Question

What potential differences is needed to stop an electron that has an initial velocity v=5.0x10^5 m/s ?

Answer 1

The change of kinetic energy of an electron is equal to work done by an electric field

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

Hence,

$$V=\frac{mv^2}{2e}=\frac{9.1\times 10^{-31}\times (5.0\times 10^5)^2}{2\times 1.6\times 10^{-19}}=0.71 \:\rm V.$$