De Broglie Wave

Louis de Broglie extended the wave-particle duality of light to particles that have a mass by introducing de Broglie wavelengths:

De Broglie Wavelength

$$\lambda =\frac{h}{p}=\frac{h}{mv}$$

Note

• $\lambda$ = Wavelength (in $\text{m}$)
• $h$ = Planck’s Constant $\approx 6.26\times 10^{-34}\text{Js}$
• $p$ = Linear Momentum (in $\text{kgm/s or Ns}$)
• $m$ = Mass (in $\text{kg}$)
• $v$ = Velocity (in $\text{m/s}$)

This applies to both relativistic and non-relativistic velocities.

Since $h$ is so small, this can only be observed when the particle has either a very small mass.

$$\text{De Broglie Wavelength of an electron: }{\lambda }_e\approx 10^{-10}$$

Electron diffraction: A crystal lattice can be used as a diffraction experiment