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/c² ————-(2)

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

λ = wavelength of light

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

Rewriting the equation we get

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  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