De Broglie Wavelength Calculator
Calculate the de Broglie wavelength of a particle from its mass and velocity.
Shows why electrons behave as waves while everyday objects do not.
De Broglie Wavelength
In 1924, Louis de Broglie proposed that all matter has wave properties. The wavelength associated with a particle is:
λ = h/(mv) = h/p
Where:
- λ = De Broglie wavelength (meters)
- h = Planck’s constant = 6.626 × 10⁻³⁴ J·s
- m = Mass of the particle (kg)
- v = Velocity of the particle (m/s)
- p = mv = momentum (kg·m/s)
Particle masses for reference:
- Electron: m = 9.109 × 10⁻³¹ kg
- Proton: m = 1.673 × 10⁻²⁷ kg
- Neutron: m = 1.675 × 10⁻²⁷ kg
Why wavelength shrinks with mass:
At everyday speeds (e.g., v = 1 m/s):
- Electron: λ ≈ 7.27 × 10⁻⁴ m = 0.727 mm (huge — wave effects dominate!)
- Proton: λ ≈ 3.96 × 10⁻⁷ m = 396 nm (UV light scale)
- Golf ball (0.046 kg): λ ≈ 1.44 × 10⁻³² m (completely unmeasurable)
This is why quantum effects are important for subatomic particles but not for everyday objects.
Applications:
- Electron microscopy: Electrons accelerated to high voltage have λ < 0.1 nm — smaller than atoms. This allows imaging of individual atoms.
- Neutron diffraction: Thermal neutrons have λ ~ 0.1 nm, similar to crystal lattice spacings, enabling crystal structure determination.
- Quantum tunneling: A particle’s wave nature allows it to “tunnel” through energy barriers — the basis of nuclear fusion in stars and tunnel diode operation.