Final answer:
An electron falling through a potential difference of 326 x 10^16 V gains 326 x 10^16 eV, which, when converted to joules using the conversion factor 1 eV = 1.602 x 10^-19 joules, results in the electron gaining approximately 5.2152 x 10^-2 joules of kinetic energy.
Step-by-step explanation:
The question concerns the amount of kinetic energy an electron will gain when it falls through a certain potential difference. When an electron is accelerated through a potential difference of 1 volt (V), it gains an energy of 1 electronvolt (eV). Thus, if an electron falls through a potential difference of 326 x 1016 V, it will gain 326 x 1016 eV of energy. To convert this into joules, we need to use the conversion factor where 1 eV equals 1.602 x 10-19 joules.
To calculate the kinetic energy in joules, we use the formula:
Kinetic Energy (in Joules) = Energy (in eV) × 1.602 x 10-19 (conversion factor)
So, the kinetic energy gained by the electron will be:
326 x 1016 eV × 1.602 x 10-19 joules/eV = 5.2152 x 10-2 joules.