The final speed of an electron accelerated through a potential difference of 200 V can be calculated using energy principles. The potential difference provides energy to the electron, which can be quantified as the product of charge and voltage, resulting in an energy gain of 3.2 x 10^-17 J. The initial kinetic energy of the electron can be determined from its initial speed, which is 1.8 x 10^-24 J. By adding the energy gained from the potential difference to the initial kinetic energy, the total energy can be converted back into speed using the kinetic energy formula. Thus, the final speed of the electron can be calculated based on these energy considerations.