Potential difference is the work done per unit charge by an electric field.

$$ V = \frac{W}{Q} $$

and work done on an electron in an electric field is

$$ W = eV $$

where e is the charge on an electron, \( e = 1.6 \times 10^{-19} \text{ C}\)

When an electron enters an electric field that opposes its motion the field does work on the electron and reduces its kinetic energy.

So

$$ KE_{final} = KE_{initial} - eV $$

To completely stop an electron the work done by the electric field against the electron must equal its kinetic energy.

So

$$ KE_{initial} = eV_{stopping} $$

for example if an electron is travelling at \( 2 \times 10^5 \text{ m/s} \)

$$ KE_{initial} = \frac{1}{2}m_ev^2 $$

$$ KE_{initial} = \frac{1}{2} \times 9.11 \times 10^{-31} \times 2 \times 10^5 $$

$$ KE_{initial} = 1.82 \times 10^{-20} \text{ J} $$

so the stopping potential is

$$ V_{stopping} = \frac{KE}{e} $$

$$ V_{stopping} = \frac{1.82 \times 10^{-20}}{1.6 \times 10^{-19}} $$

$$ V_{stopping} = 0.114 \text{ V} $$