A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Nuclear Energy and Binding Energy — mark scheme explained
The short answer
In this section, we will explore the fundamental principles of nuclear physics, focusing on the relationship between mass and energy as described by Einstein's famous equation E = mc 2 . We will also delve into the concepts of binding energy, atomic mass units, and how these relate to fission and fusion processes.
The question
Calculate the binding energy of a nucleus with a mass defect of 0.012 u.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculations involving mass difference and binding energy, ensure that all steps are shown clearly. Use correct units throughout the calculation and provide a final answer with the appropriate unit. For conceptual questions, provide clear and concise explanations, using relevant physics principles.
What the command words demand
- Calculate
- Perform a numerical calculation to find a specific value.
- Explain
- Provide a detailed account of the reasons or causes for something.
- Identify
- Recognize and name key features or components.
- Describe
- Give a detailed account of characteristics, events, or processes.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate approximately 5-7 minutes for each question in this section to ensure you have enough time to show all working and provide detailed answers.
- Convert the mass defect from atomic mass units to kilograms: 0.012 u × 1.66 × 10 -27 kg/u = 1.992 × 10 -29 kg.1 mark
- Calculate the binding energy in joules using E = mc 2 : 1.992 × 10 -29 kg × (3 × 10 8 m/s) 2 = 1.7928 × 10 -12 J.2 marks
- Convert the binding energy from joules to MeV: 0.012 u × 931.5 MeV/u = 11.178 MeV.1 mark
Final answer: The binding energy of the nucleus is 11.178 MeV.
Work through every step correctly and you earn all 4 marks.
Another worked example
A uranium-235 nucleus undergoes fission, producing two lighter nuclei with a total mass defect of 0.2 u. Calculate the energy released in this reaction.
- Convert the mass defect from atomic mass units to kilograms: 0.2 u × 1.66 × 10 -27 kg/u = 3.32 × 10 -28 kg.1 mark
- Calculate the energy released in joules using E = mc 2 : 3.32 × 10 -28 kg × (3 × 10 8 m/s) 2 = 2.988 × 10 -11 J.2 marks
- Convert the energy released from joules to MeV: 0.2 u × 931.5 MeV/u = 186.3 MeV.1 mark
Final answer: E = 2.98 × 10 -11 J (≈ 186 MeV)
Work through every step correctly and you earn all 4 marks.
Common mistakes
Forgetting to convert the mass defect from atomic mass units (u) to kilograms before using E = mc 2 .
Why it happens: Students often skip this step, leading to incorrect calculations of energy in joules.
Fix: Always convert the mass defect from u to kg by multiplying by 1.66 × 10 -27 kg/u before using E = mc 2 .
Using the wrong conversion factor between atomic mass units and energy in MeV.
Why it happens: Students might use 931.5 eV/u instead of 931.5 MeV/u, leading to incorrect results.
Fix: Always use the correct conversion factor: 1 u = 931.5 MeV.
Confusing fission and fusion processes.
Why it happens: Students might mix up which process releases energy for lighter or heavier nuclei.
Fix: Remember that fission releases energy for heavy nuclei, while fusion releases energy for light nuclei.
Forgetting to calculate the total mass of reactants in a fusion reaction.
Why it happens: Students might only consider the mass defect without summing the masses of all reactants.
Fix: Always calculate the total mass of the reactants and then subtract the mass of the products to find the mass defect.
Using the wrong units for energy in calculations.
Why it happens: Students might use joules instead of MeV or vice versa, leading to incorrect answers.
Fix: Ensure that all units are consistent throughout the calculation. Convert between joules and MeV as needed using 1 u = 931.5 MeV.
Misinterpreting the graph of average binding energy per nucleon.
Why it happens: Students might not understand that the peak indicates the most stable nuclei.
Fix: Study the graph carefully and note that elements with higher binding energy per nucleon are more stable, such as iron-56.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Binding Energy | Convert a mass defect into energy and express the binding energy in correct units. | 4 |
| Calculate Fission Energy | Convert a mass defect into the energy released during nuclear fission. | 4 |
| Calculate Fusion Energy | Find the energy released by converting the mass difference in a fusion reaction. | 3 |
| Binding Energy Per Nucleon | Convert mass defect to energy, then divide by the number of nucleons. | 3 |
| Total across these question types | 14 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.