De Broglie Wavelength Calculator
The de Broglie wavelength quantifies the wave-like nature of a moving particle. Proposed by Louis de Broglie in 1924, the relationship lambda = h / (m v) connects a particle's momentum to its associated wavelength, where h is Planck's constant (6.626 x 10^-34 J s). For electrons accelerated to moderate energies, this wavelength falls in the angstrom to nanometer range, making electron diffraction a powerful tool in materials characterization. For a 1 kg ball moving at 10 m/s, the wavelength is about 6.6 x 10^-35 m, far below any detectable scale and explaining why wave behavior is absent from everyday experience. Enter the particle mass in kilograms and velocity in meters per second to compute the wavelength.
De Broglie wavelength formula
lambda = h / (m * v)
Where h = 6.62607015 x 10^-34 J s (Planck's constant, exact per SI 2019), m is the rest mass in kg, and v is the velocity in m/s. The result is the wavelength in meters.
Physical interpretation
- For an electron (m = 9.109 x 10^-31 kg) moving at 1,000,000 m/s, the de Broglie wavelength is approximately 0.727 nm, comparable to atomic spacings.
- This wave nature was confirmed by Davisson and Germer (1927) who observed electron diffraction from nickel crystals.
- Thermal neutrons (v around 2,200 m/s) have wavelengths of about 0.18 nm, making neutron diffraction a key structural analysis tool.
- The formula assumes non-relativistic speeds. For speeds above about 10% of c, use the relativistic momentum p = gamma m v in the denominator.
De Broglie wavelength: frequently asked questions
What is the de Broglie wavelength?
The de Broglie wavelength is the quantum mechanical wavelength associated with a moving particle. Louis de Broglie proposed in 1924 that matter, like light, has a wave-particle dual nature. The wavelength equals Planck's constant divided by the particle's momentum.
What is the formula for de Broglie wavelength?
The formula is lambda = h / (m * v), where h is Planck's constant (6.626 x 10^-34 J s), m is the mass of the particle in kilograms, and v is its velocity in meters per second.
Why are de Broglie wavelengths of everyday objects negligible?
For macroscopic objects, the mass m is very large, making the denominator m*v enormous compared to Planck's constant. This yields a wavelength far smaller than any measurable scale, which is why wave behavior is undetectable for everyday objects.
What units should I use?
Enter mass in kilograms and velocity in meters per second. The result is given in meters. For an electron (mass 9.109 x 10^-31 kg), typical de Broglie wavelengths are on the order of nanometers to angstroms.
How does this relate to electron diffraction?
When the de Broglie wavelength of electrons is comparable to the spacing of atoms in a crystal lattice (about 0.1 to 0.5 nm), electrons diffract from the lattice. This was confirmed experimentally by Davisson and Germer in 1927, directly validating de Broglie's hypothesis.
Official sources
- NIST: Planck Constant (CODATA 2018).
- OpenStax University Physics Vol. 3: De Broglie's Matter Waves.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.