Derive de-Broglie wave equation (wavelength) for a material particle.

Explanation

The momentum of photon of frequency v is given by
`p = (h upsilon)/(c) = (h)/(lambda)` since `c = upsilon lambda`
The wavelength of a photon in terms of its momentum is
`lambda = (h)/(p)" "...(1)`
According to de Broglie, the above equation is completely a general one and this is applicable to material particles as well. Therefore, for a particle of mass m travelling with speed v, the wavelength is given by
`lambda = (h)/(mv) = (h)/(p)" "...(2)`
This wavelength of the matter waves is known as de Broglie wavelength. This equation relates the wave character (the wave length `lambda`) and the particle character (the momentum p) through Planck.s constant.