These H2 Physics quantum notes cover the photoelectric effect, matter waves, uncertainty, box-model energy ladders, and line spectra.
Key points
Master wave-particle duality, \\( \psi \\)-algebra, uncertainty maths, and spectra links to move faster in Paper 1 MCQ, Paper 2 explanations, and Modern Physics revision.
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1 Particle nature of light
2 Wave nature of matter
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.
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Light and matter both show wave-particle behaviour
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Photoelectric effect, de Broglie wavelength, and spectra
100 seconds
The first photon energy and momentum setup
10 minutes
Uncertainty, box models, and line spectra
Concrete example: how to use this page
If a photoelectric question changes intensity, think number of photons. If it changes frequency, think photon energy. Keeping those two levers separate makes the explanation much shorter.
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. For the full topic map and paper weightings, see our
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.
Need structured practice on Quantum 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 19 Syllabus outcomes
Candidates should be able to:
(a) show an understanding that the existence of a threshold frequency in the photoelectric effect provides evidence that supports the particulate nature of electromagnetic radiation while phenomena such as interference and diffraction provide evidence that supports its wave nature.
(b) state that a photon is a quantum of electromagnetic radiation, and recall and use the equation E=hf for the energy of a photon to solve problems, where h is the Planck constant.
(c) show an understanding that while a photon is massless, it has a momentum given by p=cE and p=λh, where c is the speed of light in free space.
(d) show an understanding that electron diffraction and double-slit interference of single particles provide evidence that supports the wave nature of particles.
(e) recall and use the equation λ=ph for the de Broglie wavelength to solve problems.
(f) show an understanding that the state of a particle can be represented as a wavefunction ψ, e.g. for an electron cloud in an atom, and that the square of the wavefunction amplitude ∣ψ∣2 is the probability density function (including calculation of normalisation factors for square and sinusoidal wavefunctions).
(g) show an understanding that the principle of superposition applies to the wavefunctions describing a particle's position, leading to standing wave solutions for a particle in a box and phenomena such as single-particle interference in double-slit experiments.
(h) show an understanding that the Heisenberg position-momentum uncertainty principle ΔxΔp≳h relates to the necessity of a spread of momenta for localised particles, and apply this to solve problems.
(i) show an understanding of standing wave solutions ψn for the wavefunction of a particle in a one-dimensional infinite square well potential.
(j) solve problems using En=8mL2h2n2
(k) show an understanding of the existence of discrete electronic energy levels for the electron's wavefunction in isolated atoms (e.g. atomic hydrogen) and deduce how this leads to the observation of spectral lines.
(l) distinguish between emission and absorption line spectra.
(m) solve problems involving photon absorption or emission during atomic energy level transitions.
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.
