Question

Derive an expression for de Broglie wavelength of matter waves.

Answer 1

de Broglie equated the energy equations of Planck (wave) and Einstein (particle).

$E=hv$ (planck's relation)

$E=m{c}^2$ (Einstein's mass - energy relation)

$hv=m{c}^2$

$\frac{hc}{\lambda }=m{c}^2$ (or)

$\lambda =\frac{h}{mc}$

For a particle moving with a velocity $V$,

$\lambda =\frac{h}{mV}=\frac{h}{p}$

where $p=mV$ is the momentum of the particle.