De Broglie Wavelength Calculator

Yes, but it is immeasurably small. A 1 kg ball at 1 m/s has λ ≈ 6.6 × 10⁻³⁴ m—about 10¹⁹ times smaller than a proton. Quantum wave effects are completely undetectable at macroscopic scales.

In 1927, Davisson and Germer observed electron diffraction from a nickel crystal, and independently G.P. Thomson showed electron diffraction through thin metal foils. The measured diffraction patterns matched predictions from de Broglie's wavelength formula.

Since p = √(2mKE), the wavelength is λ = h/√(2mKE). Wavelength decreases with increasing kinetic energy—faster particles have shorter wavelengths and can probe finer structures.

Electron microscopes accelerate electrons to high energies, giving them very short de Broglie wavelengths (0.001–0.1 nm). This allows resolution far beyond the ~200 nm limit of optical microscopes, enabling visualization of individual atoms.

Thermal neutrons at room temperature (~0.025 eV) have λ ≈ 0.18 nm, comparable to atomic spacings. This makes neutron diffraction ideal for studying crystal structures, especially for locating light atoms like hydrogen.

Photons have zero rest mass, so the formula λ = h/(mv) doesn't directly apply. Instead, use the photon momentum relation p = h/λ = E/c. The de Broglie relation λ = h/p remains valid with relativistic momentum.

When particle velocity exceeds about 10% of c (3 × 10⁷ m/s), use relativistic momentum: p = γmv where γ = 1/√(1−v²/c²). For electrons above ~10 keV, relativistic effects become significant.

It is λ_th = h/√(2πmkT), representing the average wavelength of particles at temperature T. When λ_th approaches the interparticle spacing, quantum statistics (Bose-Einstein or Fermi-Dirac) become important.

A well-defined wavelength implies well-defined momentum (p = h/λ) but complete uncertainty in position (the wave extends everywhere). The uncertainty principle Δx·Δp ≥ ħ/2 quantifies this tradeoff between position and momentum knowledge.