A-Level Physics: Quantum Physics Guide
Download printable cheat-sheet (CC-BY 4.0)14 Jul 2025, 00:00 Z
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)
- List givens under every quantum problem before manipulating equations — avoids dropping \(h\) or \(c\).
- Box problems: write Eq.(2) once, then plug numbers; do not derive under exam pressure.
- Convert wavelengths to energy first; the rest is simple bookkeeping.
8 Further reading
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.
