What Is the De Broglie Wavelength Calculator?
The de Broglie wavelength is the wavelength associated with any moving material particle, as proposed by Louis de Broglie in 1924.
This quantum mechanical wave-particle duality explains why electrons exhibit interference patterns and underpins transmission electron microscopy.
How Does the De Broglie Wavelength Calculator Work?
The calculator computes particle momentum p from rest mass m and velocity v.
Wavelength λ is derived by dividing Planck constant h by momentum.
Classical kinetic energy in both Joules and electron-volts (eV) is evaluated alongside wave parameters.
De Broglie Wavelength Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
Matter wavelength λ equals Planck constant h (6.626 × 10⁻³⁴ J·s) divided by momentum p = m · v.
How to Use the De Broglie Wavelength Calculator
- Select a preset particle (electron, proton, neutron) or choose Custom Mass.
- Specify velocity in meters per second.
- Review matter wavelength, momentum, and kinetic energy in the results breakdown.
Step-by-Step Example Calculation
Electron at 1,000,000 m/s
Input Values:
Understanding Your Result
Matter wavelengths around 0.1 nm are comparable to atomic lattice spacings in crystal diffraction.
Sub-picometer wavelengths require relativistic corrections at extreme beam voltages.
Factors That Affect the Result
- Particle Mass: Heavier particles produce vastly smaller de Broglie wavelengths at equivalent velocity.
- Beam Voltage / Velocity: Higher acceleration speed compresses wavelength proportionally.
When Should You Use This Calculator?
- Transmission and scanning electron microscopy (TEM / SEM) beam calibration.
- Quantum mechanics coursework and particle beam accelerator problem sets.
Assumptions & Limitations
- Non-relativistic approximation valid for particle velocities significantly below the speed of light.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Calculations use the CODATA 2018 exact Planck constant (6.62607015 × 10⁻³⁴ J·s).