Question

Find the potential difference ΔVe required to stop an electron (called a "stopping potential") moving with an initial speed of 1.96 107 m/s.

Answer 1

We need to know the charge and mass of an electron. I'll assume you have these values handy (let me know otherwise and I can look them up).

Volts have units of \[\rm joules \over coulombs\]If work also have units of joules. We can use the work-energy theorem, which states\[W = \Delta KE + \Delta PE\] we will assume there is no change in potential energy, therefore\[W = \Delta KE = {1 \over 2} m (v_f-v_i)\]
This being said, let's observe that\[V = {(1/2) m (v_f-v_i) \over q}\]where q is the charge of an electron (in coulombs).