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final_ay11 - Chemistry 21b Final Examination Out 11 March...

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Chemistry 21b Final Examination Out: 11 March 2011 Due: 16 March 2011, 5 pm This is an open book examination, and so you may use McQuarrie or Harris and Bertolucci along with the posted Lecture Notes and Problem Sets (with Solutions). Use of a calculator or packages such as Mathematica is also permitted, but the final is closed-Web (use of the class web site is fine, to access Lecture notes, Solution Sets, etc.). The exam must be done in one continuous sitting of three hours. I believe you should be able to complete the exam in the time allocated; but if not, please draw a line across where the time limit is reached and continue if you wish to. The TAs will record the grades for points awarded within the time allocated and that after. The problems are worth: 1=15 2=20 (10 for a,b) 3=30 (spread over a-g) 4=15 5=20 (10 for a, 5 each for b,c) To facilitate the grading of the exam, please begin the solution of each problem on a new sheet , and remember to sign your name on every page of your solutions if you use loose note paper. Good luck!
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1. Use group theoretical arguments to answer the following. You can be brief! a). Imagine a perfect surface of a transparent dielectric solid in the (x,y) plane, with the space-fixed z-axis being normal to the surface. Suppose we trap water molecules on this surface so that they are not free to rotate, and further that they are oriented perpendicular to it. If you try to take the vibrational spectrum of these adsorbed molecules, what polarizations of the applied E&M field are needed to detect the three fundamental vibrations and their overtones and combination bands? Figure 14.3 will
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