Question 10.6: Elastic collision between two electrons In an elastic collis...

Since the collision is elastic and the electrons have equal mass, the opening angle between the emerging paths must be 90°. The target electron must therefore recoil at an angle of 60° to the initial direction of the incoming electron. Let the speed of the incoming electron be u and speeds of the electrons after the collision be $u_{1} \text { and } u_{2}$ respectively. Then conservation of linear momentum implies that

$\begin{aligned} m u &=m u_{1} \cos 30^{\circ}+m u_{2} \cos 60^{\circ}, \\ 0 &=m u_{1} \sin 30^{\circ}-m u_{2} \sin 60^{\circ},\end{aligned}$

hich gives $u_{1}=\frac{1}{2} \sqrt{3} u \text { and } u_{2}=\frac{1}{2} u$. Hence, after the collision, the electrons have energies $\frac{3}{4} E \text { and } \frac{1}{4} E$ respectively.