The potential energy of a particle of mass m is given by $U\left(x\right)=\left\{\begin{array}{cc}{E}_0;& 0\le x\le 1\\ 0;& x>1\end{array}\right.\left.\begin{array}{r} \\ \end{array}\right\}$.  ${\lambda }_1$ 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 2E₀,the ratio $\frac{{\lambda }_1}{{\lambda }_2}$ will be 

• A

  2

• B

  1

• C

  $\sqrt{2}$

• D

  $\frac{1}{\sqrt{2}}$