An electron moving with speed v and a photon moving with speed c ,...

${\lambda}_{e} = {\lambda}_{Ph}$

$\dfrac{h}{{p}_{e}} = \dfrac{h}{{p}_{ph}}$

$\sqrt{2m{k}_{e}} = \dfrac{{E}_{ph}}{c}$

$2m{k}_{e} = \dfrac{{\left({E}_{ph}\right)}^{2}}{{c}^{2}}$

$\dfrac{{k}_{e}}{{E}_{ph}} = \dfrac{{E}_{ph}}{{c}^{2}}\left(\dfrac{1}{2m}\right)$

$= \dfrac{{p}_{ph}}{c}\left(\dfrac{1}{2m}\right)$

$= \dfrac{{p}_{e}}{c}\left(\dfrac{1}{2m}\right)$

$= \dfrac{mv}{c}\dfrac{1}{2m}$

$= \dfrac{v}{2c}$