With the advancement in technology, the nature and behaviour of particles is studied very precisely. When we see the case of light, the phenomenon like interference, polarization, diffraction suggests that it is wave while photoelectric effect, compton effect suggests that light is a matter. So, light exhibit dual character. Like light wave, other waves can can also be treated as particle motion. Similarly motion of a particle can also be treated as wave motion. This is explained by Duality principle proposed by De-Broglie.
According to De-Broglie,’Every particle in motion has wave character. The wave associated with matter is called matter wave. The wavelength associated with the the matter is given by:
λ = h/mv where, h = Planck’s constant, m is the mass and v is the velocity of the particle.
According to Einstein’s relation,
E = mc2………(i)
From Planck’s quantum theory of radiation,
E = hf……..(ii)
Now, From equation (i) and (ii),
hf = mc2
We know, f = c/λ
∴ hc/λ = mc2
or h/λ = mc
Now, momentum of the photon is given by P =mc, Then:
P = h/λ
or, λ = h/P = h/mv……..(iii)
Equation (iii) is called D-Broglie’s Relation.