Chapter 10: Problem 21
What is a Cooper pair, and what role does it play in superconductivity?
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Chapter 10: Problem 21
What is a Cooper pair, and what role does it play in superconductivity?
These are the key concepts you need to understand to accurately answer the question.
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Section 10.2 discusses \(\sigma\) -bonds and \(\pi\) -bonds for \(p\) -states and \(\sigma\) -bonds for s-states. but not \(\pi\) -bonds for s-states. Why not?
The energy necessary to break the ionic bond between a sodium ion and a fluorine ion is \(4.99 \mathrm{eV}\). The energy necessary to separate the sodium and fluorine ions that form the ionic NaF crystal is \(9.30 \mathrm{eV}\) per ion pair. Explain the difference qualitatively.
Describe the similarities and differences between Type-l and Type-Il superconductors.
A semime tal (e.g. antimony, bismuth) is a material in which electrons would fill states to the top of a band the valence band- -except for the fact that the top of this band overlaps very slightly with the bottom of the nexthigher band. Explain why such a material, unlike the "real" metal copper, will have true positive charge carners and equal numbers of negative ones, even at zero temperature.
In Section 10.2. we discussed two-lobed \(p_{\text {re }} p_{\text {s }}\) and \(p_{z}\) states and four-lohed hybrid \(s p^{3}\) states. Another kind of hybrid state that sticks out in just one direction is the sp. formed from a single \(p\) state and an \(s\) state. Consider an urbitrary combination of the \(2 s\) state with the \(2 p_{x}\) state. Let us represent this by \(\cos \tau \psi_{2.0 .0}+\sin T \psi_{2.1 .0}\) (The trig factors ensure norinalization. In carrying out the integral, crow terms integrate to \(0 .\) leaving \(\cos ^{2}+\int\left|\psi_{2,0,0}\right|^{2} d b^{\prime}+\sin ^{2} \tau \int\left|\psi_{21,0}\right|^{2} d V\). which is \(\left.1 .\right)\) (a) Calculate the probability that an electron in such a state would be in the \(+z\) -hemisphere. (Nore: Here. the cross tems do nor integrate to \(0 .\) ) (b) What value of \(r\) leads to the maximum probability. what is the value of the maximum probability, and what is the cotresponding ratio of \(\psi_{2,0.0}\) to \(\phi_{2,1,0} ?\) (c) Using a computer, make a density (shading) plot of the probability density - density versus \(r\) and \(\theta\) for the \(r\) -value found in part (b).
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