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Chapter 10: Q22CQ (page 467)
Describe the similarities and differences between Type-I and Type-II superconductors.
Both Type-I and Type-II superconductors relay on formation of cooper pairs and they exhibit isotopic effect.
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What are the some of the properties of fullerenes that make them potentially so useful?
Question: The photons emitted by an LED arise from the energy given up in electron-hole recombinations across the energy gap. How large should the energy gap be to give photons at the red end of the visible spectrum (700nm) ?
Question:If electrical conductivity were determined by the mere static presence of positive ions rather than by their motion the collision time would be inversely proportional to the electron's average speed. If however, it were dominated by the motion of the ions, it should be inversely proportional to the 鈥渁rea" presented by a jiggling ion, which is in turn proportional to the square of its amplitude as an oscillator. Argue that only the latter view gives the correct temperature dependence in conductors of . Use the equipartition theorem (usually covered in introductory thermodynamics and also discussed in Section 9.9).
As a crude approximation, an impurity pentavalent atom in a (tetravalent) silicon lattice can be treated as a one-electron atom, in which the extra electron orbits a net positive charge of 1. Because this "atom" is not in free space, however, the permitivity of free space, . must be replaced by , where is the dielectric constant of the surrounding material. The hydrogen atom ground-state energies would thus become
Given for silicon, how much energy is needed to free a donor electron in its ground state? (Actually. the effective mass of the donor electron is less than , so this prediction is somewhat high.)
Exercise 29 notes that more energy is required to ionize sodium that is retrieved by adding that electrons to an isolated chlorine atom, but the NaCl bond represents a lower energy because the attracting ions draw close together. Quantifying the energy-lowering effect of having alternating plus and minus charges can be rather involved for 3D lattice, but a one dimensional calculation is instructive. Consider an infinite line of point charges alternating between +e and 鈥揺, with a uniform spacing between adjacent opposite charge of a. (a) The electrostatic potential energy per ion is the same for a given positive ion as for a given negative ion. Why? (b) Calculate the electrostatic potential energy per ion for simplicity. Assume that a positive charge is at the origin. The following power series expansion will be helpful: .
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