Physics 9702 · syllabus 23
Cambridge A Level Physics 9702 — Nuclear physics topical past papers
Mass–energy equivalence, mass defect and binding energy per nucleon, fission and fusion, and the random, exponential nature of radioactive decay.
- Questions
- 104
- Years
- 2009–2026
- With mark scheme
- 100%
- Questions 2022–2026
- 32
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What Nuclear physics covers
Mass and energy are equivalent, E = mc². A nucleus has less mass than its separate protons and neutrons, and this mass defect, multiplied by c², is the binding energy: the energy needed to separate the nucleus into its nucleons. A graph of binding energy per nucleon against nucleon number rises steeply for light nuclei, peaks near iron and falls slowly for heavy ones.
That curve explains where nuclear energy comes from. Fusing light nuclei and splitting a heavy nucleus by fission both produce nuclei with a higher binding energy per nucleon, and the increase in total binding energy is released, mostly as kinetic energy of the products. You calculate the energy released from the difference in mass between the reactants and the products, E = c²Δm.
Radioactive decay is spontaneous and random: you cannot predict when a particular nucleus will decay, and fluctuations in a count rate are the evidence. For a large number of nuclei, though, the activity is proportional to the number remaining, A = λN, which gives exponential decay, x = x₀e^(−λt), and a constant half-life t½ = 0.693/λ. This is A Level content, examined on Paper 4, and it extends particle physics from AS.
In the syllabus
The headings this topic has in the Cambridge International 2025–2027 syllabus, as the board prints them.
- 23 Nuclear physics
- 23.1 Mass defect and nuclear binding energy
- 23.2 Radioactive decay
What you should be able to do
- Use E = mc² and calculate mass defect and binding energy, working in kilograms or unified atomic mass units
- Sketch the binding energy per nucleon curve and use it to explain energy release in fission and fusion
- Balance nuclear equations and calculate the energy released from the masses involved
- Explain what spontaneous and random mean for decay, and the evidence from count-rate fluctuations
- Define activity, decay constant and half-life, and use A = λN and λ = 0.693/t½
- Use x = x₀e^(−λt) for activity, number of nuclei or count rate, correcting for background where needed
Key ideas
- E = mc², with c = 3.00 × 10⁸ m s⁻¹; 1 u = 1.66 × 10⁻²⁷ kg
- Mass defect = total mass of the separate nucleons − mass of the nucleus; binding energy = mass defect × c²
- Activity A = λN (Bq, decays per second); half-life t½ = 0.693/λ
- Exponential decay x = x₀e^(−λt), where x is the activity, number of undecayed nuclei or received count rate
How Nuclear physics has been examined
From 2022 to 2026, Nuclear physics was on Paper 4 · A Level Structured Questions in 11 of 11 exam series, worth about 11% of that paper’s marks.
| Paper | Questions | Share of marks | Series |
|---|---|---|---|
| Paper 4 · A Level Structured Questions | 32 | 11% | 11 of 11 |
Momentum’s own count, over the questions in its bank for these years: a series is one exam session, every zone included, and a question filed under two chapters counts in both. Median marks per question: 10. Some of these questions sit in a bank chapter that also covers a neighbouring topic, so the counts can run a little high.
Filed in Momentum under: Particle & Nuclear Physics.
A worked example
A radioactive sample has an activity of 8.0 × 10⁵ Bq, and its half-life is 6.0 hours. Find the number of undecayed nuclei now and the activity 15 hours later.
- Half-life in seconds: t½ = 6.0 × 3600 = 2.16 × 10⁴ s
- Decay constant: λ = 0.693 / 2.16 × 10⁴ = 3.21 × 10⁻⁵ s⁻¹
- Number of nuclei: N = A/λ = 8.0 × 10⁵ / 3.21 × 10⁻⁵ = 2.5 × 10¹⁰
- After 15 h: A = A₀e^(−λt) = 8.0 × 10⁵ × e^(−0.693 × 15/6.0) = 8.0 × 10⁵ × 0.177 = 1.4 × 10⁵ Bq
Answer: 2.5 × 10¹⁰ nuclei; activity after 15 hours 1.4 × 10⁵ Bq
Written by Momentum for this page, with its own numbers; it is not taken from a past paper.
Mistakes that cost marks
- Using a decay constant in h⁻¹ with A = λN and quoting the result in becquerels — convert the half-life to seconds first, because 1 Bq is one decay per second
- Saying fission releases energy because the products have less binding energy — they have more binding energy per nucleon, and that increase is what is released
- Describing decay as random because the count rate falls — random means the moment a particular nucleus decays cannot be predicted, shown by the fluctuations in count rate
- Forgetting background radiation in count-rate data — subtract it before finding a half-life
- Calculating binding energy as the mass of the nucleus × c² — only the mass defect is converted
Exam technique
- In binding-energy questions, keep every decimal place of the masses and subtract before rounding, because the mass defect is a small difference between large numbers
- When sketching binding energy per nucleon, show the peak near a nucleon number of 56, the steep rise at low nucleon numbers and the gentle fall at high ones
- To find a half-life from a decay graph, read at least two successive halvings and take the mean
Practising in Momentum
- Every question in a chapter as one list, from every paper and year in the bank, newest first or shuffled.
- Each question turns over to its own part of the mark scheme, where the board published one.
- Narrow by paper, year, session, zone and marks, and star the questions worth keeping.
- Pick chapters, a number of questions and a time, and the exam builder draws a mock to sit and mark.
Past-paper questions and mark schemes are the copyright of Cambridge International. Momentum shows them to signed-in learners for revision and does not publish them on these pages.