De Broglie wavelength calculator
The wavelength of a particle from its mass and speed.
Fill in the fields and the result will appear here automatically.
A particle’s de Broglie wavelength follows from its momentum: λ=h/p. This page uses the nonrelativistic approximation p=mv, with mass in units of 10⁻²⁷ kg and speed in km/s. It reports wavelength, momentum, kinetic energy and the fraction of light speed β. Near c the relativistic momentum is required; this page does not calculate it.
How it works
Formula and logic
λ = h/p, with h = 6.62607015·10⁻³⁴ J·s. Multiply the entered mass by 10⁻²⁷ kg and speed by 1000 m/s; p=mv; K=mv²/2; β=v/c. All results belong to the nonrelativistic approximation.
Example
An electron at 1000 km/s has a wavelength of 7.27·10⁻¹⁰ metres — under a nanometre.
Fields and units
- Particle mass — ×10⁻²⁷ kg
- Speed — km/s
How to use
- — An electron mass of 9.1093837·10⁻³¹ kg corresponds to 0.00091093837 in the field. Convert kilograms first. Speed must be positive and below 299792.458 km/s; satisfying the field limits does not establish the accuracy of the nonrelativistic approximation.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax §6.5: λ=h/p, limits of p=mv and matter-wave frequency NIST CODATA 2022: exact h, c, e and measured ε₀
- Limitation
- All results belong to the nonrelativistic approximation. Speed must be positive and below 299792.458 km/s; satisfying the field limits does not establish the accuracy of the nonrelativistic approximation.
FAQ
Why has a ball no noticeable wave?
For a 150 g ball at 30 m/s, p=4.5 kg·m/s and λ≈1.472·10⁻³⁴ m. This is about 19 orders below the 10⁻¹⁵ m scale; the comparison depends on the chosen nuclear size.
Why use mass units of 10⁻²⁷ kg?
Scaled units make the small mass convenient to enter as a decimal. A field value of 1 means 10⁻²⁷ kg. This is an input-unit convention, not a different physical mass.
What does wavelength say about a microscope?
A short wavelength enables high resolving power, but actual microscope resolution also depends on lenses, aberrations and the specimen. A wavelength alone does not predict instrument resolution.
Does the formula hold near light speed?
No: use p=γmv. For the same mass and speed the relativistic wavelength is shorter by a factor of γ. The displayed β is a diagnostic; a relativistic calculation mode is not implemented.
Why show a fraction of light speed rather than frequency?
β=v/c helps assess when p=mv is applicable. Matter-wave frequency relates to energy through E=hf; the particle speed and wavelength cannot simply be combined as f=v/λ for an ordinary wave.