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Nuclear physics

The nuclear atom, random and exponential radioactive decay, alpha, beta and gamma radiation, nuclear equations, mass defect, binding energy, fusion and fission, for H2 Physics.

  • GCE A-Level H2 Physics 2027
  • 10 lessons
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Before you begin

Nuclear physics is about the nucleus: what it is made of, why some nuclei decay and where nuclear energy comes from. The lessons start with the scattering evidence for a small, massive nucleus, move on to random decay and the exponential law it produces, then use conservation laws and E = mc² to explain binding energy, fusion and fission.

Be comfortable with: O-Level radioactivity, because this topic builds on alpha, beta and gamma radiation and half-life, and with exponentials and natural logarithms.

Learning goals
  • Interpret nuclear structure, isotopes and Rutherford scattering.
  • Analyse random radioactive decay, activity and half-life.
  • Relate binding energy per nucleon to fission, fusion, applications and hazards.
  • Apply conservation laws to nuclear equations, including beta decay.
  • Use mass-energy equivalence, mass defect and binding energy.
Syllabus statements covered
  • infer from the results of the Rutherford α-particle scattering experiment the existence and small size of the atomic nucleus
  • distinguish between nucleon number (mass number) and proton number (atomic number)
  • show an understanding that an element can exist in various isotopic forms, each with a different number of neutrons in the nucleus, and use the notation ᴬZX for the representation of nuclides
  • show an understanding of the spontaneous and random nature of nuclear decay
  • infer the random nature of radioactive decay from the fluctuations in count rate
  • show an understanding of the origin and significance of background radiation
  • show an understanding of the nature and properties of α, β and γ radiations (knowledge of positron emission is not required)
  • define the terms activity and decay constant and recall and solve problems using the equation A = λN
  • infer and sketch the exponential nature of radioactive decay and solve problems using the relationship x = x₀e⁻λᵗ where x could represent activity, number of undecayed particles or received count rate
  • define and use half-life as the time taken for a quantity x to reduce to half its initial value
  • solve problems using the relation λ = ln 2/t½
  • discuss qualitatively the applications (e.g. medical and industrial uses) and hazards of radioactivity based on: (i) half-life of radioactive materials; (ii) penetrating abilities and ionising effects of radioactive emissions
  • represent simple nuclear reactions by nuclear equations of the form ¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H
  • state and apply to problem solving the concept that nucleon number, charge and mass-energy are all conserved in nuclear processes
  • show an understanding of how the conservation laws for energy and momentum in β decay were used to predict the existence of the (anti)neutrino (knowledge of the antineutrino and the zoo of particles is not required)
  • show an understanding of the concept of mass defect
  • recall and apply the equivalence between energy and mass as represented by E = mc² to solve problems
  • show an understanding of the concept of nuclear binding energy and its relation to mass defect
  • sketch the variation of binding energy per nucleon with nucleon number
  • explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission

How the ideas connect

  1. Scattering shows that an atom has a tiny, massive, positive nucleus.
  2. Each nucleus decays at random, but a large sample decays exponentially.
  3. Nuclear processes conserve nucleon number, charge, mass-energy and momentum.
  4. Binding energy per nucleon explains why fusion and fission both release energy.
Explore the lessons

Lessons

Work through them in order.

Core lessons

  1. Nuclear structure and nuclidesExplain how alpha-particle scattering shows a small, massive nucleus, then use nuclide notation and identify isotopes.
  2. Random decay and background radiationExplain why count readings fluctuate, name the sources of background radiation and subtract background as a rate.
  3. Activity, half-life and exponential decayUse activity, the decay constant and half-life to calculate how a sample and its corrected count rate fall with time.
  4. Alpha, beta-minus and gamma radiationUse the nature and charge of each radiation to explain its ionisation, penetration and deflection in electric and magnetic fields.
  5. Applications and hazards of radioactivityChoose a radioactive source for a job from its penetration and half-life, and explain its hazards and how to control them.
  6. Nuclear equations and conservation lawsBalance nuclear equations using nucleon number and charge, and apply conservation of mass-energy and momentum to nuclear processes.
  7. Beta decay and the neutrinoExplain how the continuous beta spectrum and the conservation of energy and momentum predicted the (anti)neutrino.
  8. Mass defect and binding energyUse E = mc² to explain the mass defect, and calculate the binding energy of a nucleus in MeV and in joules.
  9. Binding energy per nucleonCompare nuclei by binding energy per nucleon, then sketch and explain the shape of its curve against nucleon number.
  10. Binding energy in fusion and fissionUse binding energy per nucleon to explain why fusion and fission release energy, and calculate the energy released.

