Unit 5: Nuclear Decay

This guide covers sub-topic 5.4 Nuclear Decay, the second of four sub-topics in Unit 5: Thermodynamics, Radiation, Oscillations and Cosmology, from the Pearson Edexcel International Advanced Level in Physics (YPH11), Issue 3 specification. This topic is commonly studied using applications such as medical physics and carbon dating.

Before studying this

This topic connects closely with Unit 4’s Nuclear and Particle Physics sub-topic (mass-energy equivalence, ΔE = c²Δm) and assumes familiarity with exponential decay from Unit 4 sub-topic 4.4’s capacitor discharge content.

Syllabus coverage

PEARSON EDEXCEL INTERNATIONAL A LEVEL PHYSICS (YPH11) — Sub-topic 5.4

Candidates will be assessed on their ability to: understand the concept of nuclear binding energy and use the equation ΔE = c²Δm in calculations of nuclear mass (including mass deficit) and energy; use the atomic mass unit (u) to express small masses and convert between this and SI units; understand the processes of nuclear fusion and fission with reference to the binding energy per nucleon curve; understand the mechanism of nuclear fusion and the need for very high densities of matter and very high temperatures to bring about and maintain nuclear fusion; understand that there is background radiation and how to take appropriate account of it in calculations; understand the relationships between the nature, penetration, ionising ability and range in different materials of nuclear radiations (alpha, beta and gamma); write and interpret nuclear equations given the relevant particle symbols; CORE PRACTICAL 15: investigate the absorption of gamma radiation by lead; understand the spontaneous and random nature of nuclear decay; and determine the half-lives of radioactive isotopes graphically and use the equations for radioactive decay, activity A = λN, dN/dt = −λN, t½ = ln2/λ, N = N₀e^(−λt) and A = A₀e^(−λt), and derive and use the corresponding log equations.

Binding energy, fusion and fission

Nuclear binding energy is the energy released when nucleons combine to form a nucleus, equivalent to the mass deficit (the difference between the mass of the separate nucleons and the mass of the assembled nucleus), via:

ΔE = c² Δm

Small masses at this scale are conveniently expressed in the atomic mass unit (u), convertible to SI units. Plotting binding energy per nucleon against nucleon number gives a curve that peaks around iron, explaining why both nuclear fusion (combining light nuclei) and nuclear fission (splitting heavy nuclei) release energy — both move nuclei towards the more stable, higher binding-energy-per-nucleon region of the curve. Fusion requires very high densities of matter and very high temperatures to overcome electrostatic repulsion between positively charged nuclei and bring them close enough for the strong nuclear force to act.

Background radiation and types of nuclear radiation

Background radiation is present in all radioactivity measurements (from cosmic rays, rocks, medical sources, etc.) and must be accounted for — typically by subtracting a measured background count rate from experimental readings. The three types of nuclear radiation — alpha, beta and gamma — differ in their nature, penetration, ionising ability and range in different materials: alpha particles (helium nuclei) are strongly ionising but weakly penetrating (stopped by paper or a few cm of air); beta particles (high-speed electrons) are moderately ionising and penetrating (stopped by a few mm of aluminium); gamma rays (electromagnetic radiation) are weakly ionising but highly penetrating (substantially reduced only by thick lead or concrete). CORE PRACTICAL 15 investigates the absorption of gamma radiation by lead. Candidates must be able to write and interpret nuclear equations, correctly balancing nucleon and proton numbers on each side.

Radioactive decay and half-life

Nuclear decay is spontaneous (not triggered by external factors) and random (any individual nucleus’s decay time cannot be predicted, only described statistically). The activity A of a sample is the rate of decay:

A = λN
dN/dt = −λN

where λ is the decay constant and N is the number of undecayed nuclei. This gives exponential decay:

N = N0 e^(-λt)
A = A0 e^(-λt)

The half-life t½ — the time for the activity (or number of undecayed nuclei) to fall to half its value — relates to the decay constant by:

t½ = ln2 / λ

Half-lives can be determined graphically, either directly from a decay-against-time graph, or from the gradient of the corresponding straight-line log graphs (e.g. lnN = lnN₀ − λt).

Worked example. A radioactive isotope has a decay constant of 0.0231 per year. Find its half-life, and the fraction of a sample remaining after 60 years.

t½ = ln2 / λ = 0.6931 / 0.0231 = 30.0 years

After 60 years (= 2 half-lives), fraction remaining = (½)² = 0.25 (25%).

Common mistakes

Forgetting to subtract background radiation before analysing count-rate data. Confusing mass deficit (the mass “missing” as binding energy) with the total mass of a nucleus. Using half-life directly in the exponential decay equations instead of the decay constant λ (or forgetting to convert between them via t½ = ln2/λ). Assuming radioactive decay of an individual nucleus can be predicted — only the statistical behaviour of a large sample follows the exponential decay law.

Quick revision checklist

• Use ΔE = c²Δm for binding energy and mass deficit, and convert masses to/from the atomic mass unit.
• Explain fusion and fission in terms of the binding-energy-per-nucleon curve.
• Explain why fusion requires high density and temperature.
• Compare the nature, penetration, ionising ability and range of alpha, beta and gamma radiation.
• Describe CORE PRACTICAL 15 (gamma absorption by lead) and account for background radiation.
• Write and balance nuclear equations.
• Use A = λN, N = N0e^(-λt), A = A0e^(-λt) and t½ = ln2/λ, including graphical determination of half-life.

Related resources

• Unit 5: Thermodynamics — the previous sub-topic
• Unit 5: Oscillations — the next sub-topic
• Unit 4: Nuclear and Particle Physics — related mass-energy content
• Pearson Edexcel International A Level Physics hub

This guide is intended to support, not replace, engagement with the official Pearson Edexcel specification and your own teacher’s guidance. Always check the current version of the specification for authoritative detail.