Potential energy of a particle varies as a function of $x$ and is given as $ U(x)$ \[ \begin {bmatrix} E_{\circ} & 0 \leq x \leq 1 \\ 0 & x > 1 \end {bmatrix} \] The de-Broglie wavelengths of the particle in the region $ 0 \leq x \leq1$ and $x>1$ are $ \lambda_1$ and $ \lambda_2$ respectively. If the total energy of the particle is $2E_{\circ}$, the ratio $ \large\frac{\lambda_1}{\lambda_2}$is

Question

$\begin {array} {1 1} (a)\;\large\frac{1}{\sqrt 2} & \quad (b)\; \sqrt 2 \\ (c)\;2 & \quad (d)\;\large\frac{1}{2} \end {array}$