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midterm_ay11 - Chemistry 21b Midterm Examination Out 04...

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Chemistry 21b Midterm Examination Out: 04 February 2011 Due: 10 February 2011 This is an open book, and closed web, examination. So, you may use the texts along with the posted Lecture Notes and Problem Sets (with Solutions), but no browsing. In particular, Harris & Bertolucci has more a more extensive list of character tables, and you’ll likely find this handy. Use of a calculator or packages such as Mathematica is also permitted. The exam must be done in one continuous sitting of three hours. The problems are worth: 1=20 (5 each for a, b, 10 for c); 2=20 (5 for a, 15 for b); 3=20 (10 for a, 10 for b); 4=10; 5=30 (5 each a,b,d,e, 10 for 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 your solutions. If you run out of time, please draw a line across the page at the limit and continue, within reason. Good luck!
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1. For atoms, Eq. (9.85) in McQuarrie, p. 470, derives the formula for the number of ways to assign N electrons to G spin orbitals belonging to the same sub-shell (two for s , six for p , etc.): G ! N !( G N )! a) Show that the number of sets of magnetic quantum numbers ( m l ) and spin quantum numbers ( m s ) associated with any term symbol is equal to (2 L + 1)(2 S + 1).
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