IB Physics HL Topic 5 — Quantum Physics Paper 1 & 2 wave + particle ~15 min read

Wave-Particle Duality

We’ve reached one of the strangest truths in all of physics. Light diffracts and interferes like a wave — but the photoelectric effect proves it also arrives as particles. Electrons are obviously particles — but they diffract through crystals like waves. So which is it? The honest answer: both. Everything in the quantum world carries a wave nature and a particle nature at the same time, and simply reveals whichever one your experiment is set up to detect. This idea is called wave-particle duality, and it took physics 300 years to accept.

📘 What you need to know

Wave-particle duality: light and matter each behave as both a wave and a particle
You only ever see one nature at a time — whichever the experiment probes
Light behaves as a particle in the photoelectric effect (and Compton scattering)
Light behaves as a wave in diffraction and interference (Young’s double-slit)
Matter (e.g. electrons) behaves as a particle in collisions, and as a wave in electron diffraction
The two natures are bridged by two equations: E = hf and λ = h/p
Both equations contain a wave quantity (f or λ) and a particle quantity (E or p), tied together by h
The idea developed over centuries and was only settled in the early 20th century

Two faces of the same coin

Wave-particle duality doesn’t mean something is sometimes a wave and sometimes a particle, flipping back and forth. It means it is always both — but any single experiment can only bring out one of those faces. Ask a “wave question” (shine it through slits) and you get wave behaviour. Ask a “particle question” (bounce it off an electron) and you get particle behaviour.

Light and matter each carry both natures. The experiment you choose decides which one shows up — a “wave question” reveals the wave, a “particle question” reveals the particle.

The evidence, side by side

Here’s the whole story in one table. Notice the beautiful symmetry: light and matter have swapped what used to be their “obvious” nature.

	Behaves as a WAVE	Behaves as a PARTICLE
Light	Diffraction & interference (Young’s double-slit)	Photoelectric effect; Compton scattering
Matter (electrons)	Electron diffraction through graphite	Collisions; deflection in fields

The classic wave proof for light is Young’s double slit: two overlapping light beams produce bright-and-dark interference fringes, which only waves can do. The classic particle proof is the photoelectric effect, where one photon knocks out one electron. Same light — two totally different behaviours, depending on what you ask of it. Learn one wave example and one particle example for both light and matter, and you’re covered for the exam.

Two overlapping light beams from the slits create interference fringes on the screen — bright where waves add, dark where they cancel. Particles can’t do this, so it proves light’s wave nature.

The two bridging equations

What makes duality more than a vague idea is that it’s held together by real equations. Each one links a wave property to a particle property through Planck’s constant h — that’s duality made mathematical.

The two faces, connected by h E = hf and λ = h/p particle words: E, p • wave words: f, λ • bridge: h

Particle side
E, p

joined by h
through E=hf, λ=h/p

Wave side
f, λ

WE 1

Explain how the behaviour of light in (a) Young’s double-slit experiment and (b) the photoelectric effect together demonstrate wave-particle duality.

(a) double-slit → wave nature Light through two slits makes interference fringes — bright and dark bands. only waves can interfere, so this shows light’s WAVE nature (b) photoelectric effect → particle nature Light frees electrons only above a threshold frequency, one photon per electron. energy arrives in packets, so this shows light’s PARTICLE nature The same light shows both: a WAVE in one experiment, a PARTICLE in the other. Neither picture alone is complete — that’s exactly what wave-particle duality means. Always name the experiment AND the nature it reveals.

WE 2

Light of wavelength 500 nm can be described as either a wave or a stream of photons. Calculate (a) the energy of one photon (its particle property) and (b) confirm the wavelength links to a photon momentum via p = h/λ. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹)

(a) particle property: photon energy E = hc/λ = (6.63 × 10⁻³⁴)(3.00 × 10⁴) / (500 × 10⁻⁹) E = 4.0 × 10⁻¹⁹ J = 2.5 eV (b) same light, momentum via p = h/λ p = (6.63 × 10⁻³⁴) / (500 × 10⁻⁹) p = 1.3 × 10⁻²⁷ kg m s⁻¹ The very same beam has a wave property (λ = 500 nm) AND particle properties (E and p). One description, two natures — the equations E = hf and p = h/λ are how we move between them.

A 300-year argument

Duality wasn’t accepted overnight — it was the resolution of centuries of debate about what light really is. Each generation added evidence, until neither the “wave camp” nor the “particle camp” could claim victory, and physics realised both were right.

Milestone	Who & what	Nature supported
1670s	Newton: light is a stream of tiny corpuscles	Particle
1690s	Huygens: light is a wave	Wave
1800s	Young: double-slit interference fringes	Wave
1900s	Planck & Einstein: quantised energy, the photon	Particle
1924	de Broglie: matter waves — particles are waves too	Both (duality)

Don’t memorise every date — but do remember the shape of the story: particle (Newton) → wave (Huygens, Young) → particle again (Planck, Einstein) → and finally de Broglie’s leap that unified them. The lesson examiners want is that no single model won; nature needed both, and that’s the birth of quantum physics.

⚛ Answering a duality question

Name a wave experiment: diffraction / interference (double-slit for light, electron diffraction for matter).
Name a particle experiment: photoelectric effect / Compton (light), collisions (matter).
State what each reveals: fringes → wave; one-photon-one-electron → particle.
Conclude: the same thing shows both natures — that is duality.
Calculation? Use E = hf for the particle side, λ = h/p for the wave side.

💡 Top tips

Duality = both natures at once; the experiment decides which one you see.
Have one wave and one particle example ready for both light and matter.
Light: wave → double-slit; particle → photoelectric effect.
Matter: wave → electron diffraction; particle → collisions.
The two bridging equations are E = hf and λ = h/p.

⚠ Common mistakes

Saying something is “a wave or a particle” — it’s both, always
Thinking it physically switches nature — the experiment just reveals one
Giving only light examples and forgetting matter shows duality too
Naming an experiment but not stating which nature it demonstrates
Confusing interference (wave) with the photoelectric effect (particle)
Forgetting that h is the constant linking the wave and particle equations

Quick recap: Wave-particle duality says light and matter each behave as both a wave and a particle, and any one experiment reveals only one nature. Light is a wave in diffraction/interference (double-slit) and a particle in the photoelectric effect; matter is a particle in collisions and a wave in electron diffraction. The two natures are tied together by E = hf and λ = h/p, each linking a wave quantity to a particle quantity through Planck’s constant. The idea took 300 years and was settled by de Broglie in the 1920s.

We’ve seen light act as a particle in the photoelectric effect — but there’s a second, even more dramatic demonstration. Fire a high-energy X-ray photon at an electron and it bounces off like a billiard ball, handing over energy and momentum exactly as a particle should. The photon even comes away with a longer wavelength. That collision is Compton scattering, and it’s the final piece of this chapter. Next page: Compton Scattering.