Physics - Modern Physics Question with Solution | TestHub

Initial velocity of electron, 

$v=v_0\hat{\mathrm{i}}+v_0\hat{\mathrm{j}}\Rightarrow \left|u\right|=\sqrt{v_0^2+v_0^2}=v_0\sqrt{2}$

Initial de Broglie wavelength associated with electron, 

${\lambda }_0=\frac{h}{p}=\frac{h}{m{v}_0\sqrt{2}}$

now,

$v=u+at$
Velocity as a function of time $=v_0\widehat{i}+v_0\widehat{j}+\frac{e{E}_0}{m}t\widehat{k}$
so wavelength $\lambda =\frac{h}{m\sqrt{2v_0^2+\frac{e^2{E}_0^2}{m^2}{t}^2}}$
$\lambda =\frac{{\lambda }_0}{\sqrt{1+\frac{e^2{E}_0^2}{2m^2{v}_0^2}{t}^2}}$