Problem 20.3

20.3. a)
Work is just the change in kinetic energy, which in terms of potentials is just given by
$W = \Delta K = q \Delta V$
Here, the change in kinetic energy is just
$\Delta K = \frac{1}{2} mv^{2}$
and the charge is just that of an electron. Solving yields, for a proton $v = \sqrt{\frac{2 e \Delta V}{m}}$
$v = \sqrt{\frac{3.84 \times 10^{-17} J}{m_{proton}}}$
$v = 1.52 \times 10^{5} m/s$

b) And, for an electron, this yields
$v = \sqrt{\frac{2 e \Delta V}{m}}$
$v = \sqrt{\frac{3.84 \times 10^{-17} J}{m_{electron}}}$
$v = 6.49 \times 10^{6} m/s$