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 held on, and elastic. The ratio of the de-Broglie wavelength ${\lambda }_A$ to ${\lambda }_B$ after the collision is

• A. $\frac{{\lambda }_A}{{\lambda }_B}=2$
• B. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{2}{3}$
• C. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{1}{2}$
• D. $\frac{{\lambda }_A}{{\lambda }_B}=\frac{1}{3}$

Answer 1

The correct option is A $\frac{{\lambda }_A}{{\lambda }_B}=2$

By conservation of linear momentum $mV={mV}_1+\frac{m}{2}{V}_2$

$2V=2V_1+V_2⟶\left(1\right)$ ${\lambda }_1=\frac{h}{p_1}$ ; ${\lambda }_2=\frac{h}{O_2}$

By law of collision

$e=\frac{V_2-V_1}{U_1-U_2}$ $\frac{{\lambda }_1}{{\lambda }_2}=\frac{2}{1}$

$u=V_2-V_1⟶\left(2\right)$ ${\lambda }_1:{\lambda }_2=2:1$

equ $\left(1\right)$ and $\left(2\right)$

$V_1=\frac{V}{3};V_2=\frac{4V}{3}$