# de Broglie Wavelength Calculator

Matter-wave λ = h/p via particle & speed (γmv optional), direct momentum, or electron voltage (relativistic + h/√(2mE) comparison). Units from m to fm/Å with wavelength scale.

> Canonical page: https://elysiatools.com/en/tools/de-broglie-wavelength

- **Category:** Science & Education

- **Keywords:** de broglie wavelength, matter wave, quantum mechanics, electron diffraction, planck constant, momentum, wave-particle duality

## Overview

The de Broglie Wavelength Calculator computes the matter-wave wavelength (λ = h/p) of particles using particle speed, direct momentum, or electron accelerating voltage with optional relativistic corrections.

## Inputs

- **Input mode** (select)
- **Particle** (select)
- **Custom mass (kg)** (number): e.g. 0.058 for a tennis ball
- **Speed v (m/s)** (number): e.g. 30
- **Relativistic correction (p = γmv)** (checkbox)
- **Momentum p (kg·m/s)** (number): e.g. 1e-20
- **Accelerating voltage V (volts)** (number): e.g. 100

## When to use

- Analyzing electron diffraction experiments or crystal lattice interactions.
- Solving quantum mechanics homework involving wave-particle duality.
- Evaluating relativistic momentum effects on subatomic particles at high velocities.

## How it works

- Choose an input mode: particle with velocity, direct momentum, or electron accelerating voltage.
- Select a standard particle (electron, proton, neutron, alpha) or enter a custom mass.
- Toggle relativistic corrections if dealing with high-speed particles where p = γmv.
- Receive the computed de Broglie wavelength across multiple metric scales (m, pm, Å, fm) alongside physical scale context.

## Use cases

- Calculating electron beam wavelengths for transmission electron microscopy (TEM) setups.
- Comparing matter wavelengths of macroscopic objects against subatomic particles.
- Determining thermal neutron wavelengths for crystallography and scattering studies.

## Frequently asked questions

### What is the de Broglie wavelength formula?

The wavelength is calculated as λ = h/p, where h is Planck's constant and p is the momentum of the particle.

### When should relativistic corrections be applied?

Apply relativistic corrections when particle velocities exceed roughly 1% of the speed of light (v/c > 0.01) to account for relativistic momentum.

### Which preset particles are available?

Preset options include electrons, protons, neutrons, and alpha particles, alongside custom mass inputs.

### How does electron accelerating voltage determine wavelength?

Accelerating voltage V determines kinetic energy E = eV, which calculates momentum via relativistic formulas and classical approximations.

### What units are displayed in the results?

Outputs are displayed in meters (m), picometers (pm), ångströms (Å), and femtometers (fm) depending on the magnitude.

## Related tools

- [Bohr Model Calculator](https://elysiatools.com/en/tools/bohr-model-calculator): Hydrogen level n: r_n = n²a₀, E_n = −13.605693/n² eV, v_n = αc/n, orbital period, plus optional transition energies with named series lines.
- [Double-Slit Interference Calculator](https://elysiatools.com/en/tools/double-slit-interference): Δy = λL/d with first-order angle and the first four fringes each side — the ruler-measurable student bench classic.
- [Hydrogen Spectrum Series Calculator](https://elysiatools.com/en/tools/hydrogen-spectrum-series): Rydberg lines for Lyman/Balmer/Paschen/Brackett/Pfund: vacuum wavelengths, photon energies, named lines with Balmer colors, series limit.
- [LC Oscillation Frequency Calculator](https://elysiatools.com/en/tools/lc-oscillation-frequency): LC tank resonance f = 1/(2π√(LC)) with inductance and capacitance selectors, plus ω, period, and characteristic impedance √(L/C).
- [Numerical Aperture Calculator](https://elysiatools.com/en/tools/numerical-aperture-calculator): NA = n·sinα with the full acceptance cone and Abbe limit λ/(2·NA) — dry versus oil-immersion microscopy.
- [Photoelectric Effect Calculator](https://elysiatools.com/en/tools/photoelectric-effect-calculator): E_k(max) = hν − φ with preset metal work functions or custom φ: threshold frequency, cutoff wavelength, emission verdict, stopping voltage, and photoelectron speed.
- [Single-Slit Diffraction Calculator](https://elysiatools.com/en/tools/single-slit-diffraction): a·sinθ = mλ minima with the double-wide central maximum and optional screen positions.
- [Microscope Scale Bar Calibrator](https://elysiatools.com/en/tools/microscope-scale-bar-calibrator): Calculate microscope object scale, field of view, diffraction limits, Nyquist sampling, and download a transparent SVG scale bar.

## Samples

- [Copyright-Free MP3 Audio Samples](https://elysiatools.com/en/samples/mp3-samples): Collection of royalty-free audio samples for testing and development purposes including nature sounds, meditation music, and ambient audio
- [Copyright-Free WAV Audio Samples](https://elysiatools.com/en/samples/wav-samples): Uncompressed PCM WAV audio samples for testing and development, mirrored from MP3 set with nature sounds and meditation music
- [Copyright-Free Raw PCM Audio Samples](https://elysiatools.com/en/samples/pcm-samples): Raw PCM s16le audio samples featuring nature ambience and relaxing music for waveform, playback, and conversion workflows
- [Speech Learning & Safety Audio Samples](https://elysiatools.com/en/samples/audio-learning-safety-samples): Deterministic synthetic WAV inputs for pronunciation comparison, dictation preflight, alert degradation, and voice privacy tools.