Answer
The kinetic energy of the electron when it leaves the space between the plates is $6.0\times 10^{-15}~J$
Work Step by Step
We can find the potential difference in the motion of the electron:
$\Delta V = (\frac{3.0~mm}{12.0~mm})~(100.0~kV) = 25,000~V$
We can use conservation of energy to find the final kinetic energy $K_2$:
$K_2+U_2 = K_1+U_1$
$K_2 = U_1-U_2 + K_1$
$K_2 = -\Delta V~q +K_1$
$K_2 = (-25,000~J/C)(-1.6\times 10^{-19}~C)+2.0\times 10^{-15}~J$
$K_2 = 6.0\times 10^{-15}~J$
The kinetic energy of the electron when it leaves the space between the plates is $6.0\times 10^{-15}~J$
