An electron (mass m ) with initial velocity → v = v _ 0 ^ i + v _ 0...

Initial velocity of electron,

v = {v}_{0}\overset{^}{i} + {v}_{0}\overset{^}{j} ⇒ \left|u\right| = \sqrt{{v}_{0}^{2} + {v}_{0}^{2}} = {v}_{0}\sqrt{2}

Initial de Broglie wavelength associated with electron,

${\lambda}_{0} = \dfrac{h}{p} = \dfrac{h}{m{v}_{0}\sqrt{2}}$

now,

$v = u + at$
Velocity as a function of time = {v}_{0}\overset{^}{i} + {v}_{0}\overset{^}{j} + \dfrac{e{E}_{0}}{m}t\overset{^}{k}
so wavelength $\lambda = \dfrac{h}{m\sqrt{2{v}_{0}^{2} + \dfrac{{e}^{2}{E}_{0}^{2}}{{m}^{2}}{t}^{2}}}$
$\lambda = \dfrac{{\lambda}_{0}}{\sqrt{1 + \dfrac{{e}^{2}{E}_{0}^{2}}{2{m}^{2}{v}_{0}^{2}}{t}^{2}}}$