How to Use De Broglie Wavelength Calculator
The De Broglie Wavelength Calculator computes a particle’s de Broglie wavelength from any of three inputs.
- Pick the input - Speed, kinetic energy, or momentum. Choose whichever quantity you know from your experiment or problem statement.
- Enter the mass - Type a custom mass in kg, or select a preset particle (electron, neutron, proton) to load the standard rest mass automatically.
- Toggle relativistic mode - For high-energy electrons or particles approaching c, switch to relativistic mode so the calculator uses the full momentum p = γmv rather than the classical p = mv.
- Read λ and compare - The De Broglie Wavelength Calculator displays the wavelength in both meters and angstroms. Use the angstrom value to compare directly with crystal lattice spacings (~1–5 Å) for diffraction feasibility.
Formula & Theory - De Broglie Wavelength Calculator
The De Broglie Wavelength Calculator uses the original de Broglie relation:
λ = h / p
p (non-rel) = m · v
p (rel) = γ · m · v
KE (non-rel) = p² / (2 m)
E (rel) = √( (pc)² + (mc²)² )| Symbol | Meaning |
|---|---|
| h | Planck constant |
| p | Particle momentum |
| m | Rest mass |
| v | Speed |
| γ | Lorentz factor = 1 / √(1 − v²/c²) |
Worked Example
An electron accelerated through V = 100 V gains kinetic energy KE = eV = 100 eV = 1.602 × 10⁻¹⁷ J. Non-relativistic momentum:
p = √(2 m_e KE) = √(2 × 9.109×10⁻³¹ × 1.602×10⁻¹⁷)
≈ 5.40 × 10⁻²⁴ kg·m/s
λ = h / p ≈ 1.23 nmFor a thermal neutron at room temperature (KE ≈ 0.025 eV), λ ≈ 1.8 Å — well matched to crystal lattice spacings.
Assumptions and Limits
In non-relativistic mode the calculator uses p = mv. Switch to relativistic mode whenever v / c exceeds about 0.1 or the kinetic energy approaches mc². For photons and massless particles, the de Broglie relation reduces to λ = h/E · c.
Use Cases for De Broglie Wavelength Calculator
The De Broglie Wavelength Calculator is useful when you need a quick, transparent calculation for wave-particle problems:
- Electron microscopy - Estimate resolution limits at a given accelerating voltage. A 100 kV TEM produces λ ≈ 3.7 pm, enabling sub-ångstrom imaging when corrected for aberrations.
- Neutron scattering - Convert thermal neutron energies to wavelengths matching crystal lattice spacings to confirm whether Bragg diffraction is feasible.
- Atom interferometry - Predict fringe spacing for cold-atom beams (λ ~ nm range) used in inertial sensing and gravitational wave detection experiments.
- Physics teaching - Show how λ shrinks dramatically with increasing mass and speed, illustrating why quantum effects vanish at macroscopic scales.
- Electron diffraction - Calculate LEED beam wavelengths for surface crystallography experiments and confirm their compatibility with target lattice planes.
- Ion beam lithography - Estimate diffraction limits for focused ion beams to assess whether ion optics approaches will be resolution-limited by wave optics.
For photons (massless), use the photon energy / wavelength calculator instead. The De Broglie Wavelength Calculator provides the foundational wave-particle duality calculation for all massive particles.