de Broglie Wavelength
Convert a particle's kinetic energy into momentum and matter-wave wavelength and compare electrons with neutrons.
Free theory articleConvert a particle's kinetic energy into momentum and matter-wave wavelength and compare electrons with neutrons.
Concept & interpretation
The de Broglie hypothesis associates every moving particle of momentum p with a matter-wave wavelength λ = h/p, where h = 6.62607015 × 10−34 J·s is Planck's constant. In the nonrelativistic regime (v/c ≪ 1), a particle of mass m and kinetic energy K has momentum p = √(2mK) and speed v = √(2K/m).
Experiment
In the de Broglie Wavelength module, compare how kinetic energy and particle mass determine momentum, speed, and matter-wave wavelength:
- Select Particle as "Electron" and Kinetic energy eV as 1, then increase energy to 4 and 9. Because p ∝ √K, quadrupling energy doubles momentum and halves the wavelength to 0.613192240564 nm.
- Switch Particle to "Neutron" (m = 1.675 × 10−27 kg) at 1 eV. The heavier mass increases momentum to 23.167416178547 × 10−24 kg·m/s and shortens the wavelength to 0.028600816332 nm.
- Set Kinetic energy eV to 0. At rest, momentum and speed are zero and the wavelength is unbounded (reported as "Unavailable").