What is the wave-particle duality of light?

Definition

Wave-particle duality is a fundamental concept in quantum physics stating that light (and all quantum particles) exhibits both wave-like and particle-like properties. This means that, depending on the experiment, light can behave as a continuous electromagnetic wave or as discrete packets of energy called photons.

Explanation

• Wave behavior: Light shows interference and diffraction, phenomena explained by treating light as a wave.
• Particle behavior: Light also transfers energy in quantized amounts (photons), as seen in the photoelectric effect.

Worked Example: The Photoelectric Effect

Problem:
When light of frequency $f$ shines on a metal surface, electrons are emitted only if $f$ is above a certain threshold. Why does this happen, and how is it explained by wave-particle duality?

Step 1: Classical Wave Prediction
Classical theory predicts that increasing light intensity (wave amplitude) should always eject electrons, regardless of frequency.

Step 2: Experimental Observation
Electrons are only emitted if the light frequency $f$ exceeds a threshold $f_0$, regardless of intensity.

Step 3: Quantum Explanation (Particle Nature)
Einstein proposed that light consists of photons, each with energy

$$ E = h f $$

where $h$ is Planck's constant.

• If $E \geq \phi$ (work function of the metal), electrons are emitted.
• If $E < \phi$, no electrons are emitted.

Step 4: Energy of Emitted Electrons

$$ K_{\text{max}} = h f - \phi $$

where $K_{\text{max}}$ is the maximum kinetic energy of emitted electrons.

Takeaways

• Light exhibits both wave-like (interference, diffraction) and particle-like (photoelectric effect) properties.
• The wave-particle duality is essential for understanding quantum phenomena.
• Experiments like the photoelectric effect directly demonstrate the particle aspect of light.