Through what potential difference must an electron be accelerated to give it a speed of 0.99c ?

Step-by-step solution

The rest mass energy of an electron is m₀ c^2 = 0.511 MeV . The kinetic energy of a relativistic particle is given by K = ( - 1)m₀ c^2 , where = 1 1 - v^2 c^2 . Given v = 0.99c , we calculate as: = 1 1 - (0.99)^2 = 1 1 - 0.9801 = 1 0.0199 7.089 The kinetic energy is: K = (7.089 - 1) 0.511 MeV = 6.089 0.511 MeV 3.11 MeV Since the kinetic energy is gained by accelerating the electron through a potential difference V , we have K = eV . eV = 3.11 MeV V = 3.1 MV