A-Level Physics — 20) Nuclear Physics (IP-Friendly Guide)

Download printable cheat-sheet (CC-BY 4.0)

14 Jul 2025, 00:00 Z

TL;DR
The nucleus is tiny yet mighty: its femtometre scale explains why most alpha particles sail straight through foil \((>99.9\% \space \text{path})\) 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 \(10^{-14} \space \text{m}\) across — about \(1 \space \text{fm}\) — because only a few \(\alpha\) 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 \({Z}^{A} \mathrm{X}\). Example: \({6}^{14} \mathrm{C}\) 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 \(\alpha\), \(\beta\), \(\gamma\) 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 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, \(N = N_0/8\).

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 (\(~8.8 \space \text{MeV}\)).

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: \(\lambda = 0.693/t_{1/2}\).

10 Further reading

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.