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.
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.
Nuclear route-selection map
Use this map before choosing a formula. Most mistakes come from using the right equation for the wrong nuclear story.
Question cue
First move
Equation or check
Common trap
"After this time", "remaining", "count rate", or "activity"
Convert all times to one unit and count the number of half-lives if it is exact.
Use A=λN, x=x0e−λt
Reviewed by
Chee Wei Jie·Academic Advisor (Physics)
, or repeated halving.
Mixing minutes, days, and seconds before calculating λ.
Nuclear reaction equation with a missing particle
Balance total nucleon number and total proton number on both sides.
Check A, Z, and charge before naming the particle.
Treating γ emission as changing A or Z.
"Mass defect", "binding energy", or "energy released"
Work out initial mass minus final mass using one mass unit system.
Use E=Δmc2 or 1u=931.5MeV.
Mixing u, kg, MeV, and J in the same line.
Fission, fusion, or binding-energy-per-nucleon graph
Ask whether the products move closer to the iron-region peak.
Energy is released when binding energy per nucleon increases.
Saying "mass decreases" without linking it to a more tightly bound final state.
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.
If you searched for A-Level nuclear physics notes
Use this page as the Topic 20 owner for nuclear physics a level notes, a level nuclear physics, and half-life formula queries. The SEAB 9478 topic moves from nuclear structure into decay, conservation laws, mass defect, binding energy, fission, and fusion, so the first step is choosing the right story before writing an equation.
Search clue
First owner
Next route
nuclear physics a level notes
This page
Use the route-selection map above before deciding between decay, conservation, and binding-energy work.
activity formula or lambda half-life
This page
Keep time units consistent, then use A=λN or λ=ln2/t1/2.
a level quantum physics while revising Modern Physics
Use tuition for script diagnosis, timed explanations, and binding-energy graph feedback.
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.
Decay-equation bookkeeping checkpoint
Before naming a missing particle, balance nucleon number A and proton number Z separately.
Decay or emission cue
Change in A
Change in Z
What to check first
Common trap
α emission
−4
−2
Daughter nucleus has four fewer nucleons and two fewer protons.
Subtracting only charge and forgetting mass number.
β− emission
no change
+1
A neutron changes into a proton, so the element changes.
Treating the emitted electron as coming from the electron shell.
γ emission
no change
no change
The nucleus loses energy, not nucleons or protons.
Changing the isotope after gamma emission.
Missing-particle equation
depends on the balance
depends on the balance
Add total A and total Z on each side before naming the particle.
Guessing the particle from the wording before balancing.
Worked check: if X614X26214C undergoes β− decay, A stays 14 and Z increases from 6 to 7, so the daughter is X714X27214N.
Misconception check: a balanced nuclear equation is not just a chemically familiar equation. The totals of A and Z must match across the arrow.
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.
Radiation hazard-choice checkpoint
For application and safety questions, choose the radiation by matching penetration, ionisation, and half-life to the situation. Do not pick the "strongest" radiation in isolation.
Situation cue
First property to check
Suitable reasoning
Common trap
External source outside the body
Penetration through tissue and shielding
α is stopped easily, β needs thin shielding, and γ needs dense shielding such as lead or concrete.
Calling α most dangerous for all cases just because it is highly ionising.
Source inhaled, swallowed, or trapped in tissue
Ionisation inside the body
α can be very harmful internally because it deposits energy over a short range.
Using the external-penetration rule after the source is already inside the body.
Medical tracer
Half-life and detectability
Choose a source with enough penetration to detect and a short enough half-life to limit dose after diagnosis.
Choosing the longest half-life because it is easier to detect for longer.
Thickness gauge or smoke detector
Penetration matched to the material
Use radiation that changes count rate noticeably when the material thickness or smoke density changes.
Using γ when a less penetrating source would give a more sensitive change.
Misconception check: hazard is not one number. A safe answer names the exposure route, radiation type, penetration or ionisation effect, and half-life.
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.
