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Chapter 10: Q21CQ (page 467)
What is Cooper pair, and what role does it play in superconductivity?
Cooper pairs are a pair of electrons at states slightly above Fermi energy and attract each other mediated via photons.
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In a buckyball, three of the bonds around each hexagon are so called double-bonds. They result from adjacent atoms sharing a state that does not participate in the sp2 bonding. Which state is it, and what is this extra bond σ-bond or a π-bond? Explain.
The accompanying diagrams represent the three lowest energy wave functions for three "atoms." As in all truly molecular states we consider, these states are shared among the atoms. At such large atomic separation, however, the energies are practically equal, so anelectron would be just as happy occupying any combination.
(a) Identify algebraic combinations of the states (for instance, 5+11/2+11/2 ) that would place the electron in each of the three atoms.
(b) Were the atoms closer together, the energies of states 1.11, and III would spread out and an electron would occupy the lowest energy one. Rank them in order of increasing energy as the atoms draw closer together. Explain your reasoning.
Question: From the qualitative shapes of the interatomic potential energies in Fig. 10.21, would you expect the vibrational level in the excited electronic state to be spaced the same. Farther apart, or closer together than those in the lower energy electronic state? Explain what about the rotational levels?
Section 10.2 discusses - bonds and - bonds for p - states and -bonds for s-states but not - bonds for - states. Why not?
The effective force constant of the molecular “spring” in HCL is , and the bond length is .
(a) Determine the energies of the two lowest-energy vibrational states.
(b) For these energies, determine the amplitude of vibration if the atoms could be treated as oscillating classical particles.
(c) For these energies, by what percentages does the atomic separation fluctuate?
(d) Calculate the classical vibrational frequencyand rotational frequency for the rotational frequency, assume that L is the its lowest non zero value, and that the moment of inertia is .
(e) Is is valid to treat the atomic separation as fixed for rotational motion while changing for vibrational?
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