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
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matter wave
- Momentum p = mv
- —
- λ de Broglie wavelength · h Planck constant · p momentum · m rest mass · v speed
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.
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