A-Level Physics — 19) Quantum Physics (IP-Friendly Guide)

TL;DR
Quantum is not woo; it is the rule-book that caps every WA mark from optics to semiconductors. Master wave-particle duality, ψ-algebra, uncertainty maths and box-model energy ladders to fast-track Paper 1 MCQ, Paper 2 data handling and Paper 4 practicals.

1 Particle Nature of light

1.1 Photoelectric Effect

• Threshold frequency: No electrons emerge when incident light has a frequency below a critical threshold \(f_0\); intensity alone cannot compensate. This contradicts classical wave theory and signals discrete packets of energy.
• Photon energy: Each packet carries \(E=hf\). Memorise \(h = 6.63 \times 10^{-34}\space \pu{J.s}\).
• Photon momentum: Even though \(m=0\), a photon steers a solar sail via

\[ p = \frac{E}{c} = \frac{h}{\lambda} \]

Mini-drill

Calculate the momentum of a \(500\space\pu{nm}\) photon.

\[ p = \frac{h}{\lambda} = \frac{6.63 \times 10^{-34}}{5.00 \times 10^{-7}} = 1.33 \times 10^{-27} \space \pu{kg.m.s-1}. \]

2 Wave Nature of Matter

2.1 Electron diffraction

• The Davisson-Germer nickel crystal experiment produced concentric rings identical to X-ray patterns, confirming electron wavelengths.

2.2 Firing single particles at a double-slit

• Fire electrons one by one: the screen still builds an interference fringe, proving every particle 's wavefunction passes through both slits until detected.

2.3 de Broglie Formula

\[ \lambda = \frac{h}{p} = \frac{h}{mv}. \tag{1} \]

Use Eq.(1) to explain why soccer balls never show diffraction — their \(\lambda\) is \(\lt 10^{-34} \space \pu{m}\).

3 Wavefunctions & probability

• A particle 's state is \(\psi(x,t)\); \(|\psi|^2\) yields a probability density that integrates to 1 after normalisation.
• Superposition lets us add legitimate \(\psi\)s. Sum two slits and you recover the interference pattern in §2.2, or clamp endpoints to get standing waves in a box.

Quick normalisation hack
For \(\psi = A \sin \bigl( \tfrac{n \pi x}{L} \bigr) \) in \([0,L]\):

\[ \int_0^L |\psi|^2 dx = A^2 \frac{L}{2} = 1 \space \Rightarrow \space A= \sqrt{\tfrac{2}{L}}. \]

4 Heisenberg uncertainty

Localising a particle into \(\Delta x\) demands a spread of momenta \(\Delta p\). Their product obeys

\[ \Delta x \space \Delta p \gtrsim h. \]

Tight boxes (\downarrow \Delta x\) force high kinetic energy (\uparrow \Delta p\).

Exam cue: convert \(\gtrsim\) to \(\ge\) when using \(\tfrac{h}{4\pi}\) instead of \(h\).

5 Particle in a box

Solving the 1-D Schrödinger equation with \(\psi(0)=\psi(L)=0\) yields

\[ E_n = \frac{h^2}{8mL^2} n^2 \quad (n=1,2,3\dots). \tag{2} \]

• Zero-point energy: even at \(n=1\), the electron cannot be at rest.
• Energy gaps widen with smaller \(L\) — reason organic dyes with shorter conjugation lengths absorb bluer light (box model for \(\pi\) electrons).

6 Quantised atoms & spectra

• Electrons in hydrogen occupy discrete orbits. Transitions release/absorb photons that match energy differences, giving line spectra.
• Emission lines appear when excited electrons drop to lower levels; absorption lines appear when ground-state electrons jump up, leaving dark gaps in a continuous spectrum. James Webb 's spectrographs use the same principle to fingerprint exoplanet atmospheres.

Problem type

A \(656 \space \pu{nm}\) photon (Balmer H-\(\alpha\)) is emitted. Find the energy gap.
\(E = \tfrac{hc}{\lambda} = 3.03x10^{-19} \space \pu{J}\). Identify initial and final \(n\) via Rydberg table and award 2 marks.

7 WA timing rules (modern-paper edition)

1. List givens under every quantum problem before manipulating equations — avoids dropping \(h\) or \(c\).
2. Box problems: write Eq.(2) once, then plug numbers; do not derive under exam pressure.
3. Convert wavelengths to energy first; the rest is simple bookkeeping.

8 Further reading

• SEAB H2 Physics 9478 syllabus (2026)
• ChemLibreTexts — Photoelectric Effect
• HyperPhysics — Photoelectric Effect
• Lumen Learning — Photon Momentum
• HyperPhysics — Davisson-Germer
• Wikipedia — Double-slit Experiment
• ChemLibreTexts — de Broglie Wavelength
• PhysLibreTexts — Heisenberg Uncertainty
• ChemLibreTexts — Particle in a 1-D Box
• Hydrogen Spectral Series
• Webb Telescope — Spectroscopy 101

Parents: Book a 60-min Quantum Starter session before Prelim physics practicals.
Students: Practise threshold-frequency Qs with three metals tonight; they are Paper 1 free marks hiding in plain sight.

Last updated 14 Jul 2025. Review after SEAB 's 2027 draft release.