Explain the concept of de Broglie wave (matter wave).....

According to de Broglie’s hypothesis, a moving material particle sometimes acts as a wave and sometimes as a particle; or a wave is associated with moving material particle, which controls the particle in every respect. The wave associated with moving particle is called matter wave or de Broglie wave, λ = h/(mv)

Where, m and v are the mass and velocity of the particle and h is Planck’s constant

According to Planck’s quantum theory, the energy of a photon of a radiation of frequency ν and wavelength λ is

E = hν

According to Einstein’s mass-energy relation,

E = mc² 

From (i) and (ii), we obtain

hν = mc²

=> m = hv/c²

Since each photon moves with the same velocity c, the momentum of photon, 

p = Mass × Velocity

So, p = (hv/c²)× c = hv/c = h/λ

That is, 

λ = h/p

This equation is equally applicable to both the photons of radiation and other material particles.