
you work in Joules, since that's just your regular Kinetic energy formula that is derived from F=ma etc.
You could also figure it out this way: The units of mass is kg, velocity is m/s. Therefore

, which is equivalent to 1 Joule.

is measured in C/V - which is another definition of Joule (1 Joule is how much energy 1 Coulomb of charge would gain after passing through 1 Volt). So yes, it is measured in Joules, but you can use it to define the electron volt. Subsequently this will allow you to work with that unit of energy. An electron volt is how much energy an electron gains after passing through 1 volt.
If you want the conversion factor for eV to Joules, you can find what 1 electron volt is in Joules:
But yeah: Referring back to Unit 1&2 stuff, charge is in Coulombs and V is J/C:


So for the max Ek, you have this relationship:

This really just tells you that you can figure it out if you the stopping voltage in electron volts, or if you happen to know the max velocity and mass of the particle (i think, haven't done much light stuff since the start of term). It also allows you to find out how fast the electron is going if you know the stopping voltage in electron volts (but you will have to convert to Joules, since the 0.5mv^2 bit doesn't work in electron volts).