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1 The nuclear atom
2 Nuclear bookkeeping: \(Z\), \(A\) and isotopes
Q: What do these H2 Physics nuclear notes cover? A: They cover radioactivity, half-life, decay law, mass defect, binding energy, fission, fusion, and common A-Level 9478 nuclear applications.
TL;DR These H2 Physics nuclear notes cover the decay law, half-life algebra, mass defect, binding energy, and fission-vs-fusion logic for A-Level 9478. Master the radioactivity workflow and conservation checklist so nuclear questions become methodical instead of memorised.
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1 second
Nuclear questions are conservation plus decay laws
10 seconds
Half-life, activity, mass defect, and binding energy
100 seconds
Nuclear bookkeeping and the first decay setup
10 minutes
Fission, fusion, safety, and energy calculations
Concrete example: how to use this page
For a decay question, identify the starting number of nuclei, the half-life, and the elapsed time before using the exponential model. For an energy question, convert mass defect to energy only after units are consistent.
Round out the Modern Physics arc (Quantum → Nuclear → Particle) via our free H2 Physics notes; it links this guide to the preceding quantum chapter plus extra decay drills. For the full topic map and paper weightings, see our H2 Physics Syllabus 2026-27 overview.
1 The nuclear atom
Rutherford's alpha-scattering revealed a dense, positively-charged core with size on the order of femtometres (10−15m)
, because only a small fraction of
α
particles were deflected through large angles.
2 Nuclear bookkeeping: Z, A and isotopes
Symbol
Meaning
Typical size
Z
Proton (atomic) number
1→118
A
Nucleon (mass) number
1→300
Write nuclides as XZAX2Z2AX. Example: X614X26214C has 6 protons and 8 neutrons.
Isotopes share the same Z but different A; their chemical behaviour is identical, yet nuclear stability varies.
3 Radioactive decay fundamentals
3.1 Randomness & background
Each nucleus decays spontaneously; count-rate fluctuations seen on a GM tube histogram are statistical proof. Natural background comes from cosmic rays, terrestrial isotopes and internal potassium-40.
3.2 α, β, γ radiations
Radiation
Composition
Charge
Ionising
Penetration
α
Helium nucleus 24He
+2
Very strong
Paper
β−
Electron e−
-1
Moderate
5mmAl
γ
Photon
0
Weak
cm-thick Pb
Penetration inversely tracks ionising power.
4 Measuring decay
Define activityA (in Bq) as decays per second; A=λN. The decay law
N=N0e−λt
gives an exponential curve. Half-life is
t1/2=λln2.
⮕ Mini-drill: show that after 3 half-lives, N=N0/8.
Answer:N=N0(21)3=N0/8.
5 Conservation laws & the (anti)neutrino
Nuclear equations conserve nucleon number, charge and mass-energy. Example:
714N+24He→817O+11H
In β− decay, missing energy and momentum led Pauli to postulate an elusive neutral particle - the neutrino - restoring conservation.
6 Mass defect & E=mc2
A nucleus weighs less than its separated nucleons; the deficit Δm converts to binding energy
Eb=Δmc2.
This is Einstein's mass-energy equivalence. For 4He, Eb≈28MeV.
7 Binding-energy curve: fusion vs fission
Plotting binding energy per nucleon against A peaks near iron-56 (8.8MeV).
Fusion of light nuclei moves uphill, releasing energy - the Sun fuses hydrogen via the proton-proton chain, while experimental reactors (ITER, NIF) target deuterium-tritium (D-T) reactions.
Fission of A>235 splits heavy nuclei into medium ones, also moving toward the peak.
8 Applications & hazards
Sector
Isotope
Half-life
Radiation
Why chosen
PET imaging
18F
110 min
β+
Short t1/2, emits annihilation γ pairs.
Thickness gauge
90Sr
29 y
β−
Medium penetration, long life.
Smoke detector
241Am
432 y
α
Strong ioniser, low penetration.
Hazards: danger depends on penetrating ability, ionising effect, and half-life. Alpha particles ionise heavily but stop in skin or paper - mainly a risk if inhaled or ingested. Beta particles penetrate a few millimetres of tissue - aluminium or thick plastic shielding is adequate. Gamma rays penetrate deeply - lead or concrete shielding is needed. Long half-lives extend contamination risk because the source stays active for longer. Reduce dose by minimising exposure time, maximising distance, and using appropriate shielding.
9 WA timing hacks
Draw a decay curve sketch before diving into algebra.
Label nuclei with Z and A first to avoid conservation slips.
Use ln key for half-life Qs: λ=0.693/t1/2.
Need structured practice on Nuclear Physics? Our H2 Physics tuition programme covers this topic with weekly problem sets and Paper 4 practical drills.
Comprehensive revision pack
9478 Section VI, Topic 20 Syllabus outcomes
Candidates should be able to:
(a) infer from the results of the Rutherford α-particle scattering experiment the existence and small size of the atomic nucleus.
