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

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Ans : (b)

Total energy = Kinetic energy + Potential energy

For the region $ 0 \leq x \leq 1,$

Kinetic energy = Total energy – Potential energy

$= 2E_{\circ} – E_{\circ} = E_{\circ}$

So, $ \lambda_1 = \large\frac{h}{ \sqrt {2m(E_{\circ})}}$…………..(i)

For the region $x>1$,

Kinetic energy = Total energy – Potential energy

$= 2E_{\circ} – 0 =2 E_{\circ}$

So, $ \lambda_2 = \large\frac{h}{ \sqrt{2m(2E_{\circ})}}$…………….(ii)

From (i) & (ii),

$ \large\frac{ \lambda_1}{ \lambda_2} = \sqrt 2$

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