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.

 

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