Final answer:
An electron gains kinetic energy when accelerated by an electric field, with the energy gained equal to the product of the electron's charge and the potential difference it is accelerated through. This relationship can be used to calculate the potential difference needed to accelerate an electron to a specific velocity.
Step-by-step explanation:
When an electron is accelerated through an electric field, it gains kinetic energy proportional to the potential difference it travels through. This can be understood using the concept that the kinetic energy (KE) gained by the electron is equal to the charge (q) of the electron multiplied by the voltage (V) it is accelerated through, described by the equation KE = qV. Given that the charge of an electron is -1.60 × 10-19 C, we can calculate the potential difference required to accelerate an electron from rest to a certain speed using its kinetic energy.
For example, if an electron accelerates from 0 to 10 × 104 m/s, we use the equation KE = ½mv2 to find its kinetic energy. Using the mass of the electron, 9.11 × 10-31 kg, and substituting into the equation yields the kinetic energy. From there, we can then use the equation KE = qV to find the potential difference by dividing the kinetic energy by the charge of the electron.