Derive an expression for De Broglie wavelength.

Explanation

i. The momentum of photon of frequency v is given by
`p = ( h v)/( c ) = ( h )/( lambda)`
(ii) The wavelength of a photon in terms of its momentum is
`lambda = ( h )/( p ) `
(iii) 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 ) `
(iv) 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 Plancks' constant.