Two parallel metal plates X and Y in a vacuum have a potential difference V across them - Scottish Highers Physics - Question 10 - 2015

To determine the speed of the electron as it reaches plate Y, we need to apply the principle of energy conservation.

1. Initial Energy: The electron starts from rest, so its initial kinetic energy is zero. The potential energy (PE) gained by the electron as it moves through the electric potential difference (V) is given by:

   $PE = eV$

2. Final Kinetic Energy: When the electron reaches plate Y, all the potential energy is converted into kinetic energy (KE). The kinetic energy of the electron is:

   $KE = \frac{1}{2}mv^2$

3. Energy Conservation Equation: Setting the potential energy equal to the kinetic energy gives:

   $eV = \frac{1}{2}mv^2$

4. Solving for Speed: Rearranging the equation to solve for the speed (v) of the electron:

   $v^2 = \frac{2eV}{m}$

   Taking the square root of both sides yields:

   $v = \sqrt{\frac{2eV}{m}}$

Thus, the correct option for the speed of the electron as it reaches plate Y corresponds to choice C: $\sqrt{\frac{2eV}{m}}$.