2.2.4 Wave-particle duality

Wave-Particle Duality of Light and Matter

Wave-particle duality describes the concept that light and particles can exhibit both wave and particle properties.

• Wave-Particle Duality of Electrons:
  • Electron Diffraction: Electrons, which are generally considered particles, also exhibit wave properties. When a beam of electrons passes through a crystal lattice or diffraction grating, it creates a diffraction pattern of concentric rings, which only waves can produce. This duality suggests that particles like electrons have wave-like characteristics, as shown through experiments involving electron diffraction.

De Broglie's Hypothesis

Louis de Broglie proposed that if light (typically a wave) exhibits particle properties, then particles should also exhibit wave-like properties. He derived an equation to calculate the wavelength $\lambda$ of a particle based on its momentum $p = mv$:

$$\lambda = \frac{h}{mv}$$

where:

• $h$ is Planck's constant $(6.63 \times 10^{-34} \, \text{Js})$,
• $m$ is the mass of the particle,
• $v$ is the velocity of the particle.

Explanation of De Broglie's Equation:

• Higher Momentum (e.g., faster particles) results in a shorter wavelength, leading to less diffraction. The diffraction pattern rings become closer together.
• Lower Momentum (e.g., slower particles) results in a longer wavelength, causing more diffraction and a spread-out pattern with rings further apart. This equation connects particle motion with wave-like properties and supports the idea that particles like electrons can behave as waves under certain conditions.

Acceptance of Wave-Particle Duality

Initially, the scientific community was sceptical of the concept that particles exhibit wave properties. However, as experimental evidence accumulated, including electron diffraction and the photoelectric effect, wave-particle duality became widely accepted.

The scientific process relies on gathering experimental evidence, which must be published and peer-reviewed to be validated. This peer review ensures that findings are rigorously tested and accepted by the scientific community, contributing to the evolving understanding of concepts like wave-particle duality.