question_answer

The potential energy of a particle of mass m is given by \[V\left( x \right)=\left\{ \begin{matrix}    {{E}_{0}}; & 0\le x\le 1  \\    0; & x>1  \\ \end{matrix} \right\}\]\[{{\lambda }_{1}}\] and \[{{\lambda }_{2}}\]are the de-Broglie wavelengths of the particle, when \[0\le x\le 1\] and \[x>1\]respectively. If the total energy of particle is\[2{{E}_{0}}\], find \[{{\lambda }_{1}}/{{\lambda }_{2}}\].

A) \[\sqrt{2}\]

B) \[\sqrt{3}\]

C) \[\sqrt{5}\]  

D) \[2\sqrt{2}\]