To calculate the final speed of an electron accelerated through a 25,000 V potential difference, the kinetic energy gained by the electron is equated to the electrical potential energy, resulting in the electron's final speed of about 9.37 × 10^7 m/s.
The speed of an electron after being accelerated through a potential difference can be found using the relationship between electrical potential energy and kinetic energy. The kinetic energy (KE) gained by the electron when it is accelerated through a potential difference (V) is equal to the electrical potential energy given by the charge of the electron (e) multiplied by the potential difference: KE = eV. The formula for kinetic energy of the electron when it achieves non-relativistic speeds is KE = ½ mv^2, where m is the mass of the electron and v is the final speed. We can set these equations equal to each other since the electron is accelerated from rest, so eV = ½ mv^2.
Solving for v gives us the equation v = √(2eV/m). By inserting the values for the charge of an electron (e = 1.60 × 10^-19 C), the mass of an electron (m = 9.11 × 10^-31 kg), and the potential difference (V = 25,000 V), we can calculate the speed of the electron. After calculating, the final speed (v) of the electron is approximately 9.37 × 10^7 meters per second (m/s) assuming non-relativistic speeds.