exam1ans_1976

# exam1ans_1976 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

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MIT OpenCourseWare http://ocw.mit.edu 5.80 Small-Molecule Spectroscopy and Dynamics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Chemistry 5.76 Spring 1976 Examination #1 ANSWERS March 12, 1976 Closed Book Slide Rules and Calculators Permitted Answer any THREE of the four questions. You may work a fourth problem for extra credit. All work will be graded but no total grade will exceed 80 points. 1. A. (10 points) Give a concise statement of Hund’s three rules. First rule: The lowest energy state belonging to a configuration has maximum S. Second Rule: Of the states of maximum spin, the lowest term has maximum L. Third Rule: The lowest J–state of the lowest term is the one with maximum J for a more than half-filled shell and minimum J for less than half-filled shell. None of the Hund’s rules apply to any but the lowest energy term belonging to a configuration. B. (10 points) State the definition of a vector operator. B is a vector with respect to A if [ A i , B j ] = ǫ i jk i B k C. (10 points) If B and C are vector operators with respect to A , then what do you know about matrix elements of B · C in the | AM A basis? B C is scalar with respect to A , therefore · A M A | B · C | AM A = δ A A δ M A M A A B · C A independent of M A . D. ( 5 points) The atomic spin-orbit Hamiltonian has the form H SO = ξ ( r i ) i · s i i Classify H SO as vector or scalar with respect to J , L , and S . State whether H SO is diagonal in the | JM J LS or | LM L S M S basis.
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