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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 5.04 Principles of Inorganic Chemistry II Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Chemistry 5.04 (F08) Problem Set 4 Due Monday, 3 November 1. The raising and lowering operators are: L (L, M L , S, M) = h [(L M L + 1)(L m M L )] (L, M L 1, S, M S ) S (L, M L , S, M) = h [(S M S + 1)(S m M S )] (L, M L , S, M S 1) L ( m l 1 , m s 1 ; m l N , m s N ) = h ! = N 1 i [( l i m l i +1)( l i m m l i )] ( m l 1 , m s 1 ; m l i 1, m s i ; m l N , m s N ) S ( m l 1 , m s 1 ; m l N , m s N ) = h ! = N 1 i [( 2 3 m s i )( 2 1 m m s i )] ( m l 1 , m s 1 ; m l i , m s i 1; m l N , m s N ) (a) For the p 2 configuration, we found that (L = 1, M L = 1, S = 1, M S = 1) for the 3 P state was = 0, S = 1, M S = 1) of the 3 P . Using the angular momentum operator , show that you obtain the result, (L = 1, M L = 0, S = 1, M S = 1) = (b) The states encompassed by (L, M L = 0, S, M S = 0) are defined by three configurations, . Beginning with your result for (L = 1, M L = 0, S = 1, M S = 1) of the 3 P state, determine the linear combination that defines (L = 1, M L = 0, S = 1, M S = 0). defined by a unique configuration ! " # $ % & + + , 1 . Similarly, (L = 1, M L state is defined by the unique configuration, !...
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This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.

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5_04_f08_ps4 - MIT OpenCourseWare http://ocw.mit.edu 5.04...

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