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Q: What do these H2 Physics quantum notes cover? A: They cover photoelectric effect, de Broglie wavelength, wavefunctions, Heisenberg uncertainty, particle in a box, and spectra for A-Level 9478.
TL;DR These H2 Physics quantum notes cover the photoelectric effect, matter waves, uncertainty, box-model energy ladders, and line spectra. Master wave-particle duality, ψ-algebra, uncertainty maths, and spectra links to move faster in Paper 1 MCQ, Paper 2 explanations, and Modern Physics revision.
Revisit the Modern Physics sequence (photoelectric effect → quantum → nuclear) via the H2 Physics notes hub so each derivation here links straight to the nuclear/particle follow-ups.
1 Particle nature of light
1.1 Photoelectric effect
Threshold frequency: No electrons emerge when incident light has a frequency below a critical threshold f0; intensity alone cannot compensate. This contradicts classical wave theory and signals discrete packets of energy.
Photon energy: Each packet carries E=hf
. Memorise
h=6.63×10−34J⋅s
.
Photon momentum: Even though m=0, a photon steers a solar sail via
p=cE=λh.
Mini-drill
Calculate the momentum of a 500nm photon.
p=λh=5.00×10−76.63×10−34=1.33×10−27kg⋅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
λ=ph=mvh.(1)
Use Eq. (1) to explain why soccer balls never show diffraction - their λ is <10−34m.
3 Wavefunctions & probability
A particle's state is ψ(x,t); ∣ψ∣2 yields a probability density that integrates to 1 after normalisation.
Superposition lets us add legitimate ψ functions. 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 ψ=Asin(Lnπx) in [0,L]:
∫0L∣ψ∣2dx=A22L=1⇒A=L2.
4 Heisenberg uncertainty
Localising a particle into Δx demands a spread of momenta Δp. Their product obeys
ΔxΔp≳h.
Tight boxes (↓Δx) force high kinetic energy (↑Δp).
Exam cue: the SEAB syllabus uses the order-of-h form above; when you need the full textbook constant, swap in ΔxΔp≥4πh=2ℏ.
5 Particle in a box
Solving the 1-D Schrödinger equation with ψ(0)=ψ(L)=0 yields
En=8mL2h2n2(n=1,2,3,…).(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 π 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 656nm photon (Balmer H-α) is emitted. Find the energy gap. E=λhc=3.03×10−19J. Identify initial and final n via the Rydberg table.
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.
Comprehensive revision pack
9478 Section VI, Topic 19 Syllabus outcomes at a glance
Outcome (a) - describe the photoelectric effect and photon energy.
Outcome (b) - apply de Broglie relation to matter waves.
Outcome (c) - interpret wavefunctions, probability densities, and normalisation.
Outcome (d) - use uncertainty principle and particle-in-a-box energy levels.
Outcome (e) - explain discrete atomic spectra in terms of quantised energy levels.
Concept map (in words)
Photons deliver energy E=hf to liberate electrons above threshold frequency. Matter exhibits wave behaviour with λ=ph.
Wavefunctions ψ give probability distributions when ∣ψ∣2 is normalised.
Confining particles quantises energy via En=8mL2n2h2.
Spectral lines correspond to transitions obeying ΔE=hf=λhc.
Key relations
Concept
Expression / reminder
Photon energy
E=hf=λhc
Photoelectric equation
hf=ϕ+21mvmax2 (work function ϕ)
Stopping potential
eVs=21mvmax2
de Broglie wavelength
λ=ph=mvh
Uncertainty principle
ΔxΔp≥4πh (use ≳h for quick estimates)
Particle-in-box energies
En=8mL2n2h2
Transition energy
ΔE=hf=λhc
Derivations & reasoning to master
Photoelectric graph: derive the linear relation between stopping potential and frequency; the slope gives eh.
de Broglie: show consistency with diffraction experiments (Davisson-Germer) using λ=ph.
Particle-in-box normalisation: integrate ψ2 to unity to obtain amplitude A=L2
Spectral identification: use the Rydberg formula to map photon energies to transitions.
Worked example 1 - stopping potential
Ultraviolet light of frequency 8.0×1014Hz shines on a metal with work function 2.6eV. Determine maximum kinetic energy and stopping potential for emitted electrons.
Solution: Kmax=hf−ϕ. Convert to joules with 1eV=1.60×10−19J, then compute Vs=eKmax.
hf=(6.63×10−34)(8.0×1014)=5.30×10−19J.
ϕ=2.6eV=2.6(1.60×10−19)=4.16×10−19J.
Kmax=hf−ϕ=1.14×10−19J⇒Vs=eKmax≈0.71V.
Worked example 2 - particle in a box transition
An electron confined to a one-dimensional box of length 0.35nm makes a transition from n=3 to n=2. Calculate the photon wavelength emitted.
Method: Use En=8mL2n2h2, compute ΔE, convert to wavelength via λ=ΔEhc, and compare to the visible spectrum.
ΔE=(32−22)8mL2h2=58mL2h2.
With L=0.35nm=3.5×10−10m, h=6.63×10−34J⋅s, me=9.11×10−31kg:
ΔE≈2.46×10−18J,λ=ΔEhc≈8.1⋅10−8m≈81nm.
So the photon is in the ultraviolet (visible light is roughly 400–700 nm).
Practical & data tasks
Analyse photoelectric experiment data (Vs vs f) to extract Planck's constant.
Simulate particle-in-box wavefunctions with Desmos/Python; verify nodal structure for each n.
Examine hydrogen spectra using a school spectroscope; identify Balmer lines.
Common misconceptions & exam traps
Believing intensity affects photoelectron kinetic energy (it affects number only).
Forgetting to convert eV to J or vice versa.
Mixing de Broglie wavelength with photon wavelength when comparing massive vs massless particles.
Ignoring normalisation when interpreting probability densities.
Quick self-check quiz
What happens to photoelectron emission if light frequency drops below threshold? - No electrons emitted regardless of intensity.
State de Broglie's relation. - λ=ph.
Why can't an electron in a box have zero energy? - Boundary conditions enforce non-zero momentum, so E1>0.
How does confinement length affect energy spacing? - Shorter L increases spacing (proportional to L21).
What information does a line spectrum provide? - Discrete energy level differences of the atom or molecule via ΔE=hf.
Revision workflow
Re-derive the photoelectric equation and practise slope/intercept interpretation weekly.
Solve mixed problems on de Broglie wavelengths for electrons, neutrons, and atoms.
Build flashcards linking spectral series (Lyman, Balmer, Paschen) with wavelength ranges.
Attempt uncertainty principle estimation questions to build physical intuition.
Parents: Book a 60-min Quantum Starter session before Prelim physics practicals.
Students: Practise threshold-frequency questions with three metals tonight; they are Paper 1 free marks hiding in plain sight.
