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Chapter 10: Q49E (page 469)
In Figure 10.24, the band n = 1 ends at , while in Figure 10.27 it ends at. Are these compatible? If so, how?
It is proved that two ends are compatible.
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Carbon(diamond) and silicon have the same covalent crystal structure, yet diamond is transparent while silicon is opaque to visible light. Argue that this should be the case based only on the difference in band gaps roughly 5 eV for diamond in eV is silicon.
Starting with equation (10-4), show that if is as a photon is emitted by a diatomic molecule in a transition among rotation-vibration states, but can be . Then the allowed photon energies obey equation (10-6).
As we see in Figures 10.23, in a one dimensional crystal of finite wells, top of the band states closely resemble infinite well states. In fact, the famous particle in a box energy formula gives a fair value for the energies of the band to which they belong. (a) If for nin that formula you use the number of anitnodes in the whole function, what would you use for the box length L? (b) If, instead, the n in the formula were taken to refer to band n, could you still use the formula? If so, what would you use for L? (c) Explain why the energies in a band do or do not depend on the size of the crystal as a whole.
What factors decrease the conductivity of a conductor as temperature increases? Are these factors also present in a Semiconductor, and if so, how can its conductivity vary with temperature in the opposite sense?
In section 10.2 , we discussed two-lobed and states and 4 lobed hybrid 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 arbitrary combination of the 2s state with the state. Let us represent this by(The trig factors ensure normalization in carrying out the integral , cross terms integrate to 0.leaving Which is 1.)
(a) Calculate the probability that an electron in such a state would be in the +z-hemisphere.(Note: Here, the cross terms so not integrate to 0 )
(b) What value of𝛕leads to the maximum probability, and what is the corresponding ratio of and ?
(C) Using a computer , make a density (Shading) plot of the probability density-density versus r and𝛉- for the𝛕-value found in part (b).
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