Science calculator

de Broglie wavelength.

Find a particle's matter wavelength, mass or speed using its non-relativistic momentum. Enter two values and leave one blank.

Wavelength λSolved
matter wave
Momentum p = mv
λ=hp=hmv

Assumptions

  • A free, massive particle whose momentum is well approximated by p = mv.
  • The speed is much less than the speed of light; use relativistic momentum at high speed.
  • Mass and speed are positive magnitudes, so this tool reports wavelength magnitude.
  • Planck's constant is the exact SI value 6.62607015 × 10⁻³⁴ J·s.

How it works

Quantum mechanics associates a wavelength with every particle momentum. A larger momentum produces a shorter matter wavelength.

For a slow massive particle, momentum is mass multiplied by speed. Substituting p = mv into λ = h/p gives the relationship used here.

Leave one field blank to rearrange the equation. Electron-scale inputs often produce nanometre or sub-nanometre wavelengths, so scientific notation is accepted.