Answer to Question 8

An electron is accelerated by a voltage of 1.5 V. It travels along a horizontal path that is 15 cm long. (a) Show that the speed of the electron is about 730 km s^{1} (b) Calculate how far the electron deviates from the horizontal path.
Mass of an electron = 9.11 × 10^{31} kg; Charge on an electron = 1.6 × 10^{19} C 
(a) Formula:
v^{2} = (2 × 1.6 × 10^{19} C × 1.5 V) ÷ (9.11 × 10^{31} kg) = 5.27 × 10^{11} m^{2} s^{2}
v = 7.26 × 10^{5} m s^{1} = 730 km s^{1}
(b) Time taken to travel 15 cm:
t = s/v = 0.15 m ÷ 7.26 × 10^{5} m s^{1} = 2.07 × 10^{7} s
Now use s = ut + 1/2at^{2} to work out the deviation:
s = 0 + 1/2 × 9.81 m s^{2} × (2.07 × 10^{7} s)^{2} = 2.1 × 10^{13} m
That is about 1000th the diameter of an atom, so the deviation is not that big.
