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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Convert the mass defect from atomic mass units to kilograms: 0.012 u × 1.66 × 10 -27 kg/u = 1.992 × 10 -29 kg.
- S2
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.
- S3
Convert the binding energy from joules to MeV: 0.012 u × 931.5 MeV/u = 11.178 MeV.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Convert the mass defect from atomic mass units to kilograms: 0.012 u × 1.66 × 10 -27 kg/u = 1.992 × 10 -29 kg.
- S2
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.
- S3
Convert the binding energy from joules to MeV: 0.012 u × 931.5 MeV/u = 11.178 MeV.
Final answer: The binding energy of the nucleus is 11.178 MeV.
Common mistakes
- Forgetting to convert the mass defect from atomic mass units (u) to kilograms before using E = mc 2 . — 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. — Always use the correct conversion factor: 1 u = 931.5 MeV.
- Confusing fission and fusion processes. — 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. — 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. — 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. — 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
- Full worked solution (all marking points)4 marks