de Broglie formulaequation
Everything around us — not just light, but also matter particles, such as electrons — behaves like waves! Every moving particle has its own wavelength, calculated using the de Broglie formula. For large objects, this wavelength is vanishingly small, so we don't see a ball bending around corners. But for tiny particles, it is large enough to exhibit wave properties.
How it works
Electron microscopes use beams of electrons with a very short de Broglie wavelength, allowing them to see details thousands of times smaller than in an optical microscope. Neutron diffraction helps study crystal structures. Even atomic orbitals in quantum chemistry are standing matter waves around the nucleus!
💡 If you throw a baseball, its de Broglie wavelength would be billions of times smaller than an atomic nucleus — no diffraction would be noticeable. But for a slowly moving electron, it can be the size of a molecule!
\lambda = \frac{h}{p}
λ — de Broglie wavelength (m); h — Planck's constant (h = 6.62607015×10⁻³⁴ J·s); p — particle momentum (kg·m/s)
\lambda = \frac{h}{mv}
λ — de Broglie wavelength (m); h — Planck's constant (6.62607015×10⁻³⁴ J·s); m — particle mass (kg); v — particle speed (m/s), p = mv