Through what potential difference must an electron be accelerated to give it a speed of 0.6c ?

Step-by-step solution

The speed of the electron is v = 0.6c , which is comparable to the speed of light, so relativistic mechanics must be used. The relativistic kinetic energy K of the electron is given by K = ( - 1)m₀ c^2 , where = 1 1 - v^2 c^2 . Substituting v = 0.6c : = 1 1 - (0.6)^2 = 1 1 - 0.36 = 1 0.64 = 1 0.8 = 1.25 The kinetic energy gained by the electron is: K = (1.25 - 1)m₀ c^2 = 0.25 m₀ c^2 The rest mass energy of an electron is m₀ c^2 511 keV . K = 0.25 511 keV = 127.75 keV 128 keV Since the kinetic energy gained by accel