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A particle A of mass m and initial velocity $v$ collides with a particle $B$ of mass $\large\frac{m}{2}$ which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $\lambda_A$ to $\lambda_B$ after the collision is :

$\begin{array}{1 1} (1)\;\large\frac{\lambda_A}{\lambda_B}=\frac{1}{3} \\ (2) \large\frac{\lambda_A}{\lambda_B}=2 \\ (3) \large\frac{\lambda_A}{\lambda_B}=\frac{2}{3} \\ (4) \large\frac{\lambda_A}{\lambda_B}=\frac{1}{2} \end{array} $

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