MotionLab

de Broglie Wavelength Calculator

Every moving particle has a wavelength — usually too small to notice, but electrons show it clearly.

Particle mass (kg)

Velocity (m/s)

de Broglie wavelength (m)

λ = h / (mv)

What you entered

Particle mass (kg): 9.109e-31Velocity (m/s): 1000000

1
Momentum p = mv
9.109e-31 × 1000000= 9.1090e-25 kg·m/s
2
λ = h ÷ p
6.626e-34 ÷ 9.1090e-25= 7.2742e-10 m

Result

de Broglie wavelength (m): 0

A particle of mass 9.109e-31 kg moving at 1.000e+6 m/s has a de Broglie wavelength of 7.2742e-10 m.

De Broglie wavelength of matter

Every moving object has a wavelength equal to Planck's constant divided by its momentum. For anything macroscopic it is unmeasurably small.

Mass (kg)	Velocity (m/s)	Wavelength (m)	Object
9.11e-31	1e6	7.2734e-10	Electron at 1000 km/s
9.11e-31	1e7	7.2734e-11	Faster electron
1.67e-27	1000	3.9677e-10	Proton
0.145	40	1.1424e-34	Baseball
70	1	9.4658e-36	Walking person

The electron rows land near 1e-10 m, which is roughly the spacing of atoms in a crystal - and that is precisely why electron diffraction works and why electron microscopes can resolve far finer detail than light ones. The baseball's wavelength of 1e-34 m is some twenty orders of magnitude smaller than a proton, which is why nobody observes wave behaviour in everyday objects: the wavelength is not just small but unmeasurable in principle. Wavelength is inversely proportional to momentum, so speeding a particle up shortens it.

Wave-particle duality for matter

Louis de Broglie proposed in 1924 that all matter has wave properties, not just light — the wavelength is λ = h/(mv). For everyday objects (a baseball), this wavelength is absurdly small (~10⁻³⁴ m), but for electrons it's comparable to atomic spacings, which is why electron diffraction and electron microscopy work.

Why this matters for technology

Electron microscopes exploit de Broglie wavelengths to image objects far smaller than visible light allows — accelerated electrons have wavelengths of picometers, letting us see individual atoms and molecular structures.

Frequently asked questions

An electron is accelerated through 100 V. What's its de Broglie wavelength?

KE = eV = 1.6×10⁻¹⁹ × 100 = 1.6×10⁻¹⁷ J. v = √(2KE/m) = √(2×1.6×10⁻¹⁷/9.11×10⁻³¹) = 5.93×10⁶ m/s. λ = h/mv = 6.626×10⁻³⁴/(9.11×10⁻³¹ × 5.93×10⁶) = 0.123 nm — comparable to atomic spacings, enabling electron diffraction.

Why don't we notice the wave nature of everyday objects?

A 0.15 kg baseball at 40 m/s has λ = h/(mv) = 6.626×10⁻³⁴/(0.15 × 40) = 1.1×10⁻³⁴ m. That's 10¹⁹ times smaller than a proton — utterly unmeasurable. Wave effects only matter when λ is comparable to the system's dimensions, which only happens for subatomic particles.

How are electron microscopes related to de Broglie wavelength?

Electron microscopes use high-voltage electrons (10-300 kV) with wavelengths of 0.002-0.01 nm — far shorter than visible light (400-700 nm). Since resolution is limited by wavelength, electron microscopes can image individual atoms. Higher voltage = shorter wavelength = finer resolution.

Does the de Broglie wavelength apply to photons?

Photons have zero rest mass, so λ = h/(mv) doesn't apply directly. Instead, photons follow λ = h/p where p = E/c = hf/c, giving λ = c/f — the standard wave equation. de Broglie's insight was extending wavelength to massive particles, not photons.