573finalexam

573finalexam - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall 2002 Professor Robert W Field FINAL EXAMINATION DUE at 11:00AM

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall , 2002 Professor Robert W. Field FINAL EXAMINATION DUE : December 11 , 2002 at 11:00AM. This is an open book , open note , open computer , unlimited time exam. You may talk to each other to clarify what the questions mean , but not how to answer them . You may also contact me and I will attempt to give you explicit help (including some direct instructions about how to solve a problem). Name: GRADING: I. II. III. TOTAL:
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5.73 Final Exam Page 1 I. Aufbau for Adults. Look at page 31-9 of the lecture notes. Now consider the following problems of spectrum identification and prediction. A. You have an absorption spectrum and you do not know whether it comes from atomic C , N , or O. You do not have access to a table of energy levels or assigned spectral lines. What are the features in the spectrum that would enable you to conclusively identify the carrier of the spectrum? Here are the rules: a . The atom starts out in its ground electronic state. You cannot rely on any state being initially populated other than the lowest L–S–J state predicted by Hund s rules. b. The selection rules for electronic transitions are l = ±1. This is consistent with L = 0 , ±1 , S = 0 , J = 0 , ±1. An off-diagonal matrix element of H SO between same-configuration , same-J , L = 0 , ±1 , S = 0 , ±1 states could make weakly observable certain S 0 transitions. The intensity “borrowed” by a nominally forbidden transition is directly related to level shifts of both the borrowing and lending state. c. The nuclear spins of 12 C , 14 N , 16 O are I = 0 , 1 , and 0 respectively. You can use the presence or absence of hyperfine structure to make assignments , but you must make some predictions about the qualitative nature of the hfs. d. You can use the Zeeman effect in a variety of ways to identify the states involved in a transition. If you do so , you must calculate g- values. e. The Landé interval rule should prove very helpful. If you use it , you should calculate the relative intensities of transitions to different J–components of an S 0 , L 0 multiplet state. The transition intensities come from the form of the transition operator as a 1-electron operator , T (1) [ r ] where r is the electron coordinate. This has l = ±1 selection rules. Z-polarized light excites m l = 0 transitions. You should answer this question by identifying the unique spectroscopic signature of each atom. I am looking for quality (very specific diagnostics) rather than quantity (vague, qualitative statements).
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5.73 Final Exam Page 2 B. Isoelectronic and isovalent comparisons. The energy level diagrams for two atoms with the same number of valence electrons will resemble each other , but the scale parameters [ ε n l , F k , G k , ζ n l ] will be systematically and predictably different. (i) How would the spectra of C , N , and O + compare. Make plausible arguments about how each of the scale parameters would change.
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This note was uploaded on 11/28/2011 for the course CHEM 5.74 taught by Professor Robertfield during the Spring '04 term at MIT.

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573finalexam - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 5.73 Quantum Mechanics I Fall 2002 Professor Robert W Field FINAL EXAMINATION DUE at 11:00AM

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