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Problem Set
1. We can study trends in effective nuclear charge using X-ray photoemission
spectroscopy (XPS),which measures the energy required to ionize an atom.
The X-radiation is energetic enough to excite electrons at all levels (even
core levels) so this technique can probe electrons in specific orbitals.In
an XPS experiment, C atoms reacted with a surface, forming C–Si bonds.
Before the reaction, the ionization energy was 36.7 eV; after the reaction,
it shifted down to 36.0 eV. How much did this reaction change the effective
charge? What does this imply about the bonds broken and formed?
2. Although a chain of atoms forms a good model for 1-dimensional polymers,
a ring topology is more appropriate for higher-dimensional materials, such
as crystals. Draw the linear combinations of 1s
orbitals for a ring of 4 H atoms. Repeat for a ring of 5 H atoms and for a
ring of 6 H atoms. In each case, rank the resulting molecular orbitals, and
place degenerate orbitals at the same ranking.
3. Draw the linear combinations of orbitals for a (hypothetical) planar form
of NH3, and predict the ordering of the orbitals. Draw a molecular orbital
energy diagram to indicate which atomic orbitals contribute to each
molecular orbital.
4. The photoelectron spectrum of methane, which reveals the energies of its
molecular orbitals, provides striking support for molecular orbital theory (
over valence bond theory). In the plot below, the area
under peak t2 is about 3 times the area under peak a1. Explain how this
spectrum is consistent with the occupied valence molecular orbitals
illustrated below. What would the spectrum look like according
to valence bond theory? |
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