⚛️ de Broglie Wavelength Calculator
Find the quantum wavelength of a moving particle (λ = h/(mv)), or solve for its mass or speed.
Wavelength λ
7.2742e-10 m
de Broglie wavelength: λ = h/(m·v), with h = 6.626×10⁻³⁴ J·s. Electron mass ≈ 9.11e-31 kg, proton ≈ 1.67e-27 kg. 🔒 Computed in your browser.
How the de broglie wavelength calculator works
Every particle has a wavelength λ = h/(m·v), its momentum mv times Planck’s constant h inverted. Enter any two of mass, speed and wavelength and the tool solves for the third. Electron and proton masses are provided as presets. Because Planck’s constant is so small (6.626×10⁻³⁴ J·s), only very light, fast particles such as electrons have a wavelength large enough to matter.
This is why electrons diffract like waves. The wavelength is tiny for everyday objects (a thrown ball is ~10⁻³⁴ m) but significant for electrons, enabling electron microscopy.
Frequently asked questions
What is the de Broglie wavelength?
The wavelength associated with a moving particle: λ = h/(mv), where h is Planck’s constant and mv the momentum. It shows that matter has wave properties.
How do I calculate it?
Divide Planck’s constant (6.626×10⁻³⁴) by the momentum (mass × speed). An electron at 10⁶ m/s has λ ≈ 7×10⁻¹⁰ m. Use the electron-mass preset.
Why don’t everyday objects show wave behaviour?
Their mass is so large that λ = h/(mv) is unimaginably small (~10⁻³⁴ m for a ball), far too tiny to observe. Wave effects only matter for very light particles.
What is de Broglie’s idea used for?
Electron microscopes exploit the short electron wavelength for high resolution, and electron/neutron diffraction confirms matter waves.
What mass do I enter for an electron?
About 9.109×10⁻³¹ kg (the preset). For a proton use 1.673×10⁻²⁷ kg.
Worked example: an electron
An electron (m ≈ 9.11×10⁻³¹ kg) at 2×10⁶ m/s has momentum p = mv ≈ 1.82×10⁻²⁴ kg·m/s, so λ = h/p ≈ 6.63×10⁻³⁴ / 1.82×10⁻²⁴ ≈ 3.6×10⁻¹⁰ m, comparable to atomic spacings, which is why electrons diffract in crystals.
Does the de Broglie relation apply to photons?
The formula λ = h/p works for photons if you use their momentum p = E/c, and it reproduces λ = hc/E. But de Broglie’s insight was that matter, particles with mass, also has a wavelength.
What units should I use?
Mass in kilograms and speed in metres per second give momentum in kg·m/s, and the wavelength comes out in metres. Use the electron or proton preset to avoid typing the tiny masses by hand.
Does the de Broglie wavelength depend on temperature?
Only indirectly, temperature sets a particle’s typical speed, and faster particles have shorter wavelengths. For a gas, the thermal de Broglie wavelength shrinks as the temperature rises because the average momentum increases.
Worked example: a proton
A proton (m ≈ 1.673×10⁻²⁷ kg) at 1×10⁵ m/s has momentum p = mv ≈ 1.673×10⁻²² kg·m/s, so λ = h/p ≈ 6.626×10⁻³⁴ / 1.673×10⁻²² ≈ 4.0×10⁻¹² m, far shorter than an electron’s at the same speed, because the proton is much heavier.