Beyond the syllabus

  1. Fission chain reactionsCalculate how a simple fission chain grows or dies away, and explain the jobs of the moderator, control rods and coolant.Beyond the syllabus
  2. Conditions for nuclear fusionExplain why fusion needs a very high temperature, high density and confinement, and tell energy per reaction apart from power.Beyond the syllabus
  3. How a Geiger–Müller tube counts radiationExplain how a Geiger–Müller tube turns ionisation into a count, and why quenching and dead time matter.Beyond the syllabus

Practise and check

Recommended nextNuclear physics topic check

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Topic reference

Quick reference

Quantity or relationEquationNotes
neutron numberA-ZA nucleon number, Z proton number
activityA = λ Nunit Bq, one decay per second; λ in s⁻¹
exponential decayx = x₀e^(-λ t)x is the number undecayed, the activity or the net count rate
half-lifet_(1/2) = (ln 2)/λconstant for a nuclide
straight-line graphln A = ln A₀-λ tgradient -λ
mass-energyE = mc²1 u = 1.66 × 10⁻²⁷ kg; 1 u c² = 931.5 MeV
mass defectΔ m = Zmₚ + (A-Z)mₙ-m_nucleuswith atomic masses, use mH for mₚ
binding energyEb = Δ m c²energy to separate the nucleus into free nucleons
energy releasedQ = ∑ E_(b,products)-∑ E_(b,reactants)free nucleons have Eb = 0
PropertyAlpha, αBeta-minus, β⁻Gamma, γ
naturehelium nucleusfast electron from the nucleuselectromagnetic radiation
charge+ 2e-e0
ionisationstrongmoderateweak
absorbed bypaper, a few cm of aira few mm of aluminiumreduced by cm of lead
in an electric fieldtowards the negative platetowards the positive plateundeflected
Binding energy per nucleon curveBinding energy per nucleon rises steeply for light nuclei, reaches a broad maximum near iron and nickel, then decreases slowly for heavy nuclei. Arrows show suitable light-nucleus fusion increasing nucleon number and heavy-nucleus fission decreasing it, toward higher average binding.Nucleon number, ABinding energy per nucleonFe / Ni regionlightheavyfusionfission
Binding energy per nucleon curveBinding energy per nucleon rises steeply for light nuclei, reaches a broad maximum near iron and nickel, then decreases slowly for heavy nuclei. Arrows show suitable light-nucleus fusion increasing nucleon number and heavy-nucleus fission decreasing it, toward higher average binding.Binding energy per nucleonNucleon number, AFe / Ni regionlightheavyfusionfission
Schematic trend, not a plot of individual isotope data. Fusion of suitable light nuclei and fission of very heavy nuclei can increase total binding energy and release energy.

Core knowledge to remember

  • The nucleon number (mass number) A is the number of protons and neutrons in a nucleus. The proton number (atomic number) Z is the number of protons.
  • Isotopes are forms of an element with the same number of protons but different numbers of neutrons in the nucleus.
  • Radioactive decay is spontaneous, unaffected by external conditions, and random: you cannot predict when a particular nucleus will decay. Fluctuations in count rate show that decay is random.
  • Background radiation comes from radon gas, rocks and buildings, cosmic rays, food and the body, and medical and other artificial sources. Subtract it, as a rate, from every count rate.
  • The activity of a sample is the number of nuclei decaying per unit time. The decay constant is the probability that a nucleus decays per unit time.
  • The half-life is the time taken for a quantity x to fall to half its initial value.
  • Nucleon number, charge and mass-energy are conserved in nuclear processes. The continuous energy spectrum of beta particles, with conservation of energy and momentum, predicted the (anti)neutrino.
  • The mass defect is the difference between the total mass of the separate nucleons and the mass of the nucleus. The binding energy is the energy needed to separate a nucleus completely into its protons and neutrons, and equals the mass defect times c².
  • Binding energy per nucleon rises steeply for light nuclei, peaks at about 8.8 MeV near iron-56, then falls slowly. Fusion of light nuclei and fission of heavy nuclei both move towards the peak, so both release energy.

Common mistakes

  1. Treating half-life as the time by which a particular nucleus must decay. It describes a large sample.
  2. Putting a count rate into A = λ N. A detector registers only a fraction of the decays.
  3. Halving a count rate that still includes background, or subtracting counts taken over different times.
  4. Balancing protons instead of charge in a nuclear equation. In beta-minus decay a neutron becomes a proton.
  5. Mixing atomic masses with bare proton masses when finding a mass defect.
  6. Thinking more binding energy means more stored energy. A nucleus with more binding energy has less mass, and energy is released when it forms.
  7. Using the binding energy per nucleon of the products for every nucleon, including free neutrons. Find each nucleus’s total; free neutrons have zero.