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Chapter 9: Q7CQ (page 402)
When would a density of states be needed: in a sum over states? in a sum over energies? in an integral over energies? in an integral over states?
Thus, among the choices, density of states is most useful when we consider integral over energies.
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:In a certain design of helium-neon laser, the chamber containing these gases has a perfect mirror at one end. as usual, but only a window at the other, Beyond the window, is a region of free air space and then the second mirror, which is partially reflecting, allowing the beam to exit. The resonant cavity between the mirrors thus has a region free of the helium-neon gas-the "lasing material"-in which you can insert something. If you insert a sheet of clear plastic at any orientation in this region between the mirrors, the laser beam disappears. If the same sheet is placed in the beam outside the partially reflecting mirror, the beam passes through it, regardless of the orientation. Why?
At what wavelength does the human body emit the maximum electromagnetic radiation? Use Wien's law from Exercise 79 and assume a skin temperature of.
This problem investigates what fraction of the available charge must be transferred from one conductor to another to produce a typical contact potential. (a) As a rough approximation treat the conductors as 10 cm square plates apart-a parallel-plate capacitors so that , where . How much charge must be transferred from one plate to the other to produce a potential difference of ?(b) Approximately what fraction would this be of the total number of conduction electrons in a piece of copper. which has one conduction electron per atom?
Copper has one conduction electron per atom and a density of. By the criteria of equation, show that at room temperature, the conduction electron gas must be treated as a quantum gas of indistinguishable particles.
The exact probabilities of equation (9-9) rest on the claim that the number of ways of addingdistinct non-negative integer to give a total of is . One way to prove it involves the following trick. It represents two ways that distinct integers can add to and, respectively. In this special case.
The X's represent the total of the integers, -each row has . The represent "dividers" between the distinct integers of which there will of course be each row has . The first row says that is (three before the divider between it and ), is (no between its left divider with and its right divider with ), ) is . through are , is , and and are . The second row says that is . is , is , and all other are . Further rows could account for all possible ways that the integers can add to . Argue that properly applied, the binomial coefficient (discussed in Appendix ) can be invoked to give the correct total number of ways for any and .
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