# De Broglie Wavelength Formula

De-Broglie waves explain about the nature of the wave related to the particle. Einstein explained  the momentum (p) of a photon with the given formula

p=mc——–(1)

c = speed of light.

The energy (E) of a photon is given as

E = mc2,

E=hλ

hλ=mc2

m =hλ/c————-(2)

h= Planck’s constant(6.62607015×10−34 Js)

λ = wavelength of light

substituting equation (2) in equation (1) we get

$p=h/\lambda$
Rewriting the equation we get
$\lambda =h/p$
$\lambda =h/mv$
m is the mass
v is the velocity

De Broglie Wavelength Formula is used to calculate the wavelength and momentum in any given problems based on this concept.

## Solved Examples

Question 1: Find the wavelength of an electron moving with a speed of $2\times 10^{6}$ ms-1.

Solution:

Given:

Velocity of the electron, v =2×106  ms-1

Mass of electron, m =9.1×10-31   Kg

Planck’s Constant, h = 6.62607015×10−34 Js

The de-Broglie wavelength is given by λ = h/mv

=  6.62607015×10−34 /(2×106)(9.1×10-31 )

λ = 0.364×109m