Electron diffraction pattern
Demonstration of wave–particle duality. An electron gun has been fired at a thin sheet of graphite. The electrons passed through and hit a luminescent screen, producing the patterns of rings associated with diffraction. Diffraction occurs when a wave passes through an aperture similar in size to its wavelength. But electrons are particles, so should not exhibit the same phenomenon unless they can also behave like waves. de Broglie correctly deduced that this was the case and that particles have wavelengths inversely proportional to their momentum.
According to Planck's quantum theory, the energy of a photon of radiation of frequency f and wavelength λ is given by: E = hf ............(i)
where h = Planck's constant,
If photon is considered as a particle of mass m, then according to Einstein's energy–mass relation, the energy E of the photon is given by: E = mc2 ..............(ii)
For eq's. (i) and (ii) we have, hf = mc2
The quantity mc, is the momentum p of the photon having mass m and travelling with velocity c.
Eq. (iii) gives de Broglie wavelength for a photon. According to de Broglie eq. (iii) is applicable to both the photons of radiation and other material particles. Thus if a material particle has mass m and moves with a velocity v, its momentum is p = mv. According to de Broglie, the wavelength λ of the wave associated with this moving particle is
Eq.(iv) is de Broglie wave equation for a moving material particle.