Q 12-11-175JEE MainJEE Main 2017 (2 Apr)Medium
A particle $A$ of mass $m$ and initial velocity $v$ collides with a particle $B$ of mass $\dfrac m2$ 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:
Answer: (C) $\dfrac{\lambda_A}{\lambda_B} = 2$
For a head-on elastic collision with $B$ at rest:
$$v_A = \frac{m - m/2}{m + m/2}v = \frac v3,\qquad v_B = \frac{2m}{m + m/2}v = \frac{4v}{3}$$
Momenta: $p_A = \dfrac{mv}{3}$, $p_B = \dfrac m2\cdot\dfrac{4v}{3} = \dfrac{2mv}{3}$.
Since $\lambda = h/p$,
$$\frac{\lambda_A}{\lambda_B} = \frac{p_B}{p_A} = 2$$
Solution by Sreeraj P, M.Sc Physics