\begin{problem*}{28.13} % photoelectric effect
An isolated copper sphere of radius $5.00\U{cm}$, initially uncharged,
is illuminated by ultraviolet light of wavelength $200\U{nm}$.  What
charge will the photoelectric effect induce on the sphere?  The work
function for copper is $4.70\U{eV}$.
\end{problem*}

\begin{solution}
As light lands on the sphere, electrons are blasted off into oblivion.
As they leave, the sphere accumulates positive charge, so it takes a
bit more energy to pull the next electrons away.  Eventually the
system reaches equilibrium when the initial kinetic energy of electron
blasting off is not quite enough for it to escape the electro-static
attraction to the positive sphere.  In math
\begin{align}
  K_\text{max} &= hf - \phi = \frac{hc}{\lambda} - \phi
    = 2.40\E{-19}\U{J} = 1.50\U{eV} \\
    &= k_e \frac{Qq}{R} \\
  Q &= \frac{K_\text{max}R}{k_e q}
    =  \frac{2.40\E{-19}\U{J}}{8.99\E{9}\U{N$\cdot$m$^2$/C$^2$}\cdot 1.60\E{-19}\U{C}}
    = \ans{8.34\U{pC}} = \ans{52.1\E{6}\U{electrons}}
\end{align}
\end{solution}
