ps3ans_1976

ps3ans_1976 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

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Unformatted text preview: 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 . MASSACHUSETTS INSTITUTE OF TECHNOLOGY Chemistry 5.76 Spring 1976 Problem Set #3 ANSWERS 1. (a) Write out the electron configurations for the molecules O 2 + , O 2 , O 2 − , and O 2 2 − . ANSWER: O + 2 → KK (2 s σ g ) 2 (2 s σ u ⋆ ) 2 (2 p σ g ) 2 (2 p π u ) 4 (2 p π g ⋆ ) O 2 → KK (2 s σ g ) 2 (2 s σ u ⋆ ) 2 (2 p σ g ) 2 (2 p π u ) 4 (2 p π g ⋆ ) 2 O − 2 → KK (2 s σ g ) 2 (2 s σ ⋆ u ) 2 (2 p σ g ) 2 (2 p π u ) 4 (2 p π ⋆ g ) 3 O 2 2 − KK (2 s σ g ) 2 (2 s σ ⋆ u ) 2 (2 p σ g ) 2 (2 p π u ) 4 (2 p π ⋆ g ) 4 → (b) Determine the ground-state term symbols M Λ g , u ± for O + , O 2 , O − , and O 2 2 − . If there are two or more 2 2 low-lying states, select one as that of the ground state and justify your selection. ANSWER: O + 2 → 2 Π g (only term arising) O 2 → 1 Δ g , 1 Σ g + , 3 Σ g − By Hund’s rules 3 Σ − g ground state [largest S and largest Λ ] O − 2 → 2 Π (only term arising) O − 2 2 → 1 Σ + g (only term arising) 2. (a) Using symbols appropriate to the separated-atom approximation to a molecular orbital, write the elec- tronic configuration of lowest energy for the diatomic species C 2 , NO + , and S 2 . ANSWER: C 2 : KK (2 s σ g ) 2 (2 s σ ⋆ u ) 2 (2 p π u ) 4 NO + : KK (2 s σ g ) 2 (2 s σ ⋆ u ) 2 (2 p σ g ) 2 (2 p π u ) 4 S 2 : KK (2 s σ g ) 2 (2 s σ ⋆ u ) 2 (2 p σ g ) 2 (2 p π u ) 4 (2 p π ⋆ g ) 4 (2 p σ ⋆ u ) 2 (3 s σ g ) 2 (3 s σ ⋆ u ) 2 (3 p σ g ) 2 (3 p π u ) 4 (3 p π ⋆ g ) 2 (b) Write the term symbols M Λ g , u ± for all the electronic states derivable from the configuration of lowest energy for all three species. Which of these states will have non-zero magnetic moments? ANSWER: C 2 from configuration in (a) only term 1 Σ + g ground state. There will be no magnetic moment ← from this configuration. NO + only term arising is 1 Σ + there will be no magnetic moment. S 2 : 1 Δ g , 3 Σ − g , 1 Σ + g The ground state is 3 Σ − g by Hund’s Rules and it will have a magnetic moment. The 1 Δ g state will also have a non-zero magnetic moment. 5.76 Problem Set #3 ANSWERS Spring, 1976 page 2 3. Gaseous HCl is normally a 3 : 1 mixture of H 35 Cl and H 37 Cl. To a high approximation, the rotational energy levels of such diatomic rotators are E ( J )(in cm − 1 ) = J ( J + 1) B − J 2 ( J + 1) 2 D where B , the rotational constant, is larger by a factor 1.0015 for H 35 Cl than for H 37 Cl, and the centrifugal distortion constant D is the same for both molecules within the error of its measurement....
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ps3ans_1976 - MIT OpenCourseWare http/ocw.mit.edu 5.80...

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