Exam1ME501F2009wPartialAnswers

Exam1ME501F2009wPartialAnswers - 1 Name_ ME 501 Exam #1 23...

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1 Name___________________________ 23 October 2009 Prof. Lucht 1. POINT DISTRIBUTION Choose two (2) of problems 1, 2, and 3: Problem #1 50 points _________________ Problem #2 50 points _________________ Problem #3 50 points _________________ You are required to do two of the problems. Please indicate the problems you have chosen. 2. EXAM INSTRUCTIONS Write your name on each sheet. This exam is closed book and closed notes. Four equation sheets are attached. When working the problems, list all assumptions, and begin with the basic equations. If you do not have time to complete evaluation of integrals or of terms numerically, remember that the significant credit on each problem will be given for setting up the problem correctly and/or obtaining the correct analytical solution. ME 501 Exam #1
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2 ME 501 Exam #1 23 Oct 2009 Name___________________________ 1. (50 points) The system shown below has available energy levels of 0, 2, 4, and 8 units. The degeneracy of each of the four levels is 4. The thermodynamic assembly has 6 particles (N = 6) and a total system energy of 12 units (E = 12). (a) For bosons, what are the available macrostates? (There are 6.) How many microstates are associated with each of these macrostates and what is the most probable macrostate? What is the entropy of the system? For Bose-Einstein statistics, the number of microstates for a given macrostate   j N is given by: WW N g Ng mBE jBE jj ,, () ! !( )!   1 1 Partial Answer: 3404  (b) For fermions, what are the available macrostates? How many microstates are associated with each of these macrostates and what is the most probable macrostate? What is the entropy of the system? For Fermi-Dirac statistics, the number of microstates for a given macrostate   j N is given by: g N mFD jFD j jjj ! ) ! Partial Answer: 360 (c) What is the entropy of an assembly of fermions that occupies the energy levels shown with N=16 and E = 56?
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3 ME 501 Exam #1 23 Oct 2009 Name___________________________ 2. The time-independent wavefunction  nm r (, , ) fo r the 2 , , state of the hydrogen atom is given by        0 2 5/2 0 0 22 2 0 exp / 2 s in exp 8 exp / 2 sin exp 8 m mm m rr a ri a a R a     The Bohr radius am e m e 00 1 0 4 0 52918 10   ch c h / . and the electron spin is neglected. (Note: In these formulas the factor 0 is the dielectric permittivity, not an energy).
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Exam1ME501F2009wPartialAnswers - 1 Name_ ME 501 Exam #1 23...

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