Define mass defect and nuclear binding energy
Compare a nucleus with its separated nucleons and calculate the energy equivalent of a mass defect.
A Level · Cambridge International Physics 9702, 2025–2027 syllabus. The Topic 23 outcomes were also checked against Cambridge’s 2028–2030 syllabus, which reports no significant teaching changes. Online practice is self-checked and cannot replace supervised practical work, full timed assessment or human subject-teacher review.
Before you begin
- Use scientific notation, SI units, proportional reasoning and the particle numbers in nuclide notation.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What does the mass defect compare?
What you will learn
- Define mass defect
- Define nuclear binding energy
- Calculate energy released from a supplied mass change using E = c²Δm
The mass defect compares a bound nucleus with its nucleons
The mass defect is the difference between the sum of the masses of the separate nucleons and the mass of the nucleus. The nucleus has less mass than those same separated particles because energy was released when the bound nucleus formed.
Use only the masses specified in the question and keep their units consistent. If they are given in atomic mass units, convert the mass difference to kilograms using the supplied conversion before applying E = c²Δm.
Binding energy is the energy needed to separate a nucleus
The nuclear binding energy is the energy required to separate a nucleus completely into its constituent protons and neutrons. It is equal to the energy equivalent of the mass defect, ΔE = c²Δm.
The same magnitude is released when the separated nucleons form that nucleus. State whether a question asks for mass defect, binding energy or energy released; the numerical magnitude may be the same while the physical description differs.
Pause and explain
What is the binding energy of a nucleus physically?
Worked example
The mass defect of a nucleus is 3.32 × 10⁻²⁹ kg. Calculate its binding energy. Use c = 3.00 × 10⁸ m s⁻¹.
Show the worked solution
- Write ΔE = c²Δm.
- Square the speed of light: c² = 9.00 × 10¹⁶ m² s⁻².
- Multiply: ΔE = 9.00 × 10¹⁶ × 3.32 × 10⁻²⁹ = 2.99 × 10⁻¹² J.
Answer 2.99 × 10⁻¹² J (3 s.f.)
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
A supplied set of separate nucleons has total mass 4.020 × 10⁻²⁶ kg; the nucleus mass is 4.000 × 10⁻²⁶ kg. Find the mass defect.
Give me a hint
Subtract the bound-nucleus mass from the separate-nucleon total.
Compare my reasoning
- Δm = 4.020 × 10⁻²⁶ − 4.000 × 10⁻²⁶ kg.
- Keep the common power of ten.
- Δm = 0.020 × 10⁻²⁶ kg = 2.0 × 10⁻²⁸ kg.
2.0 × 10⁻²⁸ kg.
Look for these in your work
- Uses separate minus bound mass
- Subtracts the coefficients
- Normalises the power of ten
A reaction releases 4.5 × 10⁻¹² J. Calculate the corresponding mass decrease using c = 3.0 × 10⁸ m s⁻¹.
Give me a hint
Rearrange E = c²Δm to Δm = E/c².
Compare my reasoning
- c² = 9.0 × 10¹⁶ m² s⁻².
- Δm = 4.5 × 10⁻¹² / 9.0 × 10¹⁶.
- Δm = 5.0 × 10⁻²⁹ kg.
5.0 × 10⁻²⁹ kg.
Look for these in your work
- Rearranges for Δm
- Squares c
- Reports kilograms
Explain why a bound nucleus can have less mass than the same nucleons separated.
Give me a hint
Connect the mass difference with the energy released during binding.
Compare my reasoning
- Binding the nucleons releases energy.
- Mass and energy are equivalent through E = mc².
- The bound system therefore has a smaller rest mass by an amount corresponding to the released energy.
The mass decrease is the mass equivalent of the binding energy released.
Look for these in your work
- States energy is released on binding
- Uses mass–energy equivalence
- Connects the decrease to binding energy
Common mistakes
- Reversing the order and reporting a negative mass defect
- Using total nuclear mass instead of the difference in masses
- Forgetting that the binding-energy unit is joule after conversion to kilograms
What can you explain now?
What does the mass defect compare?
Compare with the explanation
The total mass of separate nucleons with the mass of the bound nucleus
Subtract the nucleus mass from the sum for its separate nucleons.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
How are mass defect and binding energy related by E = mc²?
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.