de Broglie Wavelength Calculator
Matter wavelength for an electron, proton or anything else.
Work out de Broglie Wavelength. Matter wavelength for an electron, proton or anything else. Written for the problem set you are stuck on.
Scientific notation works — 1e6 is a million metres per second.
de Broglie wavelength
0.72739 nm
comparable to atomic spacing — wave behaviour is observable
Everything has a de Broglie wavelength; almost nothing has one you could ever detect. The threshold is whether it is comparable to the object you are trying to diffract it through. An electron at a million metres per second comes out near 0.7 nm — the spacing of atoms in a crystal — which is exactly why electron diffraction works and why electron microscopes resolve far finer detail than light ones. A thrown ball lands around 10⁻³⁴ m, smaller than any aperture that exists, so it behaves classically. This is the non-relativistic form; above roughly a tenth of light speed the momentum needs the relativistic correction.
How the de Broglie Wavelength Calculator works
Every moving object has a wavelength; almost nothing has one large enough to notice. This calculates λ = h/mv for electrons, protons, neutrons or any mass you enter, and says whether the result is big enough to produce observable diffraction.
Also known as: matter wave calculator · electron wavelength calculator · lambda = h/mv calculator · wave particle duality calculator
Frequently asked questions
What is the de Broglie wavelength?
λ = h/mv — Planck's constant divided by momentum. It is the wavelength associated with any moving particle, and it is what makes electron diffraction and electron microscopy possible.
Why do we not see wave behaviour in everyday objects?
Because the wavelength is absurdly small. A 145 g baseball at 40 m/s has a wavelength around 10⁻³⁴ m — twenty orders of magnitude smaller than a proton. There is no aperture in the universe narrow enough to diffract it.
Why can electron microscopes see more detail than light microscopes?
Resolution is limited by wavelength. Visible light bottoms out near 400 nm, while an accelerated electron has a wavelength of well under a nanometre — hundreds of times finer, which is the whole basis of electron microscopy.
Does this work at relativistic speeds?
Not as written. Above roughly a tenth of the speed of light the momentum needs the relativistic correction, and this non-relativistic form starts to overestimate the wavelength.
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