Chapter 10: Problem 24
What are some of the properties of fullerenes that make them potentially so useful?
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Chapter 10: Problem 24
What are some of the properties of fullerenes that make them potentially so useful?
These are the key concepts you need to understand to accurately answer the question.
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81\. Donor and Acceptor Levels: Define \(U(x)\) with \(X_{1}, X_{2}\) and \(X_{3}\) set to \(1.2,2.4\), and \(3.6\). respectively. which gives seven equally spaced wells separated by walls of width 0.2. For \(U_{0}\) use 20 , and for \(\Lambda x\), use \(0.001\). (a) \(\mathrm{Note}:\) This part can be skipped if also working Exercise 80.) Following the Chapter 5 guidelines on choosing \(\psi(0)\) and \(\psi(\mathrm{Ax})\), test both odd and even functions at different trial values of \(E\) by finding \(\psi\) at all multiples of \(\Delta x\) and ploting the results from \(x=0 \operatorname{to} x=5\). Find 14 ullowed energies. Note that the indicator of having passed an allowed energy is the flip of the diverging large-x tail. The lowest energy or two will take the most work. Except for these, there is no need to exceed three significant figures. Afterward. make a scatter plot of \(E_{n}\) versus \(n\), where \(n\) goes from 1 to 14 . (b) Now replace Iwo atoms with impurity atoms as follows: For cither the well at \(1.2\) or the well at \(2.4\), change \(B\) from 0 to0.l. (Note: Changing one well automatically changes the corresponding well at negative \(x\). We avoid changing the outemost wells simply because it doesn't work as nicely.) This puts the bottom of the altered well at \(0.1 U_{0}\), or 2 units. Again find 14 energies. and make another scatter plot. (c) Repeat part (b). but choosing \(-0.1\) for \(B\) in the "impurity" atom. putting its bottom at \(-2\) units. (d) Discuss how the impurities added in parts (b) and (c) cotrespond to atoms whose valence differs from that of the intrinsic atoms. (e) If each intrinsic atom comes with two electrons, and the impurities come with one and three, respectively, which states would be filled in parts (b) and (c)? Remember that there are two spin states. (f) Discuss the overall result of adding the impurities.
In the boron atom, the single \(2 p\) electron does not completely fill any \(2 p\) spatial state, yet solid boron is not a conductor. What might explain this? (It may be helpful to consider again why beryllium is not an insulator.)
The isotope effect says that the critical temperature for superconductivity decreases as the mass of the positive ions increases. Can you argue why it should decrease?
It takes less enetgy to dissociate a diatomic fluorine mole. cule than a diatomic oxygen molecule (in fact. less than one-third as much). Why is it easier to dissociate fluorine?
In a concise yet fairly comprehensive way, explain why doped semiconductors are so pervasive in modem technology.
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