A particle A of mass m and initial velocity v collides with a particle

Question:

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 $\lambda_{\mathrm{A}}$ to $\lambda_{\mathrm{B}}$ after the collision is :

  1. $\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{2}{3}$

     

  2. $\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{1}{2}$

  3. $\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=\frac{1}{3}$

  4. $\frac{\lambda_{\mathrm{A}}}{\lambda_{\mathrm{B}}}=2$

Correct Option: , 4

Solution:

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