Through what potential difference must an electron be accelerated to give it a speed of 0.9c ?

Step-by-step solution

The speed of the electron is v = 0.9c , which is comparable to the speed of light, so relativistic mechanics must be used. The relativistic factor is given by: = 1 1 - v^2 c^2 = 1 1 - 0.81 = 1 0.19 2.294 The kinetic energy K of the electron is: K = ( - 1)m₀ c^2 Using the rest mass energy of an electron, m₀ c^2 0.511 MeV : K = (2.294 - 1) 0.511 MeV = 1.294 0.511 MeV 0.661 MeV = 661 keV Since the kinetic energy is gained by accelerating the electron through a potential difference V , we have K = eV . V = 661 keV e =