Learning Materials
Features
Discover
Chapter 9: 41E (page 405)
Show that the rms speed of a gas molecule, defined as , is given by.
The rms speed of a gas molecule is
Over 30 million students worldwide already upgrade their learning with 91影视!
All the tools & learning materials you need for study success - in one app.
Get started for free
Show that equation (9- 16) follows from (9-15) and (9- 10).
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 .
You have six shelves, one above the other and all above the floor, and six volumes of an encyclopedia, A, B, C, D, E and F.
(a) list all the ways you can arrange the volumes with five on the floor and one on the sixth/top shelf. One way might be.
(b) List all the ways you can arrange them with four on the floor and two on the third shelf.
(c) Show that there are many more ways, relative to pans (a) and (b), to arrange the six volumes with two on the floor and two each on the first and second shelves. (There are several ways to answer
this, but even listing them all won't take forever it's fewer than.)
(d) Suddenly, a fantastic change! All six volumes are volume X-it's impossible to tell them apart. For each of the three distributions described in parts (a), (b), and (c), how many different (distinguishable) ways are there now?
(e) If the energy you expend to lift a volume from the floor is proportional to a shelf's height, how do the total energies of distributions (a), (b), and (c) compare?
(I) Use these ideas to argue that the relative probabilities of occupying the lowest energy states should be higher for hosons than for classically distinguishable particles.
(g) Combine these ideas with a famous principle to argue that the relative probabilities of occupying the lowest states should he lower for fermions than for classically distinguishable particles.
Using density of states , which generalizes equation (9-27) to account for multiple allowed spin states (see Exercise 52), the definition and . Solve for in distributions (9-32) and (9-33) careful use of will cut your work by about half. Then plug back in and show that for a system of simple harmonic oscillators, the distributions become .
You will need the following integral:.
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.
What do you think about this solution?
We value your feedback to improve our textbook solutions.
Explanations 
Textbooks 
Flashcards 
91影视 AI 
Notes 
Study Plans 
Study Sets 
Find a degree 
Magazine