Mercury in the environment can exist in oxidation states \(0,+1\), and \(+2\). One
major question in environmental chemistry research is how to best measure the
oxidation state of mercury in natural systems; this is made more complicated
by the fact that mercury can be reduced or oxidized on surfaces differently
than it would be if it were free in solution. XPS, X-ray photoelectron
spectroscopy, is a technique related to PES (see Exercise 7.111), but instead
of using ultraviolet light to eject valence electrons, \(\mathrm{X}\) rays are
used to eject core electrons. The energies of the core electrons are different
for different oxidation states of the element. In one set of experiments,
researchers examined mercury contamination of minerals in water. They measured
the XPS signals that corresponded to electrons ejected from mercury's \(4 f\)
orbitals at \(105 \mathrm{eV}\), from an X-ray source that provided \(1253.6
\mathrm{eV}\) of energy. The oxygen on the mineral surface gave emitted
electron energies at \(531 \mathrm{eV}\), corresponding to the \(1 s\) orbital of
oxygen. Overall the researchers concluded that oxidation states were \(+2\) for
\(\mathrm{Hg}\) and \(-2\) for \(\mathrm{O}\). (a) Calculate the wavelength of the
\(\mathrm{X}\) rays used in this experiment. (b) Compare the energies of the \(4
f\) electrons in mercury and the \(1 s\) electrons in oxygen from these data to
the first ionization energies of mercury and oxygen from the data in this
chapter. (c) Write out the ground-state electron configurations for
\(\mathrm{Hg}^{2+}\) and \(\mathrm{O}^{2-}\); which electrons are the valence
electrons in each case? (d) Use Slater's rules to estimate \(Z_{\text {eff }}\)
for the \(4 f\) and valence electrons of \(\mathrm{Hg}^{2+}\) and
\(\mathrm{O}^{2-}\); assume for this purpose that all the inner electrons with
\((n-3)\) or less screen a full \(+1\).
