Question

A particle $'A'$ of mass $'m'$ moving with an initial velocity $'v'$ collides elastically with a particle $B$ of mass $2m$ which is initially at rest. The ratio of the de-Broglie wavelengths $\left(\frac{\left(\lambda \right)_{A}}{\left(\lambda \right)_{B}}\right)$ of the particles $A$ and $B$ after collision is

• A. $2$
• B. $3$
• C. $8$
• D. $4$

Answer 1

Answer: (D)

From Conservation of momentum
$mv+0=mv_{1}+2mv_{2}$
$v=v_{1}+2v_{2}\ldots \left(i\right)$
coefficient of restitution;
$e=\frac{v_{2} - v_{1}}{v}$
$v_{2}-v_{1}=v...\left(ii\right)$
from $\left(i\right)$ and $\left(ii\right)$ ;
$v_{2}=\frac{2 v}{3},v_{1}=-\frac{v}{3}$
$\frac{\lambda _{A}}{\lambda _{B}}=\frac{2 m v_{2}}{m v_{1}}=\frac{2 v_{2}}{v_{1}}=4$