect $\Delta m$	$Zm_p + Nm_n - m_{\text{nucleus}}$	The mass lost when the nucleons bind together
Binding energy $E_B$	$\Delta m c^2$ , or $\Delta m$ in u $\times$ 931.5 MeV	Energy needed to separate the nucleus completely
Binding energy per nucleon	$E_B / A$	The fair way to compare stability between nuclei
Most stable region	The peak of the BE/A curve, near $^{56}\text{Fe}$	About 8.8 MeV per nucleon

Always divide by $A$ before comparing two nuclei — a large total binding energy just means a large nucleus.

Cambridge tip. Annotate the BE/A curve with: H (low), He bump, Fe peak, U decline.

$\Delta m = Zm_p + Nm_n - m_{\text{nuc}}$ .
$E_B = \Delta m c^2$ .
BE/A peaks at Fe.

See the full worked example for mass defect and nuclear binding energy →

Quick recap

$E = mc^2$ with 1 u → 931.5 MeV.
Mass defect = lost mass on binding.
BE/A curve dictates fusion/fission energetics.

Memorise this

Verbatim phrases and definitions Cambridge mark schemes credit.

$E = mc^2$ .
1 u $\leftrightarrow$ 931.5 MeV.
BE/A peak at $^{56}\text{Fe}$ .

How it’s examined

Nuclear binding on Paper 4 typically 8-10 marks. Most-tested: mass defect → BE (7 marks), BE/A from data (5 marks).

Sources: Cambridge International A Level Physics 9702 syllabus (2025-2027); 9702 Examiner Reports 2022-2024; 9702/42 May/Jun 2024 question paper and mark scheme. Last reviewed 2026-05-11.

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Step-by-step worked examples — Mass defect and nuclear binding energy

Step-by-step solutions to past-paper-style questions on mass defect and nuclear binding energy, written exactly the way a tutor would explain them at the board.

1Mass defect of helium-4 (6 marks)
Extended• Adapted from 9702/42 May/Jun 2024• nuclear, mass-defect
Question
$^4_2\text{He}$ has nuclear mass 4.0015 u. Masses: proton = 1.00728 u, neutron = 1.00867 u. Find mass defect and binding energy in MeV. (6 marks)
Step-by-step solution
1. Step 1
  Total mass of nucleons: $2(1.00728) + 2(1.00867) = 4.03190$ u.
2. Step 2
  Mass defect: $\Delta m = 4.03190 - 4.0015 = 0.0304$ u.
3. Step 3
  Binding energy: $E = \Delta m \times 931.5 \text{ MeV/u}$ .
  $E = 0.0304 \times 931.5 \approx 28.3 \text{ MeV}$
Answer
$\Delta m = 0.0304$ u; $E \approx 28.3$ MeV.
2Balancing a nuclear reaction equation (5 marks)
Extended• Adapted from 9702/42 May/Jun 2024• nuclear-equation
Question
Complete and identify the daughter nucleus X in $^{14}_{\;7}\text{N} + {}^4_2\text{He} \to \text{X} + {}^1_1\text{H}$ , and explain why this is consistent with the conservation rules. (5 marks)
Step-by-step solution
1. Step 1
  Conserve nucleon number. $14 + 4 = A + 1 \Rightarrow A = 17$ .
2. Step 2
  Conserve proton number / charge. $7 + 2 = Z + 1 \Rightarrow Z = 8$ .
3. Step 3
  Identify X. $Z = 8$ is oxygen, so $\text{X} = {}^{17}_{\;8}\text{O}$ .
  $^{14}_{\;7}\text{N} + {}^{4}_{2}\text{He} \to {}^{17}_{\;8}\text{O} + {}^{1}_{1}\text{H}$
4. Step 4
  Conservation rules. Nucleon number AND charge are conserved on each side, in line with syllabus 11.1.6 and 23.1.2.
Answer
X = $^{17}_{\;8}\text{O}$ (oxygen-17).
3Binding energy per nucleon (4 marks)
Extended• BE/A
Question
For $^{56}\text{Fe}$ binding energy is 492 MeV. Find BE per nucleon. (4 marks)
Step-by-step solution
1. Step 1
  BE per nucleon $= E/A = 492/56 \approx 8.79$ MeV.
Answer
$\approx 8.79$ MeV per nucleon (near peak of curve).

Key Formulae — Mass defect and nuclear binding energy

The formulae you need to memorise for mass defect and nuclear binding energy on the Cambridge International A Level 9702 paper, with every variable defined in plain English and a note on when to use it.

Mass-energy equivalence
$E = mc^2$
When to use
Energy equivalent of mass. 1 u $\leftrightarrow$ 931.5 MeV.
Mass defect
$\Delta m = Z m_p + N m_n - m_{\text{nuc}}$
When to use
Difference between sum of free nucleon masses and bound nuclear mass.
Binding energy
$E_B = \Delta m \cdot c^2$
When to use
Energy that must be supplied to fully separate the nucleus into its constituent nucleons.

Key Definitions and Keywords — Mass defect and nuclear binding energy

Definitions to memorise and the exact keywords mark schemes credit for mass defect and nuclear binding energy answers — sharpened from recent examiner reports for the 2026 Cambridge International A Level 9702 sitting.

Mass defect
Examiner keyword
Difference between mass of separated nucleons and the bound nuclear mass. Positive (mass lost on binding).
Binding energy
Examiner keyword
Energy required to completely separate a nucleus into its constituent nucleons. Equivalently, energy released when assembled.
Binding energy per nucleon
Examiner keyword
Total binding energy divided by mass number A. Measure of nuclear stability. Peaks near $^{56}\text{Fe}$ .
Unified atomic mass unit (u)
1 u = 1/12 mass of $^{12}\text{C}$ atom $\approx 1.661 \times 10^{-27}$ kg.

Common Mistakes and Misconceptions — Mass defect and nuclear binding energy

The traps other students keep falling into on mass defect and nuclear binding energy questions — taken from recent Cambridge International A Level 9702 examiner reports and mark schemes — and how to avoid them.

✕Confusing binding energy sign
9702 Examiner Reports 2022-2024
Why it happens
Energy released when nucleus assembles vs. work needed to separate.
How to avoid it
BE is POSITIVE in 9702 — energy needed to separate; equivalently, energy released on formation.
✕Misplacing the BE/A peak
Why it happens
Forgetting the location of the peak on the curve.
How to avoid it
Peak near $A \approx 56$ (iron region). Fusion releases energy below peak; fission releases above.