# de Broglie’s Hypothesis

De Broglie in 1923 suggested that wave particle duality must be universal, that is all material particles should also display a dual wave particle behavior. To put it in other words all material particles, just like photons can have wave like aspects. Let is consider a photon of frequency $\nu$. Then its energy is given by $E= h\nu = mc^2$ where m is the mass of the photon particle. This photon travels with the velocity of ling c and its momentum is given by

$p = mc$

Putting this value in above equation we get

$\dfrac{h\nu}{c}=p$

$\lambda = \dfrac{h}{p}$ —— (1)

here $\lambda = \dfrac{c}{\nu}$

De Broglie assumed that equation (1) is valid for material particles like electrons. We can generalize each material particle with momentum $\vec{p}$ behaves like a group of matter waves whose wavelength $\lambda$ and wave vector k such that

$\vec{k} = \dfrac{\vec{p}}{\hbar}$ ——- (2)

Equation (1) and (2) are known as de Broglie relation which connects momentum of particle with the wavelength and wave vector of the wave corresponding to the particle.