Wave and photon models of lightEdexcel International A Level Physics: Revision notes

In the wave model, electromagnetic radiation is a transverse wave of oscillating electric and magnetic fields. It explains diffraction, interference (such as Young's double-slit fringes) and polarisation. All electromagnetic waves travel at $c = 3.00 \times 10^8$ m s⁻¹ in a vacuum and obey $c = f\lambda$.

In a double-slit experiment, bright fringes appear where waves from the two slits arrive in phase, and dark fringes where they arrive out of phase. A stream of particles could not cancel, so only a wave model explains the dark fringes.

In the photon model, electromagnetic radiation is emitted and absorbed in discrete packets of energy called photons. The energy of one photon depends on frequency:

$E = hf = \frac{hc}{\lambda}$

where $h = 6.63 \times 10^{-34}$ J s is the Planck constant.

• Higher frequency (shorter wavelength) means more energy per photon.
• A brighter beam of the same frequency has more photons per second, not more energy per photon.
• For a given power P, the number of photons per second is $P/E$.

• 17th century: Newton's particle (corpuscular) model explained reflection and refraction.
• Huygens proposed a wave model. Young (1801) showed double-slit fringes, so waves were accepted.
• Maxwell (1860s) showed light is an electromagnetic wave.
• Planck (1900) introduced quanta of energy. Einstein (1905) explained the photoelectric effect by proposing light is absorbed as photons of energy hf.

Today both models are used, as each explains different observations.

Photon energy. Red light of wavelength 650 nm: f = c/λ = 3.00 × 10⁸ / 650 × 10⁻⁹ = 4.6 × 10¹⁴ Hz, so E = hf = 6.63 × 10⁻³⁴ × 4.6 × 10¹⁴ = 3.1 × 10⁻¹⁹ J.

Photons per second. A 20 W lamp emits light with photons of energy 3.4 × 10⁻¹⁹ J: number per second = 20 / 3.4 × 10⁻¹⁹ = 5.9 × 10¹⁹ s⁻¹. The huge number is why light looks continuous.

• Wave model: how radiation travels, diffracts and interferes.
• Photon model: how radiation is emitted and absorbed, and how it interacts with matter (for example the photoelectric effect).
• Low-frequency radiation such as radio waves has tiny photon energies, so very many photons act together and the wave model is enough. High-frequency radiation such as X-rays has large photon energies, so individual photons matter.