# What is the de Broglie equation?

Mar 21, 2014

The de Broglie equation is an equation used to describe the wave properties of matter or particles. de Broglie suggested that particles can exhibit properties of waves, and proved that every moving particle has a matter wave associated with it.

The wavelength of the wave depends on the mass and the velocity of the particle:

$\lambda = \frac{h}{m v}$,

where:

• λ is wavelength in $\text{m}$.
• $h = 6.626 \times {10}^{- 34} \text{J"cdot"s}$ is Planck's constant.
• $m$ is the mass of a particle in $\text{kg}$ moving at a velocity $v$ in $\text{m/s}$.

For an electron, since it has nonrelativistic mass, one can calculate its wavelength.

EXAMPLE

Find the wavelength for an electron moving at the speed of $6.0 \times {10}^{6} \text{m/s}$ (mass of an electron: ${m}_{e} = 9.109 \times {10}^{- 31} \text{kg}$).

lambda = (6.626 xx 10^(-34) "J"cdot"s")/((9.109 xx 10^(-31) "kg")(6.0 xx 10^6 "m/s"))

Since ${\text{1 J" = "1 N"cdot"m" = "1 kg" cdot "m"^2"/s}}^{2}$,

$\lambda = 1.2 \times {10}^{- 10} \text{m}$

$=$ $\text{1.2 Å}$.