Nuclear physics

Study H1 Physics isotopes and nuclear equations, calculate decay and half-life, and use binding energy to explain fusion and fission.

GCE A-Level H1 Physics 2027
4 lessons

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Before you begin

Almost all of an atom’s mass is packed into a nucleus a hundred thousand times smaller than the atom itself. The lessons start with the scattering experiment that revealed the nucleus, nuclide notation and the Avogadro constant. They then cover radioactive decay: why it is random, the three kinds of radiation, half-life, and how radioactivity is used safely. They finish with nuclear equations and the conservation laws they obey, and with mass defect and binding energy, which explain the energy released in fusion and fission.

Be comfortable with: motion in a uniform electric field, because alpha and beta radiation are told apart by how they are deflected, and energy stores and work.

Learning goals

Interpret nuclear structure, isotopes and Rutherford scattering.
Describe isotopes as forms of an element with different numbers of neutrons, and write nuclides with nucleon number A and proton number Z before the symbol
State that one mole contains 6.02 × 10²³ particles and use the Avogadro number, 6.02 × 10²³ mol⁻¹
Describe nuclear decay as spontaneous and random, and use the term activity
Analyse random radioactive decay, activity and half-life.
Define half-life and use it to solve problems, including from tables or decay curves
Relate binding energy per nucleon to fission, fusion, applications and hazards.
Write nuclear equations for simple nuclear reactions, such as ¹⁴₇N + ⁴₂He → ¹⁷₈O + ¹₁H
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 ZA X for the representation of nuclides
state that one mole of any substance contains 6.02 × 1023 particles and use the Avogadro number NA = 6.02 × 1023 mol-1
show an understanding of the spontaneous and random nature of nuclear decay, and use the term activity
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 half-life as the time taken for a quantity x to reduce to half its initial value, and use the term to solve problems which might involve information in tables or decay curves
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 147 N + 4 2 He → 178 O + 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 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

Lessons

Work through them in order.

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Topic reference

Quick reference

Idea	Relationship	Note
nuclide	X with nucleon number A and proton number Z	neutrons = A-Z
number of particles	N = nNA	NA = 6.02 × 10²³ mol⁻¹
corrected count rate	measured rate - background rate	correct every reading
half-life	x = x₀(1/2)ⁿ	after n half-lives
mass–energy	Δ E = Δ m c²	1 u≡931.5 MeV
mass defect	Δ m = Zmₚ + (A-Z)mₙ-m_nucleus	separate nucleons minus nucleus
binding energy	Eb = Δ m c²	per nucleon: Eb/A

Core knowledge to remember

Alpha-particle scattering shows that an atom has a very small nucleus containing all its positive charge and most of its mass.
The proton number Z is the number of protons; the nucleon number A is the number of protons and neutrons. Isotopes have the same proton number but different numbers of neutrons.
One mole of any substance contains 6.02 × 10²³ particles.
Radioactive decay is spontaneous and random. Fluctuations in count rate show its random nature. Background radiation must be subtracted from measured count rates.
Alpha particles are helium nuclei; beta particles are fast electrons from the nucleus; gamma radiation is electromagnetic. Ionising ability decreases, and penetration increases, from alpha to beta to gamma.
Half-life is the time taken for a quantity x to reduce to half its initial value.
Nucleon number, charge and mass–energy are all conserved in nuclear processes.
Binding energy is the energy needed to separate a nucleus into its individual nucleons; it is the energy equivalent of the mass defect. Binding energy per nucleon peaks near iron-56, so fusion of light nuclei and fission of heavy nuclei both release energy.

Common mistakes

Saying isotopes have different proton numbers.
Forgetting to subtract background radiation before finding a half-life.
Saying a nucleus will decay after one half-life.
Balancing nucleon number but not charge in a nuclear equation.
Saying mass is conserved in a nuclear reaction, instead of mass–energy.
Comparing binding energies per nucleon instead of total binding energies when finding the energy released.