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Electron velocity from an electric field.

Given that the ground state hydrogen electron has a kinetic energy of 13.6 eV, and a velocity of 1/137 th the speed of light; what is the velocity of an electron after being accelerated by a 54.4 Volt electric field?  (Hint: 54.4/13.6 = 4)

Ans: (2/137) c, or 0.0146 c

After dropping through a 54.4 V field, the electron has four times the kinetic energy of the hydrogen electron.  Since kinetic energy is proportional to velocity squared, the velocity is only twice the velocity of the hydrogen electron.