A-Level Physics

Nuclear physics

Pearson Edexcel 9PH0 — matched to your course.

These revision notes are free. Premium unlocks the full question and retrieval-card bank for this topic.

Matched to your course

This page is matched to Pearson Edexcel 9PH0 so you can focus on the content for your course.

Revision hub

At a glance

Start practice

Learning goals6

Questions available2

Retrieval cards available1

Available question marks3

Subtopics and learning goals

Use mass defect and E = mc² to calculate nuclear binding energy.
Apply exponential radioactive-decay relationships and half-life.
Explain the physical basis of nuclear fission and fusion.
Describe radioactive decay as random for individual nuclei but statistically predictable for a large sample.
Use the meaning of half-life to interpret radioactive decay.
Explain nuclear binding energy as the energy required to separate a nucleus into its nucleons.

Revision notes

A nucleus contains protons and neutrons (nucleons). The mass of a bound nucleus is less than the total mass of its separated nucleons; this difference is the mass defect. The corresponding binding energy is E = Δmc². Binding energy per nucleon is useful when comparing nuclear stability.

Radioactive decay is random for an individual nucleus but statistically predictable for a large population. The activity A is proportional to the number N of undecayed nuclei: A = λN. The number remaining follows N = N0\(e^{-\lambda t}\), and half-life is related to decay constant by \(\dfrac{t1}{2}\) = \(\dfrac{\ln 2}{\lambda }\).

In fission, a heavy nucleus splits into smaller nuclei and releases energy, often with neutrons that can sustain a chain reaction. In fusion, light nuclei combine to form a more tightly bound nucleus. Both processes can release energy because the products have greater binding energy per nucleon; conservation of mass-energy accounts for the released energy.

Radioactive decay

Radioactive decay is random for an individual nucleus but statistically predictable for a large population. Activity A is decay rate, measured in becquerels. The number of undecayed nuclei N and activity decrease exponentially.

Half-life is the time for N or A to fall to half its value. The decay constant λ is linked by \(T_{1/2}\) = \(\dfrac{\ln 2}{\lambda }\). The equations N = N0\(e^{-\lambda t}\) and A = A0\(e^{-\lambda t}\) describe ideal exponential decay.

Nuclear equations and decay modes

Individual decay cannot be predicted from the age of one nucleus. The probability per unit time is constant for a given isotope in the simple model.

Mass defect and binding energy

The mass of a bound nucleus is less than the total mass of its separated nucleons. The difference is the mass defect. Binding energy is ΔE = Δmc² and represents the energy required to separate the nucleus completely into free nucleons.

Binding energy per nucleon helps compare nuclear stability. Energy can be released when a nuclear process moves nuclei towards more tightly bound configurations.

Fission

In nuclear fission, a heavy nucleus splits into smaller nuclei, usually after neutron absorption, releasing energy and additional neutrons. These neutrons can sustain a chain reaction. A reactor controls the neutron population while transferring released energy to a thermal system.

Fusion

Fusion combines light nuclei and can release energy because the products have greater binding energy per nucleon. Very high temperatures are required to give nuclei sufficient kinetic energy for close approach, while confinement is needed to sustain useful reaction rates.

Radiation measurements

Measured count rate can include background. Corrected activity or count rate should be used when analysing source decay. Statistical fluctuations are expected because decay is random; uncertainty becomes proportionally smaller when more counts are collected.

Exam technique

Separate activity from number of nuclei, even though they are proportional for one isotope. Use natural logarithms carefully when rearranging exponential decay equations. In binding-energy calculations, keep mass units and c² conversion consistent.

Atomic mass units and binding energy

Nuclear masses are given in unified atomic mass units: 1 u = 1.661 × 10⁻²⁷ kg, equivalent to 931.5 MeV. A mass defect in u multiplied by 931.5 gives the binding energy in MeV; 1 MeV = 1.60 × 10⁻¹³ J.

Binding energy per nucleon rises steeply for light nuclei, peaks at about 8.8 MeV near iron-56, and falls slowly for heavier nuclei. Fusion of light nuclei and fission of heavy nuclei both move towards the peak, so both release energy.

Nuclear size and Rutherford scattering

In Rutherford's alpha-scattering experiment, most alpha particles passed straight through gold foil, but a few were deflected through large angles. This showed that an atom has a tiny, dense, positively charged nucleus.

Radiation and reactors

Alpha particles are helium nuclei, stopped by paper; beta particles are fast electrons or positrons, stopped by a few millimetres of aluminium; gamma rays are high-energy photons, reduced by thick lead.

Worked example

Worked example 1: For λ = 2.0 × 10⁻⁴ s⁻¹, \(\dfrac{t1}{2}\) = \(\dfrac{\ln 2}{\lambda }\) = \(\dfrac{0.693}{2.0\times 10^{-4}}\) ≈ 3.47 × 10³ s.

Worked example 2: For a half-life of 6.0 h = 21600 s, λ = ln2 / \(T_{1/2}\) = \(\dfrac{0.693}{21600}\) = 3.21 × 10⁻⁵ s⁻¹.

A corrected activity falls from 800 Bq to 100 Bq: 800 → 400 → 200 → 100, so three half-lives have elapsed.

Worked example 3: A corrected activity of 960 Bq falls to 120 Bq through 960 → 480 → 240 → 120, so three half-lives have elapsed.

Misconception check

A short half-life does not mean each nucleus decays after exactly that time. Decay remains random; half-life describes the statistical behaviour of a large sample.

Assessment coverage

Practice this topic

2 questions available, worth 3 marks in total.

Calculation 1Recall 1

Foundation 2

Practise this topic