\sect{Baruch's A43.}
1. Consider a 3-dimensional gas of atoms with a chemical potential
$\mu$ that can adsorb on any of M sites on a surface; at each site
at most one atom can be adsorbed. At the adsorption site an atom forms
an electric dipole ${\bf d}$ that can be oriented at any direction
{\em away} from the surface (see figure). In presence of an
electric field ${\bf E}$ perpendicular to the surface the dipole
has energy $-Ed\cos \theta$ where $|\theta | \leq \pi/2$ is the
angle between ${\bf d}$ and ${\bf E}$.
\begin{itemize}
\item [(a)]
Evaluate the number N of adsorbed atoms. Normalize the phase space
of each adsorbed atom to 1. Derive the limit $E\rightarrow 0$ and explain why is the
result finite, in spite of the adsorption energy being $0$ at
$E=0$.
\item [(b)]
Find the average electric dipole perpendicular to the surface.\\
\end{itemize}
\begin{center}
\includegraphics[scale=0.45]{A34.eps}
\end{center}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%