H2 Physics Nuclear Physics Notes | A-Level 9478

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.

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.

1 The nuclear atom

Rutherford's alpha-scattering revealed a dense, positively-charged core with size on the order of femtometres $(10^{-15} \space \text{m})$, because only a small fraction of $\alpha$ particles were deflected through large angles.

2 Nuclear bookkeeping: $Z$, $A$ and isotopes

Write nuclides as $\ce{_Z^A X}$

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 $\alpha$, $\beta$, $\gamma$ radiations

Penetration inversely tracks ionising power.

Decay-equation bookkeeping checkpoint

Before naming a missing particle, balance nucleon number $A$ and proton number $Z$ separately.

Worked check: if $\ce{_6^14 C}$

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 activity $A$ (in Bq) as decays per second; $A = \lambda N$. The decay law

$$N = N_0 e^{-\lambda t}$$

gives an exponential curve. Half-life is

$$t_{1/2} = \frac{\ln 2}{\lambda} \space \text{.}$$

⮕ Mini-drill: show that after $3$ half-lives, $N = N_0/8$.

Answer: $N = N_0\left(\tfrac12\right)^3 = N_0/8$

5 Conservation laws & the (anti)neutrino

Nuclear equations conserve nucleon number, charge and mass-energy. Example:

$$^{14}_7 \mathrm{N} + ^4_2 \mathrm{He} \rightarrow ^{17}_8 \mathrm{O} + ^1_1 \mathrm{H}$$

In $\beta^-$ decay, missing energy and momentum led Pauli to postulate an elusive neutral particle - the neutrino - restoring conservation.

6 Mass defect & $E = mc^2$

A nucleus weighs less than its separated nucleons; the deficit $\Delta m$ converts to binding energy

$$E_b = \Delta m c^2\space .$$

This is Einstein's mass-energy equivalence. For $^4 \text{He}$, $E_b \approx 28 \space \text{MeV}$.

7 Binding-energy curve: fusion vs fission

Plotting binding energy per nucleon against $A$ peaks near iron-56 ($\sim 8.8 \space \text{MeV}$).

• 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

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.

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

1. Draw a decay curve sketch before diving into algebra.
2. Label nuclei with $Z$ and $A$ first to avoid conservation slips.
3. Use $\ln$ key for half-life Qs: $\lambda = 0.693/t_{1/2}$

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 $^A_Z X$ 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 $A = \lambda N$

Concept map (in words)

Start with nuclear notation (A, Z). Link decay types (alpha, beta, gamma) with changes in A and Z. Use activity $A = \lambda N$ and $N = N_0 e^{-\lambda t}$ for quantitative predictions. Binding energy per nucleon explains energy release in fission and fusion. Conservation checks keep equations balanced.

Key relations

Derivations & reasoning to master

1. Exponential decay: derive activity dependence from differential equation $\frac{\mathrm{d}N}{\mathrm{d}t} = -\lambda N$.
2. Half-life relation: show $t_{1/2} = \ln 2 / \lambda$

Worked example 1 - decay counting

A sample contains $1.2 \times 10^{18}$ nuclei of an isotope with half-life $8.0$ days. Calculate (a) decay constant, (b) initial activity, (c) activity after 24 days.

Approach: $\lambda = \ln 2 / t_{1/2}$; $A_0 = \lambda N_0$

Convert $t_{1/2}=8.0$ days to seconds: $t_{1/2}=8.0\times 24\times 3600 = 6.91\times 10^{5}\,\pu{s}$

$$\lambda = \dfrac{\ln 2}{t_{1/2}} = \dfrac{0.693}{6.91\times 10^{5}} = 1.00\times 10^{-6}\,\pu{s-1}.$$

$$A_0 = \lambda N_0 = (1.00\times 10^{-6})(1.2\times 10^{18}) = 1.20\times 10^{12}\,\pu{Bq}.$$

After 24 days (3 half-lives), $A = A_0/8 = 1.50\times 10^{11}\,\pu{Bq}$.

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 $c^2$, 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 ($\pu{u}$ vs $\pu{kg}$) 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

1. Define activity. - Rate of decay of nuclei (decays per second).
2. How many half-lives reduce activity to $1/32$? - Five.
3. Why is fusion of light nuclei energetically favourable? - Binding energy per nucleon increases toward iron peak.
4. Name the particle emitted in beta-minus decay in addition to electron. - Antineutrino.
5. State one medical application of isotopes. - PET imaging with $\ce{^18F}$

Revision workflow

1. Re-derive decay and half-life relations without notes weekly.
2. Practise binding energy calculations with mass tables to stay fluent in unit conversions.
3. Work through two past-paper questions involving decay chains and shielding.
4. 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.

10 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• Rutherford scattering experiments
• NRC - Natural background radiation

11 Call-to-action

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.