Problem 10 Four electrons, all with the same unknown initial velocity v are Snm shot against each other from infinitely far away. One pair of electrons moves along the x-axis, the other pair moves along the y-axis. The electrons reach a minimum distance of 5nm as shown in the picture on the right hand side. Find the initial velocity v of the electrons. The mass of the electron is 9.11 x 10-31kg and its charge is -1.6x10-19C. Egl + EC,2 + Be,3 + Be,4 = Ee,1 + Ee,2 + Ee,3 + Ee,4 [Ke , l + Ke , 2 + Ke , 3 + Ke A + Up , l & 2 & 3 & 4 = Ke,1 + Ke,2 + Ke,3 + Ke4 + Uel & 2 & 3 & 4 kel = Ke,2 = Ke,3 = Ke,4 = 0 beacause at minimum distance the velocity is zero Uel & 2 & 3 & 4 = 0 beacause the distance between the electrons is infinite - 4 ( # m v ? ) = ve , 1 & 2 + u e , 1 & 3 + u e, 1 & 4 + [je 2 & 3 + Ue,2 & 4 + ve,3 & 4 kee kee kee re, 1 & 2 - 4( mv) =kee kee kee re,l & 3 -+ . re,l & 4 re,2 & 3 re,2 & 4 re,3 & 4 4 (5 mv ?)= kee -+ kee kee kee kee 5 x 10-9m 5V/2 x 10-9m 5 x 10-9m . + 5 x 10-9m 5V/2 x 10-9m 5 x 10-9m - 4 (7mv?) = 4 kee kee 5 x 10-9m + 2 5V/2 x 10-9m - 2m v2 = kee 5 x 10-9m/ x 2 + k Q2 Vi = 5 x 10-9m x 2 + 1 * 2m 9 x 109 Am- (1.6 x 10-19c)2 vi = 5 x 10-9m |x (2 + - VZ X . 2 x9.11 x 10-31kg + vi = 261,658.437m