Published by Patrick Mutisya · 14 days ago
Wave‑particle duality is a cornerstone of modern physics. It states that every particle or quantum entity exhibits both wave‑like and particle‑like properties. The concept was introduced to reconcile the results of experiments such as the photoelectric effect (which supports particle behaviour) and electron diffraction (which supports wave behaviour).
De Broglie postulated that any moving particle of momentum \$p\$ is associated with a wave of wavelength \$λ\$ given by
\$\lambda = \frac{h}{p}\$
where \$h = 6.626\times10^{-34}\ \text{J·s}\$ is Planck’s constant. For a particle of mass \$m\$ moving with speed \$v\$ (non‑relativistic), the momentum is \$p = mv\$, so the de Broglie wavelength can be written as
\$\lambda = \frac{h}{mv}\$
| Particle | Speed / Energy | De Broglie Wavelength \$λ\$ | Typical Observation |
|---|---|---|---|
| Electron | Thermal (\$\sim10^5\ \text{m s}^{-1}\$) | \$\sim10^{-10}\ \text{m}\$ (0.1 nm) | Electron diffraction in crystals |
| Neutron | Cold neutrons (\$\sim10^3\ \text{m s}^{-1}\$) | \$\sim10^{-10}\ \text{m}\$ (0.1 nm) | Neutron scattering experiments |
| Macroscopic object (e.g., baseball, \$m=0.145\ \text{kg}\$) | Typical throw speed (\$\sim30\ \text{m s}^{-1}\$) | \$\sim10^{-34}\ \text{m}\$ | Wave effects are unobservable |
Understanding the de Broglie wavelength allows students to:
The most direct evidence for the de Broglie wavelength comes from diffraction experiments where particles are scattered by a crystal lattice or a narrow slit. The observed interference pattern matches the prediction from the wavelength \$λ = h/p\$.
De Broglie’s hypothesis unifies the wave and particle descriptions of matter. The wavelength associated with a moving particle is inversely proportional to its momentum. This relationship explains why wave phenomena are observable for sub‑atomic particles but not for everyday macroscopic objects, and it underpins many modern technologies such as electron microscopy and neutron scattering.