question_answer

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: [JEE Main 2017]

A) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{2}{3}\]

B) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]

C) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{B}}}=\frac{1}{3}\]

D) \[\frac{{{\lambda }_{A}}}{{{\lambda }_{_{B}}}}=2\]

Correct Answer: D

Solution :

[d]

By conservation of linear momentum

.

by law of collision

.

By equation [a] and

Option