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A particle A of mass m and initial velocity $v$ collides with a particle B of mass $\frac{m}{2}$ 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 :

( A ) $\frac{\lambda_A}{\lambda_B} = \frac{1}{2}$
( B ) $\frac{\lambda_A}{\lambda_B} = \frac{1}{3}$
( C ) $\frac{\lambda_A}{\lambda_B} = 2$
( D ) $\frac{\lambda_A}{\lambda_B} = \frac{2}{3}$

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