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Chapter 10: Q24CQ (page 467)
What are the some of the properties of fullerenes that make them potentially so useful?
The property of high tensile strength of the fullerenes makes it for potentially useful.
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Question:In Chapter 4. we learned that the uncertainty principle is a powerful tool. Here we use it to estimate the size of a Cooper pair from its binding energy. Due to their phonon-borne attraction, each electron in a pair (if not the pair's center of mass) has changing momentum and kinetic energy. Simple differentiation will relate uncertainty in kinetic energy to uncertainty in momentum, and a rough numerical measure of the uncertainty in the kinetic energy is the Cooper-pair binding energy. Obtain a rough estimate of the physical extent of the electron's (unknown!) wave function. In addition to the binding energy, you will need to know the Fermi energy. (As noted in Section 10.9, each electron in the pair has an energy of about EF.) Use 10-3 eV and 9.4 eV, respectively, values appropriate for indium.
The energy necessary to break the ionic bond between a sodium ion and a fluorine ion is . The energy necessary to separate the sodium and fluorine ions that form the ionic crystal is per ion pair. Explain the difference qualitatively.
For the four kinds of crystal binding – covalent, ionic, metallic, and molecular- how would the destiny of valence electrons vary throughout the solid? Would it be constant, centered on the atoms, or largest between the atoms? Or would it alternate, with a net charge density positive at one atom and negative at the next?
Question: The Fermi velocity VF is defined by , where is the fermi energy. The Fermi energy for silver is 5.5eV.(a) Calculate the Fermi velocity.(b) what would be the wavelength of an electron with this velocity. (c)How does this compare with the lattice spacing of 0.41 nm? Does the order of magnitude makes sence?
The bond length of themolecule is 0.11nm, and its effect the spring constant is .
(a) From the size other energy jumps for rotation and vibration, determine whether either of these modes of energy storage should be active at 300K .
(b) According to the equipartition theorem, the heat capacity of a diatomic molecule storing energy in rotations but not vibrations should be(3 translational +2rotational degrees of freedom). If it is also storing energy in vibrations. it should be(adding 2 vibrational degrees). Nitrogen's molar heat capacity is 20.8J/mol.K at 300K. Does this agree with your findings in part (a)?
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