Write de Brogile hypothesis for matter wave and find an expression for de-Broglie wave length.

Explanation

According to de-Broglie, a moving material particle can be associated with a wave i.e., motion of a particle is guided by a wave. ..The waves associated with moving material particle are known as de-broglie waves or matter waves...
Expression for the wavelength
de-Broglie proposed that although the rest mass of photon is zero, yet it should have mass while in motion. Let mass of photon be m then, according to Einstein.s mass-energy relation, `E= mc^(2)` ...(i)
We know that, E= hv (Where v is the frequency of photon) ...(ii)
From equations (i) and (ii), we have `hv= mc^(2) or h (c )/(lamda)= mc^(2) rArr lamda= (h)/(mc)`
We know that, mc= Momentum of photon.
Therefore, `lamda = (h)/(p)` ...(iii)
which is the expression de-Broglie wavelength.