Answer
The kinetic energy of the slowest electrons is zero.
Work Step by Step
We can find the photon energy:
$E = \frac{hc}{\lambda}$
$E = \frac{(6.63\times 10^{-34}~J\cdot s)(3.0\times 10^8~m/s)}{200\times 10^{-9}~m}$
$E = 9.945\times 10^{-19}~J$
$E = (9.945\times 10^{-19}~J)(\frac{1~eV}{1.6\times 10^{-19}~J})$
$E = 6.20~eV$
It is given that 4.20 eV is required to eject an electron.
Since the photon energy is greater than the required energy, then electrons can be ejected.
However, there is no non-zero lower limit on the kinetic energy of the ejected electrons. Theoretically, the kinetic energy of the slowest electrons could be zero.
