de Broglie Wavelength Calculator
Find the matter wavelength of a particle from its mass and speed using lambda = h divided by momentum.
⚛️ What is the de Broglie Wavelength Calculator?
The de Broglie wavelength calculator finds the wavelength of the matter wave associated with a moving particle. In 1924 Louis de Broglie proposed that every particle, not just light, has a wavelength set by its momentum, given by lambda = h divided by m times v. This calculator applies that relation to any particle you specify.
Students and physicists use it to see why the quantum world behaves as it does. The electron's wavelength, close to the spacing between atoms in a crystal, explains electron diffraction and the resolving power of electron microscopes. Working out that a neutron at reactor speeds has a wavelength near atomic dimensions shows why neutron scattering probes material structure. Comparing an electron's wavelength with a baseball's, which is smaller than a nucleus, shows exactly why wave behaviour is invisible in everyday life.
The essential idea is the inverse relationship with momentum. A larger momentum, from more mass or more speed, means a shorter wavelength. Because Planck's constant is so tiny (6.626 x 10^-34 joule-seconds), only very light and fast particles end up with wavelengths large enough to matter. A frequent confusion is mixing up this matter wavelength with a photon's wavelength: photons have no mass and use energy rather than m times v, so the formula is different even though both involve Planck's constant.
This tool is useful because it handles the awkward scientific notation and unit conversions for you. Pick a particle or enter a mass, give the speed, and read the wavelength in metres, nanometres, and picometres along with the momentum, with the working shown so the calculation is transparent.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Electron at a million metres per second
Example 2 - Proton at 500 km per second
Example 3 - Baseball (why big objects have no waves)
❓ Frequently Asked Questions
🔗 Related Calculators
What is the de Broglie wavelength?
It is the wavelength associated with a moving particle, given by lambda = h / (m v), where h is Planck's constant, m is mass, and v is speed. Louis de Broglie proposed that all matter has wave properties. For an electron moving at a million metres per second, the wavelength is about 0.73 nanometres.
How do you calculate the de Broglie wavelength?
Multiply the particle's mass by its speed to get the momentum, then divide Planck's constant (6.626 x 10^-34 J.s) by that momentum. For an electron (9.109 x 10^-31 kg) at 1 x 10^6 m/s, momentum is 9.109 x 10^-25 kg.m/s, so lambda = 6.626 x 10^-34 / 9.109 x 10^-25 = 7.27 x 10^-10 m.
Why don't everyday objects show wave behaviour?
Because their de Broglie wavelength is unimaginably small. A 0.145 kg baseball at 40 m/s has a wavelength of about 1 x 10^-34 metres, far smaller than an atomic nucleus, so no experiment can detect its wave nature. Only very light, fast particles like electrons have measurable wavelengths.
What is the de Broglie wavelength of an electron?
It depends on the electron's speed. At 1 x 10^6 m/s the wavelength is about 0.73 nanometres, and at higher speeds it is shorter. This wavelength is close to atomic spacings, which is why electron beams diffract from crystals and why electron microscopes can resolve atomic detail.
How does momentum affect the de Broglie wavelength?
The wavelength is inversely proportional to momentum: lambda = h / p. Doubling the momentum, by doubling either the mass or the speed, halves the wavelength. This is why heavy or fast particles have very short matter wavelengths and light, slow ones have longer wavelengths.
Can I calculate the de Broglie wavelength from kinetic energy?
Yes. For a non-relativistic particle, momentum p equals the square root of 2 m KE, so lambda = h / sqrt(2 m KE). This calculator uses mass and speed directly; if you have kinetic energy, first find the speed from KE = half m v squared, then enter it.
What units should I use?
Use SI units: mass in kilograms and speed in metres per second. Planck's constant is in joule-seconds, so the wavelength comes out in metres. This calculator also converts the result to nanometres and picometres, which are more convenient at the atomic scale.
Is the de Broglie wavelength the same as the photon wavelength?
No. The de Broglie wavelength applies to particles with mass and uses their momentum m v. A photon has no mass, and its wavelength relates to its energy by lambda = h c / E. Both use Planck's constant, but the formulas differ because photons always travel at the speed of light.