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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 ± Problem Set #3 1. (a) Write out the electron configurations for the molecules O + 2 , O 2 , O 2 , and O 2 2 . (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. 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 . (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? 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. (a) Derive an expression for the separation of the pure rotational absorption lines of H 35 Cl and H 37 Cl as a function of J , the J–value for the upper state ( Δ J = J J �� = + 1). (b) What is the spacing in cm 1 of the two lines for which J = 10? 4. The “transition moment,” or the probability of transition, between two rotational levels in a linear molecule may be assumed to depend only on the permanent electric dipole moment of the molecule and thus to be the same for all allowed pure-rotational transitions. In the pure-rotational emission spectrum of H 35 Cl gas, lines at 106.0 cm 1 and 233.2 cm 1 are observed to have equal intensities. What is the temperature of the gas? The rotational constant B for H 35 Cl is known to be 10.6 cm
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