De Broglie wavelength formulas and interpretation
De Broglie’s relation assigns a wavelength to a particle according to its momentum.
The calculator preserves mass and velocity inputs with scientific-notation output.
How to use the De Broglie wavelength calculator
- Choose a model: Select the relationship matching the problem.
- Choose the unknown: Select the quantity to calculate.
- Enter values: Enter all known values with matching units and signs.
- Calculate: Review the result, formula, units, and direction.
Formula and variables
Matter-wave wavelength equals Planck’s constant divided by particle momentum.
λ = h/p = h/(mv)- λ — Wavelength
- De Broglie matter wavelength (m)
- h — Planck constant
- Exact SI action constant (J·s)
- p — Momentum
- Particle momentum (kg·m/s)
- m — Mass
- Particle rest mass (kg)
- v — Velocity
- Nonrelativistic speed (m/s)
Electron example
An electron moves at 1 × 10⁶ m/s.
- Electron mass
- 9.109 × 10⁻³¹ kg
- Speed
- 1 × 10⁶ m/s
- λ = h/(mv)
- λ ≈ 7.27 × 10⁻¹⁰ m
Result: Wavelength is about 0.727 nm.
This scale is comparable with atomic dimensions.
Understanding your results
Interpreting the result
The basic mv form is nonrelativistic; use relativistic momentum as speed approaches light speed.
Assumptions
- The selected equation represents the physical system.
- Inputs use a consistent reference direction.
- Values are converted through coherent SI units.
Limitations
- Vector components must be resolved along a common axis.
- External forces or energy losses are not added automatically.
- Results depend on the accuracy of entered measurements.
Common mistakes
- Mixing incompatible units.
- Dropping negative signs that represent direction.
- Using weight where mass is required.
- Entering a zero divisor.
Practical use cases
Physics problems
Check classroom, laboratory, and mechanics calculations.
Practical estimates
Estimate motion, forces, and energy for real systems.
Frequently asked questions
Can a result be negative?
Yes. For directional quantities, the sign indicates direction relative to the chosen positive axis.
Should I use SI units?
The interface can convert supported units, while the formulas are evaluated through coherent SI units.
Sources and review
- SI Brochure, 9th edition — BIPM. Accessed 2026-07-11.
- Special Publication 811 — NIST. Accessed 2026-07-11.
Reviewed 2026-07-11.