De Broglie Wavelength Calculator
The matter wavelength of a particle from its mass and speed, in metres, nanometres and picometres.
Results
What this tool does
In 1924 Louis de Broglie proposed in his doctoral thesis that if light could behave as particles, particles ought to behave as waves, with a wavelength equal to Planck's constant divided by momentum. It sounded outlandish until electrons were diffracted off a nickel crystal three years later. The idea underpins electron microscopy and neutron diffraction, and it is the reason a heavier or faster particle probes finer detail.
Formula
lambda = h / (m v)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
mm | Mass | kg |
vv | Speed | m/s |
LM | Wavelength | m |
LN | Wavelength | nm |
LP | Wavelength | pm |
EV | Kinetic energy | eV |
Worked example
- Mass9.10938e-31 kg
- Speed1,000,000 m/s
- Wavelength7.2739e-10 m
- Wavelength0.72738951 nm
- Wavelength727.38951 pm
- Kinetic energy2.842815 eV
Limitations
- Mixing units is the most common source of error. Convert every input to the units shown next to each field before calculating.
Frequently asked questions
Why don't we see the wave nature of everyday objects?
Because Planck's constant is unimaginably small. A cricket ball at 40 m/s has a wavelength of around 10^-34 metres — twenty orders of magnitude smaller than a proton, so there is no slit in the universe narrow enough to diffract it. An electron, being a billion billion billion times lighter, comes out at a fraction of a nanometre, which is why electron microscopes work at all.