Quantum Physics: Photoelectric Effect and Wave-Particle Duality

Light as photons

Light (and all EM radiation) can behave as a stream of energy packets called photons. The energy of one photon depends on the frequency:

E = hf = hc ÷ λ

where h = Planck constant (6.63 × 10⁻³⁴ J s), f = frequency, c = speed of light. Higher frequency → higher energy photons.

The photoelectric effect

When light of a high enough frequency hits a metal surface, electrons (photoelectrons) are emitted. Key observations that cannot be explained by the wave model but are explained by photons:

• Emission is instant above a certain frequency.
• There is a threshold frequency (f₀) below which no electrons are emitted, however intense the light.
• Above f₀, increasing intensity increases the number of electrons, not their energy; increasing frequency increases their maximum kinetic energy.

Explanation: one photon interacts with one electron. The photon's energy must first overcome the work function (φ) — the minimum energy to release an electron — and any surplus becomes the electron's kinetic energy:

hf = φ + Ek(max)

This is Einstein's photoelectric equation. Below the threshold (hf < φ), no electron escapes.

Wave–particle duality

Light shows both wave behaviour (diffraction, interference) and particle behaviour (photoelectric effect). Conversely, particles show wave behaviour: electrons can be diffracted (electron diffraction). The de Broglie wavelength of a particle is:

λ = h ÷ p = h ÷ mv

Faster/heavier particles have shorter wavelengths — why wave effects are only noticeable for tiny particles.

Energy levels and line spectra

Electrons in atoms occupy discrete energy levels. When an electron falls to a lower level, it emits a photon of energy exactly equal to the difference between levels (E = hf). This produces line spectra — discrete lines that are evidence of quantised energy levels. The electronvolt (eV = 1.6 × 10⁻¹⁹ J) is a convenient energy unit here.

Worked example

A metal has a work function of 3.0 × 10⁻¹⁹ J. Light of frequency 6.0 × 10¹⁴ Hz shines on it. Find the maximum kinetic energy of emitted electrons.

• hf = 6.63×10⁻³⁴ × 6.0×10¹⁴ = 3.98×10⁻¹⁹ J.
• Ek = hf − φ = 3.98×10⁻¹⁹ − 3.0×10⁻¹⁹ = 9.8 × 10⁻²⁰ J. ✓

Common mistakes

• Saying more intense light gives electrons more energy — intensity affects number, frequency affects energy.
• Forgetting the threshold frequency — below it, no emission at any intensity.
• Muddling the photoelectric equation (hf = φ + Ek).

Exam tips

• Use E = hf and the photoelectric equation hf = φ + Ek(max).
• Explain why the photoelectric effect supports the photon (particle) model.
• Use λ = h/mv for de Broglie and link line spectra to quantised energy levels.

Key facts to remember

• Photon energy E = hf = hc/λ; the photoelectric effect (threshold frequency, instant emission, KE depends on frequency not intensity) shows light is particle-like.
• hf = φ + Ek(max) (work function φ); wave–particle duality: particles diffract, λ = h/mv (de Broglie).
• Discrete energy levels produce line spectra (E = hf between levels).