An electron has a velocity v = 0.990c.

(a) Calculate the kinetic energy in MeV of the electron.

(b) Compare this with the classical value for kinetic energy at this velocity. (The mass of an electron is 9.11 x 10^-31 kg.)

Strategy

The expression for relativistic kinetic energy is always correct, but for (a) it must be used since the velocity is highly relativistic (close to c). First, we will calculate the relativistic factor γ, and then use it to determine the relativistic kinetic energy. For (b), we will calculate the classical kinetic energy (which would be close to the relativistic value if v were less than a few percent of c) and see that it is not the same.