# Nuclear physics

> CIE A-Level Physics · 9702
> Source: https://www.owlsprep.com/study/cie-9702-u27-overview/
> Weight: n/a

This unit explores nuclear structure, stability, radioactive decay and nuclear energy. You will learn how mass-energy conversion powers nuclear reactions and model the random nature of decay, a foundation for modern applied physics.

**Prerequisites:** Atomic structure fundamentals; Einstein's mass-energy equivalence principle

## Learning objectives

- Calculate mass defect and binding energy, and relate binding energy per nucleon to nuclear stability
- Apply the radioactive decay law to solve problems involving activity and number of undecayed nuclei
- Use half-life to model radioactive decay and calculate decay rates from experimental data
- Distinguish between nuclear fission and fusion, and explain why both processes release energy
- Describe hazards of ionizing radiation and outline standard safety precautions for radioactive materials

## Unit at a glance

This unit follows a logical flow from nuclear stability to decay behavior to energy-releasing reactions and practical safety. We start by connecting mass differences between nucleons and whole nuclei to binding energy, the force that holds nuclei together. Next we explore the random nature of radioactive decay, derive the decay law, and learn how half-life describes decay rate. We then explain how the binding energy per nucleon curve drives energy release in fission and fusion, ending with practical radiation safety guidance.

This unit covers the following sub-topics:
- [Mass defect and binding energy](https://www.owlsprep.com/study/cie-9702-u27-mass-defect-and-binding-energy/) — Learn how mass defect arises, calculate binding energy, and relate binding energy per nucleon to nuclear stability.
- [Radioactive decay law](https://www.owlsprep.com/study/cie-9702-u27-radioactive-decay-law/) — Derive and apply the exponential decay law to calculate activity and undecayed nuclei at any point in time.
- [Half-life](https://www.owlsprep.com/study/cie-9702-u27-half-life/) — Understand half-life definitions, solve problems for decay over multiple half-lives, and calculate half-life from raw data.
- [Nuclear fission and fusion](https://www.owlsprep.com/study/cie-9702-u27-nuclear-fission-and-fusion/) — Explain energy release in fission and fusion using the binding energy curve, and describe applications for power generation.
- [Radiation safety](https://www.owlsprep.com/study/cie-9702-u27-radiation-safety/) — Learn about biological effects of ionizing radiation and standard safety precautions for working with radioactive sources.

## Common pitfalls

- **Wrong:** Confusing mass defect with binding energy directly
  - Why it fails: Mass defect is a mass difference, while binding energy is the energy equivalent of that mass difference
  - Correct: Always convert mass defect to binding energy using $E_b = \Delta m c^2$
- **Wrong:** Treating half-life as a fixed decay time for individual nuclei
  - Why it fails: Radioactive decay is random, so half-life is a statistical property of large groups of nuclei
  - Correct: Use half-life only to predict the proportion of a large sample that will decay over a given time
- **Wrong:** Forgetting energy is released when products have higher binding energy per nucleon
  - Why it fails: Students often mix up the direction of energy flow in fission and fusion calculations
  - Correct: Confirm that products sit higher on the binding energy per nucleon curve for energy to be released

## Cheatsheet

| Concept | Key Formula / Rule |
| --- | --- |
| Mass defect | $\Delta m = Zm_p + (A-Z)m_n - m_{nucleus}$ |
| Binding energy | $E_b = \Delta m c^2$ |
| Radioactive decay law (nuclei) | $N = N_0 e^{-\lambda t}$ |
| Activity of a source | $A = A_0 e^{-\lambda t} = \lambda N$ |
| Half-life relation | $t_{1/2} = \frac{\ln 2}{\lambda}$ |
| Energy release condition | Products have higher binding energy per nucleon than reactants |
| Radiation penetration in air | $\alpha$: ~5 cm, $\beta$: ~1 m, $\gamma$: ~100s of m |

## What's next

We recommend working through the sub-topics of this unit in the order listed above, starting with the first sub-topic to build your foundational understanding of nuclear stability. After completing all sub-topics in this unit, you will be ready to progress to the next unit on fundamental particles in the CIE A-Level Physics syllabus.

- [Mass defect and binding energy (first sub-topic of this unit)](https://www.owlsprep.com/study/cie-9702-u27-mass-defect-and-binding-energy/)
- [Radioactive decay law](https://www.owlsprep.com/study/cie-9702-u27-radioactive-decay-law/)
- [Half-life](https://www.owlsprep.com/study/cie-9702-u27-half-life/)

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