Derive an expression for de-Brogile wavelength of matter waves.
de Broglie's wavelength of matter waves: de Broglie equated the energy equations of Planck(wave) and Einstein(particle).
For a wave of frequency ν, the energy associated with each photon is given by Planck's relation,
E=hν ...............(1)
Where h is Planck's constant.
According to Einstein's mass energy relation, a mass m is equivalent to energy,
E=mc2 ............(2)
where c is the velocity of light.
If, hν=mc2
∴hcλ=mc2 (or) λ=hmc ...........(3)
(since ν=cλ)
For a particle moving with a velocity v, if c=v from equation (3)
λ=hmv=hp
Where p=mv, the momentum of the particle. These hypothetical matter waves will have appreciable wavelength only for very light particles.