(b) distinguish between nucleon number (mass number) and proton number (atomic number).
(c) 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 ZAX for the representation of nuclides.
(d) show an understanding of the spontaneous and random nature of nuclear decay.
(e) infer the random nature of radioactive decay from the fluctuations in count rate.
(f) show an understanding of the origin and significance of background radiation.
(g) show an understanding of the nature and properties of α, β and γ radiations (knowledge of positron emission is not required).
(h) define the terms activity and decay constant and recall and solve problems using the equation A=λN.
(i) 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.
(j) define and use half-life as the time taken for a quantity x to reduce to half its initial value.
(k) solve problems using the relation λ=t1/2ln2.
(l) discuss qualitatively the applications (e.g. medical and industrial uses) and hazards of radioactivity based on (i) half-life of radioactive materials, and (ii) penetrating abilities and ionising effects of radioactive emissions.
(m) represent simple nuclear reactions by nuclear equations of the form 714N+24He→817O+11H
(n) state and apply to problem solving the concept that nucleon number, charge and mass-energy are all conserved in nuclear processes.
(o) 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).
(p) show an understanding of the concept of mass defect.
(q) recall and apply the equivalence between energy and mass as represented by E=mc2 to solve problems.
(r) show an understanding of the concept of nuclear binding energy and its relation to mass defect.
(s) sketch the variation of binding energy per nucleon with nucleon number.
(t) explain the relevance of binding energy per nucleon to nuclear fusion and to nuclear fission.
Concept map (in words)
Start with nuclear notation (A, Z). Link decay types (alpha, beta, gamma) with changes in A and Z. Use activity A=λN and N=N0e−λt for quantitative predictions. Binding energy per nucleon explains energy release in fission and fusion. Conservation checks keep equations balanced.
Key relations
Quantity / relation
Expression / reminder
Activity
A=λN
Decay law
N=N0e−λt
Half-life
t1/2=ln2/λ
Mass defect
δm=Zmp+(A−Z)mn−mnucleus
Binding energy
Eb=δmc2
Energy released per fission
δE=(massinitial−massfinal)c2
Derivations & reasoning to master
Exponential decay: derive activity dependence from differential equation dtdN=−λN.
Half-life relation: show t1/2=ln2/λ by solving N=N0/2.
Binding energy per nucleon curve: explain why fusion of light nuclei and fission of heavy nuclei release energy.
Mass-energy conversions: practise converting atomic mass units to MeV using 1u=931.5MeV.
Worked example 1 - decay counting
A sample contains 1.2×1018 nuclei of an isotope with half-life 8.0 days. Calculate (a) decay constant, (b) initial activity, (c) activity after 24 days.
Approach: λ=ln2/t1/2; A0=λN0; A=A0e−λt.
Convert t1/2=8.0 days to seconds: t1/2=8.0×24×3600=6.91×105s.
λ=t1/2ln2=6.91×1050.693=1.00×10−6s−1.
A0=λN0=(1.00×10−6)(1.2×1018)=1.20×1012Bq.
After 24 days (3 half-lives), A=A0/8=1.50×1011Bq.
Worked example 2 - binding energy release
Using mass data for U-235 fission into Ba-141 and Kr-92 plus three neutrons, compute energy released per fission in MeV. Convert to joules and compare with chemical energy scales.
Method: determine mass defect, multiply by c2, convert units; emphasise orders of magnitude.
Practical & data tasks
Plot ln N vs t for simulated decay data to extract lambda from gradient.
Calculate shielding thickness needed for different radiation types using attenuation coefficients.
Analyse CANDU reactor fuel cycle or medical tracer half-life scheduling as case studies.
Common misconceptions & exam traps
Forgetting to convert half-life units (minutes vs seconds).
Mixing mass units (u vs kg) when calculating binding energy.
Ignoring neutrinos in beta decay when balancing energy/momentum.
Assuming gamma decay changes nucleon numbers (it does not).
Quick self-check quiz
Define activity. - Rate of decay of nuclei (decays per second).
How many half-lives reduce activity to 1/32? - Five.
Why is fusion of light nuclei energetically favourable? - Binding energy per nucleon increases toward iron peak.
Name the particle emitted in beta-minus decay in addition to electron. - Antineutrino.
State one medical application of isotopes. - PET imaging with X18X2218F, radiotherapy with X60X2260Co, etc.
Revision workflow
Re-derive decay and half-life relations without notes weekly.
Practise binding energy calculations with mass tables to stay fluent in unit conversions.
Work through two past-paper questions involving decay chains and shielding.
Summarise pros/cons of nuclear power, medical usage, and waste management for essay-style prompts.
Practice Quiz
Test yourself on the key concepts from this guide.
Parents: book a 60-min Nuclear Physics clinic two weeks before WA 2 to tackle binding-energy graph sketching.
Students: print the table in §8, stick it on your desk, and quiz yourself while waiting for downloads to finish.
Last updated 14 Jul 2025. Next review when SEAB issues the 2027 draft syllabus.
