Q: What does A-Level Physics: 20) Nuclear Physics Guide cover? A: From Rutherford 's gold-foil to binding-energy curves, this post unpacks Topic 20 of the 2026 H2 Physics syllabus for IP students and parents.
TL;DR The nucleus is tiny yet mighty: its femtometre scale explains why most alpha particles sail straight through foil (>99.9%path) while its binding-energy curve bankrolls both fission reactors and the Sun. Master the decay law, half-life algebra and conservation check-list to secure >12 marks of Paper 1 MCQs and every WA radioactivity question.
1 The nuclear atom
Rutherford 's alpha-scattering revealed a dense, positively-charged core less than 10−14m across - about 1fm
- because only a few
α
particles were deflected through large angles.
2 Nuclear bookkeeping: Z, A and isotopes
Symbol
Meaning
Typical size
\(Z\)
Proton (atomic) number
\(1 \rightarrow 118\)
\(A\)
Nucleon (mass) number
\(1 \rightarrow 300\)
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
\(\alpha\)
Helium nucleus \(^4_2 \text{He}\)
+2
Very strong
Paper
\(\beta^-\)
Electron \(e^-\)
-1
Moderate
\(~5 \space \text{mm} \space \text{Al}\)
\(\gamma\)
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.
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 (e.g. D-T) moves uphill, releasing energy - the Sun and recent stellarator records rely on this.
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
\(^{18} \text{F}\)
110 min
\(\beta^+\)
Short \(t_{1/2}\), emits annihilation \(\gamma\) pairs.
Thickness gauge
\(^{90} \text{Sr}\)
29 y
\(\beta^-\)
Medium penetration, long life.
Smoke detector
\(^{241} \text{Am}\)
432 y
\(\alpha\)
Strong ioniser, low penetration.
Hazards: ionising radiation can damage DNA; shielding, distance and time minimise dose.
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.
Comprehensive revision pack
9478 Section VI, Topic 20 Syllabus outcomes at a glance
Outcome (a) - describe nuclear structure, isotopes and decay types.
Outcome (c) - use decay equations to conserve nucleon number, charge and energy.
Outcome (d) - interpret binding energy, mass defect and fission/fusion energetics.
Outcome (e) - evaluate nuclear applications and safety considerations.
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
\(A = \lambda N\)
Decay law
\(N = N_0 e^{-\lambda t}\)
Half-life
\(t_{1/2} = \ln 2 / \lambda\)
Mass defect
\(\delta m = Zm_p + (A-Z)m_n - m_\text{nucleus}\)
Binding energy
\(E_b = \delta m \space c^2\)
Energy released per fission
\(\delta E = \left( \text{mass}_\text{initial} - \text{mass}_\text{final} \right) c^2\)
Dose reduction principles
Shielding, distance, time (ALARA)
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.
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.
